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  • 201
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 202
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 527-544 
    ISSN: 0029-5981
    Keywords: boundary strip ; elastostatics ; potential problems ; BEM ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The present paper develops the idea of the boundary strip method, and presents its fundamentals, merits, applications and also some closed-form or non-element solutions based on it. The present approach combines the Boundary Integral Equation Method (BIEM) and the finite strip method, taking the advantages of both. The finite strip method is installed into the BIEM by expanding the unknown parameters of problems in terms of trigonometric series. This combination creates a new powerful numerical method with three advantages over other numerical methods, namely, a shorter computation time, a better accuracy and a reduction of one and a half dimensions in mesh generation. Applications in two-dimensional potential and field problems demonstrate the efficiency and the accuracy of the proposed method. Finally, closed-form presentations for Laplace equation and elastostatics are given, along circular segments.
    Additional Material: 10 Ill.
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  • 203
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 549-567 
    ISSN: 0029-5981
    Keywords: unstructured mesh generation ; viscous compressible flows ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method of generating general tetrahedral meshes suitable for use in viscous flow simulations is proposed. The approach which is followed consists of the initial generation of a number of unstructured layers of highly stretched elements, in the vicinity of solid walls, followed by the discretisation of the remainder of the domain, by a standard advancing front procedure. The numerical performance of the proposed methodology is demonstrated by the generation of meshes suitable for viscous flow analysis over a number of three-dimensional aerodynamic configurations of current practical interest.
    Additional Material: 18 Ill.
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  • 204
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 585-604 
    ISSN: 0029-5981
    Keywords: large displacements ; finite volumes ; mixed formulation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper addresses the problem of the numerical solution of beam statics undergoing large displacements. A kinematic analysis outlines the beam geometrical model through the definition of its Lagrangian co-ordinate and strain parameters. A definition of the stress parameters, a constitutive law and an expression for the strain energy of the beam are then provided under the hypothesis of small strain. The equations governing the beam equilibrium are introduced and their weak form is derived. These equations are then proved to be equivalent to the primal and mixed form of Principle of Virtual Work. The numerical approximation is introduced by applying the bidiscontinuous finite elements method on the linearized weak form. The weak-weak formulation is attained by using the lowest interpolation order both for test and trial functions on two staggered decompositions of the space domain. Some numerical examples prove the capability of present formulation in handling actual problems.
    Additional Material: 9 Ill.
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  • 205
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 605-618 
    ISSN: 0029-5981
    Keywords: inverse heat conduction problem ; heat capacity determination ; non-linear problem ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An inverse analysis utilizing the conjugate gradient method and the minimization of adjoint equation is used successfully to estimate the temperature dependent heat capacity per unit volume in a homogeneous medium.No prior information is available on the functional form of the unknown heat capacity in the present study, thus, it is classified as the function estimation in inverse calculation. The accuracy of the inverse analysis is examined by using simulated exact and inexact measurements obtained within the medium. Results show that an excellent estimation on the heat capacity per unit volume can be obtained by using just boundary measurements (i.e. internal measurements are unnecessary) and the CPU time used in VAX-9420 computer is less than one second.The advantages of applying this algorithm in inverse analysis can greatly simplify the experimental set-up, diminish the sensitivity to the measurement errors and reduce the CPU time in inverse calculation, while the reliable predictions can still be achieved.
    Additional Material: 7 Ill.
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  • 206
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 635-661 
    ISSN: 0029-5981
    Keywords: fracture ; damage ; microcracking ; finite element analysis ; nonlocal models ; concrete structures ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A recently proposed new nonlocal concept based on microcrack interactions is discussed, its implementation in a smeared cracking finite element code for concrete is presented, numerical studies are reported, and comparisons with experimental results are made. The nonlocality is not merely a mathematical device to prevent excessive spurious localization into a zone of zero volume but is a necessary physical consequence of microcrack interactions. Since the constitutive law itself is strictly local, the new nonlocal concept can be combined with any type of constitutive law for strain-softening nonlocal damage, which is here chosen to be the microplane model. A simple method is formulated to approximately identify the material parameters in the model from the basic characteristics of concrete such as the tensile strength, fracture energy and maximum aggregate size. The results of finite element analysis are shown to be mesh insensitive, and good convergence is obtained. Cracking damage is found to localize into a volume whose size and shape depend on the macroscopic concrete properties as well as the current stress-strain state. Although the damage is considered to be tensile on the microlevel, due solely to mode I microcracks, the new nonlocal model can describe well not only mode I fracture tests but also complex shear-dominated and mixed-mode types of failure such a diagonal shear, and can do so for the same values of material parameters (which was not the case for previous nonlocal models). Most importantly, the new nonlocal model can correctly capture the size effect of quasibrittle fracture, in approximate agreement with Bažant's size effect law.
    Additional Material: 20 Ill.
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  • 207
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 663-686 
    ISSN: 0029-5981
    Keywords: beams ; bending ; Chebyshev approximations ; quantifier elimination ; Sturm sequences ; tensionless elastic foundation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The well-known Sturm's theorem (based on Sturm's sequences) for the determination of the number of distinct real zeros of polynomials in a finite or infinite real interval has been already used in elementary quantifier elimination problems including applied mechanics and elasticity problems. Here it is further suggested that this theorem can also be used for quantifier elimination, but in more complicated problems where the functions involved are not simply polynomials, but they may contain arbitrary transcendental functions. In this case, it is suggested that the related transcendental equations/inequalities can be numerically approximated by polynomial equations/inequalities with the help of Chebyshev series expansions in numerical analysis. The classical problem of a straight isotropic elastic beam on a tensionless elastic foundation, where the deflection function (incorporating both the exponential function and trigonometric functions) should be continuously positive (this giving rise to a quantifier elimination problem along the length of the beam) is used as an appropriate vehicle for the illustration of the present mixed (symbolic-numerical) approach. Two such elementary beam problems are considered in some detail (with the help of the Maple V computer algebra system) and the related simple quantifier-free formulae are established and seen to coincide with those already available in the literature for the same beam problems. More complicated problems, probably necessitating the use of more advanced computer algebra techniques (together with Sturm's theorem), such as the Collins well-known and powerful cylindrical algebraic decomposition method for quantifier elimination, can also easily be employed in the present approximate (because of the use of Chebyshev series expansions) symbolic-numerical computational environment.
    Additional Material: 1 Ill.
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  • 208
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 717-718 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 209
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 829-846 
    ISSN: 0029-5981
    Keywords: structural optimization ; approximation method ; convex approximation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new method for solving structural optimization problems using a local function approximation algorithm is proposed. This new algorithm, called the Generalized Convex Approximation (GCA), uses the design sensitivity information from the current and previous design points to generate a sequence of convex, separable subproblems. The paper contains the derivation of the parameters associated with the approximation and the formulation of the approximated problem. Numerical results from standard test problems solved using this method are presented. It is observed that this algorithm generates local approximations which lead to faster convergence for structural optimization problems.
    Additional Material: 5 Ill.
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  • 210
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 847-865 
    ISSN: 0029-5981
    Keywords: interlaminar shear stress ; layer reduction technique ; composite laminate ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Interlaminar stress plays an important role in the delamination failure of laminated composites. A recently presented theory, the Interlaminar Shear Stress Continuity Theory (ISSCT), can directly and accurately predict interlaminar shear stresses in laminated composites by the constitutive equations. The present study further generalizes the derivation to a complete form from which many displacement-based laminate theories can be derived. Most of all, both the single-layer and multiple-layer approaches are incorporated into the analysis in the thickness direction. The laminate is discretized into several sublaminates and, then, a layerwise theory is applied in the analysis of this reduced laminate. This reduction in the number of layers used in the analysis makes the calculation of interlaminar shear stresses on the interested interface in a thick laminate more efficient. In addition, numerical solutions in closed-form and finite element form for laminates under cylindrical bending and bidirectional bending are examined. It is found that in the thickness direction the cubic order of the interpolation function and the discretization with four to six sublaminates can reduce the computational efforts dramatically and retain the accuracy of the predicted stresses within ±8 per cent.
    Additional Material: 13 Ill.
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  • 211
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 1-32 
    ISSN: 0029-5981
    Keywords: finite volumes ; finite elements ; compressible flows ; unstructured grids ; hybrid grids ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A framework for the construction of node-centred schemes to solve the compressible Euler and Navier-Stokes equations is presented. The metric quantities are derived by exploiting some properties of C0 finite element shape functions. The resulting algorithm allows to implement both artificial diffusion and one-dimensional upwind-type discretizations. The proposed methodology adopts a uniform data structure for diverse grid topologies (structured, unstructured and hybrid) and different element shapes, thus easing code development and maintenance. The final schemes are well suited to run on vector/parallel computer architectures. In the case of linear elements, the equivalence of the proposed method with a particular finite volume formulation is demonstrated.
    Additional Material: 16 Ill.
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  • 212
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 141-163 
    ISSN: 0029-5981
    Keywords: induction heating ; coupled problem ; three-dimensional analysis ; eddy current temperature analysis ; thin conducting sheet model ; eddy current boundary condition ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents a special finite element formulation for the computer simulation of an inductive heating device for thin moving metal strips. The calculation includes both the electromagnetic field and the temperature distribution resulting from the losses of the induced currents. The electromagnetic field is described by an electric vector potential and a magnetic scalar potential, the induced eddy currents are represented by a special boundary condition for the magnetic scalar potential along the surface of the current-carrying strip. This avoids the necessity to discretize the thin secondary region. The thermal model includes the movement of the strip as well as convection and radiation as its surfaces. The field equations are discretized using the Galerkin variant of the Method of Weighted Residuals. The mutually coupled electromagnetic and temperature fields are then calculated using an iterative, staggered solution scheme. Comparisons between calculated and measured temperature profiles show the validity of the presented approach.
    Additional Material: 17 Ill.
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  • 213
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 165-184 
    ISSN: 0029-5981
    Keywords: curved unilateral contact ; augmented Lagrangian ; frictional contact element ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Based on a mixed formulation approach, a frictional contact element is proposed for the numerical solution of contact problems including strongly curved rigid obstacles. The implementation of the frictional contact element is analogous to that of a finite element. This feature facilitates its implementation in implicit finite element programmes, since the structure of the code need not be modified.For efficient modelling of the forming tool geometries by Computer Aided Geometric Design techniques and in order to achieve a high performance of the contact search, the numerical schemes of the frictional contact element operate directly on parametric polynomial surface patches. Thus, no discretization of curved contact surfaces is performed.Numerical simulations of deep drawing processes demonstrate the performance of the method in the case of large sliding increments upon curved tools and in the case of elasto-plasticity.
    Additional Material: 8 Ill.
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  • 214
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 51-65 
    ISSN: 0029-5981
    Keywords: finite element method ; shape optimization ; sensitivity analysis ; forging ; preform design ; optimal design ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper is the second part of a two-part article about shape optimization of metal forming processes. This part is focused on numerical applications of the optimization method which has been described in the first paper. The main feature of this work is the analytical calculations of the derivatives of the objective function for a non-linear, non-steady-state problem with large deformations. The calculations are based on the differentiation of the discrete objective function and on the differentiation of the discrete equations of the forging problem. Our aim here is to show the feasibility and the efficiency of such a method with numerical examples. We recall the formulation and the resolution of the direct problem of hot axisymmetrical forging. Then, a first type of shape optimization problem is considered: the optimization of the shape of the initial part for a one-step forging operation. Two academic problems allow for checking the accuracy of the analytical derivatives, and for studying the convergence rate of the optimization procedure. Both constrained and unconstrained problems are considered. Afterwards, a second type of inverse problem of design is considered: the shape optimization of the preforming tool, for a two-step forging process. A satisfactory shape is obtained after few iterations of the optimization procedure.
    Additional Material: 21 Ill.
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  • 215
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 355-356 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: No Abstract
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  • 216
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 189-217 
    ISSN: 0029-5981
    Keywords: a posteriori error ; finite element ; plasticity ; adaptativity ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, a method is developed to control the parameters of a finite element computation for time-dependent material models. This method allows the user to obtain a prescribed accuracy with a computational cost as low as possible. To evaluate discretization errors, we use a global error measure in constitutive relation based on Drucker's inequality. This error includes, over the studied time interval, the error of the finite element model and the error of the algorithm being used. In order to master the size of the elements of the mesh and the length of the time increments, an error estimator, which permits estimating the errors due to the time discretization, is proposed. These tools are used to elaborate two procedures of adaptivity. Various examples for monotonous or non-monotonous loadings, for 2-D or axisymmetric problems, show the reliability of these procedures.
    Additional Material: 14 Ill.
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  • 217
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 235-259 
    ISSN: 0029-5981
    Keywords: dynamic relaxation ; parallel processing ; non-linear mechanics ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A parallel adaptive dynamic relaxation (ADR) algorithm has been developed for non-linear structural analysis. This algorithm has minimal memory requirements, is easily parallelizable and scalable to many processors, and is generally very reliable and efficient for highly non-linear problems. Performance evaluations on single-processor computers have shown that the ADR algorithm is reliable and highly vectorizable, and that it is competitive with direct solution methods for the highly non-linear problems considered. The present algorithm is implemented on the 512-processor Intel Touchstone DELTA system at Caltech, and it is designed to minimize the extent and frequency of interprocessor communication. The algorithm has been used to solve for the non-linear static response of two- and three-dimensional hyperelastic systems involving contact. Impressive relative speed-ups have been achieved and demonstrate the high scalability of the ADR algorithm. For the class of problems addressed, the ADR algorithm represents a very promising approach for parallel-vector processing.
    Additional Material: 15 Ill.
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  • 218
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 1295-1312 
    ISSN: 0029-5981
    Keywords: finite elements ; mixed models ; hybrid models ; plates ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A mixed-hybrid formulation for stress finite elements is presented. The stresses and the displacements in the domain of the element and the displacements on the boundary are simultaneously and independently approximated using orthogonal functions. The stress approximation functions are used as weighting functions in the weighted residual enforcement of the local compatibility and constitutive equations. Similarly, the displacement approximation functions in the domain and on the boundary are used as weighting functions in the weighting residual enforcement of the local equilibrium equation and of the static boundary conditions, respectively. Legendre polynomials and Fourier series are used to illustrate the performance of the finite element formulation when applied to elastostatic problems.
    Additional Material: 13 Ill.
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  • 219
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 1313-1340 
    ISSN: 0029-5981
    Keywords: iterative methods for linear systems ; preconditioning ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The preconditioned conjugate gradient algorithm is a well-known and powerful method used to solve large sparse symmetric positive definite linear systems. Such systems are generated by the finite element discretization in structural analysis but users of finite elements in this context generally still rely on direct methods. It is our purpose in the present work to highlight the improvement brought forward by some new preconditioning techniques and show that the preconditioned conjugate gradient method performs better than efficient direct methods.
    Additional Material: 8 Ill.
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  • 220
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 1357-1382 
    ISSN: 0029-5981
    Keywords: numerical reduced minimization ; non-uniform isoparametric mapping ; unmatched coefficient ; spurious constraint ; optimal minimization ; locking ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, the effects of various numerical integrations on the behaviour of C0-continuous beam elements under non-uniform isoparametric mapping are investigated by using numerical reduced minimization theory. The theory shows that stress recovery can be achieved by sampling stresses at the optimal integration points once a reduced integration is employed. It rationalizes the continued acceptance of the conventional reduced integration of constrained strain energy as one of remedies for locking due to spurious constraint.
    Additional Material: 12 Ill.
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  • 221
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1383-1403 
    ISSN: 0029-5981
    Keywords: crashworthiness ; homogenization ; topology design ; automotive structure optimization ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The topological optimization of components to maximize crash energy absorption for a given volume is considered. The crash analysis is performed using a DYNA3D finite element analysis. The original solid elements are replaced by ones with holes, the hole size being characterized by a so-called density (measure of the reduced volume). A homogenization method is used to find elastic moduli as a function of this density. Simpler approximations were developed to find plastic moduli and yield stress as functions of density.Optimality criteria were derived from an optimization statement using densities as the design variables. A resizing algorithm was constructed so that the optimality criteria are approximately satisfied. A novel feature is the introduction of an objective function based on strain energies weighted at specified times. Each different choice of weighting factors leads to a different structure, allowing a range of design possibilities to be explored.The method was applied to an automotive body rear rail. The original design and a new design of equal volume with holes were compared for energy absorption.
    Additional Material: 25 Ill.
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  • 222
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1419-1431 
    ISSN: 0029-5981
    Keywords: integral equations ; scattering ; boundary elements ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes a boundary integral equation (boundary element) method for the solution of a variety of transient acoustic problems. The spatial and temporal discretization employs quadratic isoparametric elements with high-order Gauss quadrature, and the ensuing equations are implicit. The implicit formulation both eliminates the instabilities reported in explicit treatments, and permits a freedom of choice of timestep which can reduce costs dramatically. The accuracy of the approach is demonstrated by comparison with the analytical solution for a sphere. Results for more demanding sphere-cone-sphere geometries extending to seven wavelengths long are presented, and compared to those obtained from a related frequency domain approach.
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  • 223
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1433-1435 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 224
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1437-1454 
    ISSN: 0029-5981
    Keywords: large elastic deformations ; enhanced strain method ; finite elements ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The numerical simulation of processes undergoing finite deformations requires robust elements. For a broad range of applications these elements should have a good performance in bending dominated situations as well as in the case of incompressibility. The element should be insensitive against mesh distortions which frequently occurs during finite deformations. Furthermore, due to efficiency reasons a good coarse mesh accuracy in required in non-linear analysis. The QS6 element, developed in this paper, tries to fulfil the above-mentioned requirements. The performance is depicted by means of numerical examples.
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  • 225
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1475-1489 
    ISSN: 0029-5981
    Keywords: meshing ; three-dimensional ; surfaces ; quadrilateral ; finite element ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper discusses the extension of the paving algorithm for all quadrilateral mesh generation to arbitrary three-dimensional trimmed surfaces. Methods of calculating angles, projecting elements, and detecting collisions between paving boundaries, for general surfaces are presented. Extensions of the smoothing algorithms for three dimensions are set forth. Advances in the use of scalar sizing functions are presented. These functions can be used to better approximate internal mesh density from boundary densities and surface characteristics.
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  • 226
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 1517-1534 
    ISSN: 0029-5981
    Keywords: spectral elements ; viscoelasticity ; time-splitting method ; drag factor ; Uzawa algorithm ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The steady flow of a viscoelastic fluid past a sphere in a cylindrical tube is considered. A spectral element method is used to solve the system of coupled non-linear partial differential equations governing the flow. The spectral element method combines the flexibility of the traditional finite element method with the accuracy of spectral methods. A time-splitting algorithm is used to determine the solution to the steady problem. Results are presented for the Oldroyd B model. These show excellent agreement with the literature. The results converge with mesh refinement. A limiting Deborah number of approximately 0⋅6 is found, irrespective of the spatial resolution.
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  • 227
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    International Journal for Numerical Methods in Engineering 39 (1996) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 228
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1436-1436 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 229
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1455-1473 
    ISSN: 0029-5981
    Keywords: transient loads ; advective-diffusive equations ; Petrov-Galerkin ; Galerkin Leask-Square ; boundary layers ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A Petrov-Galerkin formulation based on two different perturbations to the weighting functions is presented. These perturbations stabilize the oscillations that are normally exhibited by the numerical solution of the transient advective-diffusive equation in the vicinity of sharp gradients produced by transient loads and boundary layers. The formulation may be written as a generalization of the Galerkin Least-Square method.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1491-1516 
    ISSN: 0029-5981
    Keywords: impact ; composite laminates ; finite element ; matrix cracking ; delamination ; contact technique ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The modelling of the behaviour of laminates during low velocity impact requires, first, an analysis of the efficiency of the numerical tool used. A logical development in relation to the numerical structure of the code and the experimental observations is proposed. Four aspects of the code implementation are discussed. The first one is the representation of the impact loading by a macro-contact model using the Lagrange multiplier technique. The second is the development of this technique on the meso-scale to represent the assembly of plies of the laminate. The third step is the modelling of the evolution of the non homogeneous cracked state in the composite with an averaging technique, based on the Laws-Dvorak-Hejazi model, developed on the finite element scale. The fourth step is the modelling of the delamination between plies as a lack of contact set off by a mixed criterion matrix-cracking/interfacial forces. Numerical results on a glass-epoxy [02/906/02] laminate impacted at 27 J are in a good agreement with experimental observations.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1535-1553 
    ISSN: 0029-5981
    Keywords: electric machinery ; electromagnetic losses ; Preisach model ; finite element-finite difference method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper deals with a numerical method for the evaluation of the magnetic iron losses in steel laminations used in rotating electric machinery. The magnetic hysteresis and the eddy current effects are directly and simultaneously taken into account. Hereby commonly used analytic expressions for the distribution function in the widely adapted Preisach hysteresis model are found to be not quite accurate. The magnetic circuit is decomposed into magnetic and air gap network elements, connected by fundamental loops. The magnetic network elements show a finite element structure. The kinematics of the electric machine is deliberately taken into account by an interpolation technique. Although the model retains the essential features of a cumbersome 3-D problem, a relatively simple algorithm may be developed. For the resulting algebraic system, we propose a suitable decoupling technique, which is efficient from the computational point of view. Numerical experiments show that the results obtained by our numerical approach are in good agreement with the known behaviour of the magnetic material.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1585-1606 
    ISSN: 0029-5981
    Keywords: adaptive mesh refinement ; solid transition element ; non-conforming modes ; superconvergent patch recovery ; error estimation ; neighbouring element ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An automated three-dimensional adaptive h-refinement strategy using the solid transition elements with variable midside nodes at edges and faces of the element is presented. The basic behaviour of these transition elements were improved by addition of associated non-conforming modes. By introducing these transition elements, some difficulties associated with imposing displacement constraints on irregular nodes to enforce interelement compatibility in the conventional adaptive h-refinement are easily overcome. A superconvergent patch recovery technique is also extended to three-dimensional problem. Numerical examples show the effectiveness of the proposed adaptive mesh refinement scheme using transition elements.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1619-1620 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1659-1680 
    ISSN: 0029-5981
    Keywords: elasticity ; stress singularity ; finite elements ; optimization ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A semianalytical singular element is proposed to model the stress fields in plane and axisymmetric elastic bodies in the vicinity of singular points. The element generation is performed taking into account the structure of analytical solution in the vicinity of such points. This renders the element well suited for any type of singular points. Introduction of specially generated shape functions in the approximating expressions for displacements enables one to ensure the displacement compatibility with the standard elements. A detailed consideration is given to the convergence of the finite-element procedure. The extensive possibilities of the proposed singular element are exemplified by solving particular elastic problems. The applicability of the elaborated singular element is discussed with respect to optimization of geometry and material properties in the vicinity of singular points. Two optimization problems are presented to illustrate a search for the body geometry providing the optimal stress distribution.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1635-1657 
    ISSN: 0029-5981
    Keywords: finite element method ; radiation boundary conditions ; absorbing boundary conditions ; discontinuous Galerkin method ; structural acoustics ; wave equation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A time-discontinuous Galerkin space-time finite element method is formulated for the exterior structural acoustics problem in two space dimensions. The problem is posed over a bounded computational domain with local time-dependent radiation (absorbing) boundary conditions applied to the fluid truncation boundary. Absorbing boundary conditions are incorporated as ‘natural’ boundary conditions in the space-time variational equation, i.e. they are enforced weakly in both space and time. Following Bayliss and Turkel, time-dependent radiation boundary conditions for the two-dimensional wave equation are developed from an asymptotic approximation to the exact solution in the frequency domain expressed in negative powers of a non-dimensional wavenumber. In this paper, we undertake a brief development of the time-dependent radiation boundary conditions, establishing their relationship to the exact impedance (Dirichlet-to-Neumann map) for the acoustic fluid, and characterize their accuracy when implemented in our space-time finite element formulation for transient structural acoustics. Stability estimates are reported together with an analysis of the positive form of the matrix problem emanating from the space-time variational equations for the coupled fluid-structure system. Several numerical simulations of transient radiation and scattering in two space dimensions are presented to demonstrate the effectiveness of the space-time method.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1721-1736 
    ISSN: 0029-5981
    Keywords: material stability ; loss of ellipticity ; discontinuous bifurcation ; numerical solution ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Material instability occurs when ellipticity is lost for symmetric constitutive equations. Prior to loss of ellipticity it is possible that the second-order work of Hill or Drucker becomes negative. There are implications in the literature that numerical solutions cease to be meaningful when a material strain softens and the second-order work is not positive. The instant that the second-order work is zero or negative simultaneously with the additional restriction that the strain increments satisfy compatibility is equivalent to the loss of the ellipticity criterion for symmetric constitutive relations. The loss of ellipticity criterion is the appropriate one for identifying when numerical solutions cease to show convergence and may also be a suitable criterion for identifying the instant at which material failure is initiated. An analytical development is provided for loss of ellipticity together with an explicit expression for the normal to the bifurcation plane. Numerical solutions are given for several sample problems. For all cases, the numerical solutions based on the finite element method conform to the theoretical expectations that unique numerical solutions exist prior to the point at which ellipticity is lost.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1681-1705 
    ISSN: 0029-5981
    Keywords: hypersingular boundary integral equations ; boundary element method ; fracture mechanics ; dynamic stress intensity factor ; wave propagation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The topic of hypersingular boundary integral equations is a rapidly developing one due to the advantages which this kind of formulation offers compared to the standard boundary integral one. In this paper the hypersingular formulation is developed for time-domain antiplane elastodynamic problems. Firstly, the gradient representation is found from the displacement one, removing the strong singularities (Dirac's delta functions) which arise due to the differentiation process. The gradient representation is carried to the boundary through a limiting process and the resulting equation is shown to be consistent with the static formulation. Next, the numerical treatment of the traction boundary integral equation and its application to crack problems are presented. For the boundary discretization, conforming quadratic elements are tested, which are introduced in this paper for the first time, and it is shown that the results are very good in spite of the lesser number of unknowns of this approach in comparison to the non-conforming element alternative. A procedure is devised to numerically perform the hypersingular integrals that is both accurate and versatile. Several crack problems are solved to show the possibilities of the method. To this end both straight and curved elements are employed as well as regular and distorted quarter point elements.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1791-1792 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1797-1820 
    ISSN: 0029-5981
    Keywords: Multilayered plates ; HSDT modelling ; C0 continuity ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Concerning composites plate theories and FEM (Finite Element Method) applications this paper presents some multilayered plate elements which meet computational requirements and include both the zig-zag distribution along the thickness co-ordinate of the in-plane displacements and the interlaminar continuity (equilibrium) for the transverse shear stresses. This is viewed as the extension to multilayered structures of well-known C0 Reissner-Mindlin finite plate elements. Two different fields along the plate thickness co-ordinate are assumed for the transverse shear stresses and for the displacements, respectively. In order to eliminate stress unknowns, reference is made to a Reissner mixed variational theorem. Sample tests have shown that the proposed elements, named RMZC, numerically work as the standard Reissner-Mindlin ones. Furthermore, comparisons with other results related to available higher-order shear deformation theories and to three-dimensional solutions have demonstrated the good performance of the RMZC elements.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1839-1857 
    ISSN: 0029-5981
    Keywords: combined methods ; finite difference method ; Ritz-Galerkin method ; coupling strategy ; penalty method ; hybrid method ; elliptic equation ; singularity problems ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents six combinations of the Ritz-Galerkin method and the finite difference method for solving elliptic boundary value problems. Not only optimal convergence rates of solutions but also superconvergence rates of solution derivatives can be achieved. The non-conforming combination and other five new combinations are given in algorithms, error analysis, convergence rates, outlines of proofs, numerical experiments and their comparisons.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1879-1888 
    ISSN: 0029-5981
    Keywords: FEM ; dynamics ; lumping ; acoustics ; accuracy ; convergence ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method for deriving hexahedral finite elements with lumped mass matrices for 3-D-problems is presented. These elements meet the theoretical conditions for high order convergence, and two numerical examples based on the 3-D scalar wave equation show that this is also the case in practice and that their accuracy is comparable to elements with consistent mass matrices.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1889-1901 
    ISSN: 0029-5981
    Keywords: coupled finite element boundary element analysis ; iterative solution ; plate-foundation interaction ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the present paper, a scheme is developed for the coupled FE/BE analysis of a plate-foundation interaction problem, in which the boundary element equations of the foundation are not explicitly assembled with the finite element equations of the plate, but instead an iterative procedure is proposed to obtain the final coupled solution. This iterative scheme preserves the nature of the BE and FE approaches and the coupled procedure can be easily implemented within an integrated FEM/BEM software environment. The scheme also reduces the computer storage requirement and avoids the error introduced by symmetrization of the BE equations. In addition, some important issues related to the scheme, such as convergence conditions and parameter selection, are discussed. A numerical example is provided to illustrate pthe benefits of the scheme. It is noted, however, that the overall performance of the proposed scheme when compared with the conventional direct solution of the unsymmetric equations arising from the explicit coupling of the FE and BE equations, depends on the choice of a free parameter and a matrix contained in the scheme.
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    International Journal for Numerical Methods in Engineering 39 (1996) 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1933-1953 
    ISSN: 0029-5981
    Keywords: structures ; optimization ; large scale ; structural design ; sequential quadratic programming ; self-scaling ; numerical algorithms ; algorithm evaluation ; test problems ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The basic idea of an implicit sequential quadratic programming (ISQP) method for constrained problems is to use the approximate Hessian of the Lagrangian without explicitly calculating and storing it. This overcomes one of the major drawbacks of the traditional SQP method where a large matrix needs to be calculated and stored. This concept of an implicit method is explained and an algorithm based on it is presented. The proposed method extends a similar algorithm for unconstrained problems where a two-loop recursion formula is used for the inverse Hessian matrix. The present paper develops a similar algorithm for not only the constrained problem but also the direct Hessian updates. Several scaling procedures for the Hessian are also presented and evaluated. The basic method and some of its variations are evaluated using a set of mathematical programming test problems, and a set of structural design test problems - small to larger scale. The ISQP method performs much better than a method that does not use any approximate Hessian matrix. Its performance is better than the full SQP method for larger scale problems. The test results also show that an appropriate scaling of the Hessian can improve both efficiency and reliability substantially.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 1981-1983 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 2005-2029 
    ISSN: 0029-5981
    Keywords: residual estimates ; singular and hypersingular residuals ; error estimates ; boundary element method ; singular integrals ; hypersingular integrals ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a new approach for a posteriori ‘pointwise’ error estimation in the boundary element method. The estimator relies upon evaluation of the residual of hypersingular integral equations, and is therefore intrinsic to the boundary integral equation approach. A methodology is developed for approximating the error on the boundary as well as in the interior of the domain. Extensive computational experiments have been performed for the two-dimensional Laplace equation and the numerical results indicate that the error estimates successfully track the form of the exact error curve. Moreover, a reasonable estimate of the magnitude of the actual error is also predicted.
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    International Journal for Numerical Methods in Engineering 39 (1996) 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 2477-2505 
    ISSN: 0029-5981
    Keywords: higher-order continua ; plasticity ; localization ; mixed elements ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Improved algorithms are proposed for a gradient plasticity theory in which the Laplacian of an invariant plastic strain measure enters the yield function. Particular attention is given to the type of finite elements that can be used within the format of gradient-dependent plasticity. Assuming a weak satisfaction of the yield function, mixed finite elements are developed, in which the invariant plastic strain measure and the displacements are discretized. Two families of finite elements are developed: one in which the invariant plastic strain measure is interpolated using C1-continuous polynomials, and one in which penalty-enhanced C0-continuous interpolants are used. The performance of both families of finite elements is assessed numerically in one-dimensional and two-dimensional boundary value problems. The regularizing effect of the used gradient enhancement in computations of elastoplastic solids is demonstrated, both for mesh refinement and for the directional bias of the grid lines.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 2509-2529 
    ISSN: 0029-5981
    Keywords: refined nonconforming element method ; hybrid element method ; quadrilateral axisymmetric element ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The general approach for constituting non-conforming displacement function has been developed for axisymmetric finite element analysis and a pure non-conforming quadrilateral axisymmetric element, from a non-conforming displacement function and without any reduced integration technique, is given.Based on a proposed functional for formulating axisymmetric element and the orthogonal approach, a quadrilateral axisymmetric refined hybrid element has been presented which can be used to achieve superior performances such as higher accuracy and free from locking.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 2555-2573 
    ISSN: 0029-5981
    Keywords: 3-D boundary element method ; elastoplastic analysis ; hypersingular formulation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A 3-D hypersingular Boundary Integral Equation (BIE) of elastoplasticity is derived. Using this formulation the displacement rate gradients and the complete stress tensor on the boundary can be evaluated directly as opposed to the classical approach, where the shape functions derivatives are to be calculated. The regularization of strongly singular and hypersingular boundary integrals, as well as strongly singular domain integrals for a source point positioned on the boundary is carried out in a general manner. Arbitrary types of elements and arbitrary positions of the source point with respect to continuity requirements can be used. Numerical 3-D elastoplastic examples (notch and crack problems) illustrate the advantages of the proposed method.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 2635-2646 
    ISSN: 0029-5981
    Keywords: non-linear elasticity ; finite element method ; Newton method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A generalized Newton method is proposed in conjunction with a higher-order Lagrangian finite element discretization of bodies undergoing finite elastic deformations. The method is based on a gradient-like modification of the Newton method, designed to suppress the sensitivity of higher-order elements during the early iterations, thus allowing for solutions to be obtained using moderately large step-sizes.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 2593-2618 
    ISSN: 0029-5981
    Keywords: space-time coupled ; p-version ; least squares ; time-marching ; accuracy and stability ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a p-version least squares finite element formulation for two-dimensional unsteady fluid flow described by Navier-Stokes equations where the effects of space and time are coupled. The dimensionless form of the Navier-Stokes equations are first cast into a set of first-order differential equations by introducing auxiliary variables. This permits the use of C0 element approximation. The element properties are derived by utilizing the p-version approximation functions in both space and time and then minimizing the error functional given by the space-time integral of the sum of squares of the errors resulting from the set of first-order differential equations. This results in a true space-time coupled least squares minimization procedure. The application of least squares minimization to the set of coupled first-order partial differential equations results in finding a solution vector {δ} which makes gradient of error functional with respect to {δ} a null vector. This is accomplished by using Newton's method with a line search.A time marching procedure is developed in which the solution for the current time step provides the initial conditions for the next time step. Equilibrium iterations are carried out for each time step until the error functional and each component of the gradient of the error functional with respect to nodal degrees of freedom are below a certain prespecified tolerance. The space-time coupled p-version approximation functions provide the ability to control truncation error which, in turn, permits very large time steps. What literally requires hundreds of time steps in uncoupled conventional time marching procedures can be accomplished in a single time step using the present space-time coupled approach. The generality, success and superiority of the present formulation procedure is demonstrated by presenting specific numerical examples for transient couette flow and transient lid driven cavity. The results are compared with the analytical solutions and those reported in the literature. The formulation presented here is ideally suited for space-time adaptive procedures. The element error functional values provide a mechanism for adaptive h, p or hp refinements.
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    International Journal for Numerical Methods in Engineering 39 (1996) 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 2693-2694 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 2673-2691 
    ISSN: 0029-5981
    Keywords: rigid body dynamics ; Coulomb friction ; inelastic impact ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper a new time-stepping method for simulating systems of rigid bodies is given which incorporates Coulomb friction and inelastic impacts and shocks. Unlike other methods which take an instantaneous point of view, this method does not need to identify explicitly impulsive forces. Instead, the treatment is similar to that of J. J. Moreau and Monteiro-Marques, except that the numerical formulation used here ensures that there is no inter-penetration of rigid bodies, unlike their velocity-based formulation. Numerical results are given for the method presented here for a spinning rod impacting a table in two dimensions, and a system of four balls colliding on a table in a fully three-dimensional way. These numerical results also show the practicality of the method, and convergence of the method as the step size becomes small.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 3195-3215 
    ISSN: 0029-5981
    Keywords: modified effective capacitance ; solidification ; tetrahedral elements ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper a new formulation for modelling solidification is discussed. The formulation has similar features to both the apparent and effective heat capacitance methods used for solidification problems where conduction predominates over other heat transfer mechanisms. The main feature of the new method is that a modified form of effective heat capacitance is calculated from the solution of non-linear equations that describe the energy loss for linear tetrahedral finite elements. This approach ensures that the predicted temperature field corresponds exactly with the energy loss and so providing an extremely stable formulation. The method is tested against a range of problems including some with non-linear liquid fractions. The predictions are compared against known analytical solutions and the method is shown to provide reasonable accuracy even for relatively large time-steps. A comparison is made between the method and the well-known temporal and spatial approximations of apparent heat capacitance, and effective capacitance. Accuracy is maintained over a greater variation in time-step and mesh density with comparable computational requirements. In addition, the method lends itself to the use of relatively simple bisection techniques for the solution of the non-linear finite element equations. Also demonstrated is the method's innate ability to predict energy loss to a high degree of accuracy for large time steps.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 3049-3064 
    ISSN: 0029-5981
    Keywords: mold cooling ; injection molding ; finite element method ; three-dimensional ; Jacobi conjugate gradient ; matrix-free algorithm ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A methodology is presented to simulate the three-dimensional heat transfer within a mold during the injection molding process. The mold cooling analysis assists cooling channel design and paves the way for part shrinkage and warpage analysis. The transient temperature distributions in the mold and the polymer part are simultaneously computed by Galerkin Finite Element Method (GFEM) using a matrix-free Jacobi Conjugate Gradient (JCG) scheme. The numerical method presented here is efficient and has shown to require a fraction of the memory and computing time required by conventional methods. The matrix-free algorithm is initially validated using an injection mold designed to produce a plaque with a molded-in hole. Subsequently, the method is further applied to a representative automotive plastic component.
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    International Journal for Numerical Methods in Engineering 39 (1996) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 3405-3405 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 3407-3437 
    ISSN: 0029-5981
    Keywords: Delaunay triangulation ; Voronoï tesselation ; convex hull ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An efficient algorithm for Delaunay triangulation of a given set of points in d dimensions is presented. Various steps of the point insertion algorithm are reviewed and many acceleration procedures are implemented to speed up the triangulation process. New features include the search for a neighbouring point by a layering scheme, locating the containing simplex by a random walk, formulas of important geometrical quantities of a new simplex based on those of an old one, a novel approach in establishing the adjacency relationship using connection matrices. The resulting scheme seems to be one of the fastest triangulation algorithms known, which enables us to generate tetrahedra in ∝3 with a linear generation rate of 15 000 tetrahedra per second for randomly generated points on an HP 735 workstation.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 3573-3573 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 3625-3639 
    ISSN: 0029-5981
    Keywords: hybrid finite element ; plate/shell ; laminated composites ; stress analysis ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A degenerated plate/shell element based on the combined energy variational principle and the equivalent single-layer model is proposed. It is derived from the 3-D continuum equation by imposing one constraint on the 3-D isoparametric solid element: a straight line normal to the mid-surface before deformation remains straight but not normal after deformation. The continuities of interlaminar stresses are satisfied at the interlaminar surface and the number of degrees of freedom per node is independent of the number of layers. In this work, the combined energy variational principle is used to overcome transverse stress continuity limitations of single-layer models. The traction-free conditions are satisfied on the upper and lower surfaces of a laminate by assuming the transverse stress components independently. The transverse normal strain is taken into account in order to consider the full 3-D effect in a laminated composite. The iso-function method and the classification method of the stress modes are used to construct the assumed stress field which contains a minimum number of stress modes and guarantees no zero energy mode in the element stiffness matrix. Three examples are presented to illustrate the efficiency and accuracy of the element.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 4183-4198 
    ISSN: 0029-5981
    Keywords: Overhauser ; triangular elements ; boundary element ; three-dimensional ; potential problems ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Interpolation to boundary data and one-dimensional Overhauser parabola blending methods are used to derive Overhauser triangular elements. The elements are C1-continuous at inter-element nodes and no functional derivatives are required as nodal parameters. These efficient parametric representation elements are used to solve three-dimensional potential problems using the Boundary Element Method (BEM). Results obtained are generally as accurate as those obtained using Overhauser quadrilateral elements.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 4199-4214 
    ISSN: 0029-5981
    Keywords: time integration ; explicit method ; predictor-corrector algorithm ; Newmark method ; structural dynamics ; large-scale dynamic problem ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new simple explicit two-step method and a new family of predictor-corrector integration algorithms are developed for use in the solution of numerical responses of dynamic problems. The proposed integration methods avoid solving simultaneous linear algebraic equations in each time step, which is valid for arbitrary damping matrix and diagonal mass matrix frequently encountered in practical engineering dynamic systems. Accordingly, computational speeds of the new methods applied to large system analysis can be far higher than those of other popular methods. Accuracy, stability and numerical dissipation are investigated. Linear and nonlinear examples for verification and applications of the new methods to large-scale dynamic problems in railway engineering are given. The proposed methods can be used as fast and economical calculation tools for solving large-scale nonlinear dynamic problems in engineering.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 2837-2862 
    ISSN: 0029-5981
    Keywords: special boundary integral formulation ; design sensitivity analysis (DSA) ; direct differentiation approach (DDA) ; three-dimensional conduction heat transfer ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A special boundary integral formulation had been proposed to analyse many engineering problems of conduction heat transfer in complex three-dimensional geometries (closely spaced surface and circular hole in infinite domain or simple modification of it) by Rezayat and Burton. One example of such geometries is the mold sets in the injection molding process. In this paper, an efficient and accurate approach for the design sensitivity analysis (DSA) is presented for these kinds of problems in the similar complex geometries using the direct differentiation approach (DDA) based on the above special boundary integral formulation. The present approach utilizes the implicit differentiation of the boundary integral equations with respect to the design variables (radii and locations of circular holes) to yield the sensitivity equations. A sample problem (heat transfer of injection molding cooling system) is solved to demonstrate the accuracy of the present sensitivity analysis formulation. Although the techniques introduced here are applied to a particular problem in heat transfer of injection molding cooling system, their potential application is quite broad.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 3047-3048 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 3175-3194 
    ISSN: 0029-5981
    Keywords: equilibrium elements ; spurious kinematic modes ; macro-elements ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper illustrates a method whereby a family of robust equilibrium elements can be formulated in a general manner. The effects of spurious kinematic modes, present to some extent in all primitive equilibrium elements, are eliminated by judicious assembly into macro-equilibrium elements. These macroelements are formulated with sufficient generality so as to retain the polynomial degree of the stress field as a variable. Such a family of macro-elements is a new development, and results for polynomials of degree greater than two have not been seen before. The quality of results for macro-equilibrium elements with varying degrees of polynomial is demonstrated by numerical examples.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 3101-3121 
    ISSN: 0029-5981
    Keywords: optimal slewing ; finite elements ; flexible beam ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new computational approach to modelling and control of a flexible beam is proposed. The structural modelling and the control design problems are formulated in a unified mathematical framework that allows simultaneous structural and control design iterations that result in an optimal overall system performance. The method employs the space-time spectral elements for simultaneous space and time discretizations of a Timoshenko beam model. Dimensionless equations of motion are derived using Hamilton's principle of variable action and an integral formulation in the framework of space-time spectral elements is introduced. An optimal control problem formulated for the continuum model is transformed by the space-time spectral element formulation into an optimization problem in a finite-dimensional parameter space. Dynamic programming is then used to obtain both open and closed loop control laws. A simulation study shows good performance of the control law applied to the nominal model. It is also demonstrated that proper discretization yields performance robustness of the system with respect to modal truncation.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 3145-3162 
    ISSN: 0029-5981
    Keywords: shotcrete ; tunnelling ; cap model ; New Austrian Tunnelling Method (NATM) ; finite element method ; viscoplasticity ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper is concerned with the parameter identification, verification and selected applications of a 3D viscoplastic material model for shotcrete proposed by Meschke. The performance of the shotcrete model is evaluated by means of reanalyses of short-term and creep tests on shotcrete specimen. The most essential items of a viscoplastic cap model used for the representation of soil including the determination of the model parameters are also presented. Both models are employed in a 3D finite element simulation of the excavation of a single-track tunnel driven according to the New Austrian Tunnelling Method. Comparisons between in situ measurements and numerical results are presented.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 3123-3143 
    ISSN: 0029-5981
    Keywords: shotcrete ; finite element method ; viscoplasticity ; smeared cracking ; aging ; Rankine criterion ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The structure of the classical theory of viscoplasticity and its algorithmic formulation in the context of an operator split scheme is extended to account for the effect of aging. Within this framework, a 3-D multisurface constitutive model for shotcrete is proposed. A rotating-crack model based on the Rankine criterion is adopted in conjunction with a Drucker-Prager yield criterion for describing the mechanical behaviour of young concrete in the compressive regime. The model is suitable for the representation of the time-dependent behaviour of shotcrete including creep and the time dependence of strength and stiffness. A computationally effective return mapping scheme is achieved by formulating the material model in terms of the principal directions and transforming the obtained relations to global axes. Linearization of the return mapping algorithm yields the algorithmic tangent moduli.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 3083-3099 
    ISSN: 0029-5981
    Keywords: EAS-method ; hybrid-method ; equivalence ; stress recovery ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An equivalence between the enhanced assumed strain (EAS) method based on the Hu-Washizu principle, recently proposed by Simo and Rifai, and assumed stress hybrid (hybrid) method based on the Hellinger-Reissner principle is investigated. It is proved that not only the displacements but also the stresses of the EAS-elements calculated from the strains are identical to those of the corresponding hybrid-elements at least at the Gauss integration points provided the spaces of the trial functions for enhanced assumed strains and for assumed stresses satisfy the orthogonality and the inclusion or the invertibility condition. By virtue of this equivalence, a stress recovery procedure of the EAS-elements is devised. This procedure is variationally consistent and more efficient than those proposed by Simo and Rifai and Andelfinger and Ramm. Since the classical method of incompatible displacement modes is a special case of the EAS-method, this procedure also can be used to evaluate variationally consistent stresses for the non-conforming elements.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 3217-3217 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 3305-3325 
    ISSN: 0029-5981
    Keywords: global ; optimization ; algorithms ; nonlinear ; engineering ; design ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: After a brief overview of the methods from the literature, two new algorithms (zooming and domain elimination) for global optimization of general NLP problems are introduced. Operations analysis and stopping criteria for the methods are discussed. Numerical evaluation of the methods is carried out using a set of mathematical programming test problems. Performance of the methods is compared with the Controlled Random Search (CRS) and the Simulated Annealing (SA) methods. The methods are superior to SA for the test problems, as they are more robust, efficient and accurate. The CRS is more efficient than the new methods; however, it is applicable to unconstrained problems only. Therefore, it is concluded that the new methods are useful for engineering optimization applications.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 3327-3349 
    ISSN: 0029-5981
    Keywords: mesh generation ; hexahedral ; whisker weaving ; duality ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper introduces a new algorithm called whisker weaving for constructing unstructured, all-hexahedral finite element meshes. Whisker weaving is based on the Spatial Twist Continuum (STC), a global interpretation of the geometric dual of an all-hexahedral mesh. Whisker weaving begins with a closed, all-quadrilateral surface mesh bounding a solid geometry, then constructs hexahedral element connectivity advancing into the solid. The result of the whisker weaving algorithm is a complete representation of hex mesh connectivity only: Actual mesh node locations are determined afterwards.The basic step of whisker weaving is to form a hexahedral element by crossing or intersecting dual entities. This operation, combined with seaming or joining operations in dual space, is sufficient to mesh simple block problems. When meshing more complex geometries, certain other dual entities appear such as blind chords, merged sheets, and self-intersecting chords. Occasionally specific types of invalid connectivity arise. These are detected by a general method based on repeated STC edges. This leads into a strategy for resolving some cases of invalidities immediately.The whisker weaving implementation has so far been successful at generating meshes for simple block-type geometries and for some non-block geometries. Mesh sizes are currently limited to a few hundred elements. While the size and complexity of meshes generated by whisker weaving are currently limited, the algorithm shows promise for extension to much more general problems.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 3367-3390 
    ISSN: 0029-5981
    Keywords: finite plasticity ; single crystals ; multisurface plasticity ; active set search ; exponential map ; stress update algorithm ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a new stress update algorithm for large-strain rate-independent single-crystal plasticity. The theoretical frame is the well-established continuum slip theory based on the multiplicative decomposition of the deformation gradient into elastic and plastic parts. A distinct feature of the present formulation is the introduction and computational exploitation of a particularly simple hyperelastic stress response function based on a further multiplicative decomposition of the elastic deformation gradient into spherical and unimodular parts, resulting in a very convenient representation of the Schmid resolved shear stresses on the crystallographic slip systems in terms of a simple inner product of Eulerian vectors. The key contribution of this paper is an algorithmic formulation of the exponential map exp: sl(3) → SL(3) for updating the special linear group SL(3) of unimodular plastic deformation maps. This update preserves exactly the plastic incompressibility condition of the anisotropic plasticity model under consideration. The resulting fully implicit stress update algorithm treats the possibly redundant constraints of single-crystal plasticity by means of an active set search. It exploits intrinsically the simple representation of the Schmid stresses by formulating the return algorithm and the associated consistent elastoplastic moduli in terms of Eulerian vectors updates. The performance of the proposed algorithm is demonstrated by means of a representative numerical example.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 3247-3272 
    ISSN: 0029-5981
    Keywords: arbitrary Lagrangian-EulerianFEM ; r-adaptation ; s-adaptation ; metal forming ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, an adaptive Arbitrary Lagrangian-Eulerian (ALE) finite element method is developed for solving large deformation problems with applications in metal-forming simulation. The ALE mesh movement is coupled with r-adaptation of automatic node relocation, to minimize element distortion during the process of deformation. Strain localization is considered in this study through the constitutive relations for ductile porous materials. Prediction of localized deformation is achieved through a multilevel mesh superimposition method, termed as s-adaptation. The model is validated by comparison with established results and codes, and a few metal-forming problems are simulated to test its effectiveness.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 3273-3304 
    ISSN: 0029-5981
    Keywords: elasticity ; boundary integral equations ; hypersingular ; continuity ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents two fully equivalent and regular forms of the hypersingular Somigliana stress identity in elasticity that are appropriate for problems in which the displacement field (and resulting stresses) is C1,α continuous. Each form is found as the result of a single decomposition process on the kernels of the Somigliana stress identity in three dimensions. The results show that the use of a simple stress state for regularization arises in a direct manner from the Somigliana stress identity, just as the use of a constant displacement state regularization arose naturally for the Somigliana displacement identity. The results also show that the same construction leads naturally to a finite part form of the same identity. While various indirect constructions of the equivalents to these findings are published, none of the earlier forms address the fundamental issue of the usual discontinuities of boundary data in the hypersingular Somigliana stress identity that arise at corners and edges. These new findings specifically focus on the corner problem and establish that the previous requirements for continuity on the densities in the hypersingular Somigliana stress identity are replaced by a sole requirement on displacement field continuity.The resulting regularized and finite part forms of the Somigliana stress identity leads to a regularized form of the stress boundary integral equation (stress-BIE). The regularized stress-BIE is shown to properly allow piecewise discontinuity of the boundary data subject only to C1,α continuity of the underlying displacement field. The importance of the findings is in their application to boundary element modeling of the hypersingular problem. The piecewise discontinuity derivation for corners is found to provide a rigorous and non-singular basis for collocation of the discontinuous boundary data for both the regularized and finite part forms of the stress-BIE. The boundary stress solution for both forms is found to be an average of the computed stresses at collocation points at the vertices of boundary element meshes. Collocation at these points is shown to be without any unbounded terms in the formulation thereby eliminating the use of non-conforming elements for the hypersingular equations. The analytical findings in this paper confirm the correct use of both regularized and finite part forms of the stress-BIE that have been the basis of boundary element analysis previously published by the first author of the current paper.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 3439-3451 
    ISSN: 0029-5981
    Keywords: finite element computation ; viscoplastic Norton-Hoff law ; metal forming ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We present a velocity based approach including acceleration to the finite element computation of metal forming problems, based on the viscoplastic Norton-Hoff law. In order to reduce computational cost, we suggest substituting the classical solution procedure based on standard Newton-Raphson method for solving the set of non-linear equations, with a new one which needs only one computation inside a time step and which is based on the linearization of the non-linear equations over time. The new procedure was introduced as an option in the existing computer code FORGE2©. Some examples are used for comparison between the classical procedure and the new one. They show that the new procedure is stable and accurate, and in comparison to the classical one it reduces the total number of resolutions of linear systems. Therefore, significant computer time reduction can be expected for 3-D problems.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 3519-3534 
    ISSN: 0029-5981
    Keywords: automatic mesh generation ; finite element technique ; Delaunay triangulation ; non-manifold topology ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes an efficient algorithm for fully automated three-dimensional finite element meshing which is applicable to non-convex geometry and non-manifold topology. This algorithm starts with sparsely placed nodes on the boundaries of a geometric model and a corresponding 3-D Delaunay triangulation. Nodes are then inserted incrementally by checking the tetrahedral mesh geometry and topological compatibility between Delaunay triangulation and the geometric model. Topological compatibility is checked in a robust manner by a method which relies more on a mesh's topology than its geometry. The node placement strategy is tightly coupled to an incremental Delaunay triangulation algorithm, and results in a low growth rate of computational time.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 3705-3713 
    ISSN: 0029-5981
    Keywords: acoustis ; radiation boundary conditions ; non-local operators ; matrix-free ; iterative methods ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This communication describes an efficient implementation of the non-local Dirichlet-to-Neumann (DtN) radiation boundary condition which arises in the solution of exterior problems in acoustics. Exterior problems in acoustics involve unbounded fluid domains whose finite element solution requires the introduction of a truncation boundary in order to obtain a finite computational domain. The non-local (DtN) condition is an exact non-reflecting boundary condition which is imposed on this truncation boundary. Unfortunately, the discretization of the non-local (DtN) boundary condition results in a dense, fully populated matrix whose storage and factorization become increasingly expensive. We describe here a matrix-free interpretation of the non-local (DtN) map suitable for iterative solution methods, which allows the use of this exact boundary condition without any storage penalties related to its non-local nature.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 3601-3623 
    ISSN: 0029-5981
    Keywords: strong discontinuity analysis ; localization ; damage ; plasticity ; strain softening ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: On the basis of the strong discontinuity analysis of standard local stress-strain constitutive equations, a finite element framework for the simulation of strong discontinuities, which belongs to the family of assumed enhanced strain methods, is presented. Taking the standard linear triangle as the underlying element, an additional incompatible mode leads to the formulation of an enriched strain field which is shown to be able to appropriately capture strong discontinuities. The presented numerical simulations show that mesh size and mesh alignment dependencies can be completely removed.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 3775-3792 
    ISSN: 0029-5981
    Keywords: co-rotational formulation ; continua ; incompatible modes ; incompressibility ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The co-rotational technique is described for the three-dimensional analysis of continua. The technique exploits the proven technology of the best continua elements for linear analysis which are embedded into a formulation that applies an element-attached local co-ordinate frame that continuously moves and rotates with the element. The geometric non-linearity is then incorporated via the rotation of this local system. The method uses similar procedures to those recently described for 2-D continua elements but introduces concepts from a more conventional ‘continuum mechanics’ approach. The general framework for the co-rotational procedure is kept. However, a much neater formulation is derived, which readily allows the extension from two to three dimensions.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 3809-3838 
    ISSN: 0029-5981
    Keywords: diffuse element method ; element-free Galerkin method ; coupledDEM-FEM technique ; mixed formulation ; two-phase deforming media ; stability ; accuracy ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A coupled Diffuse Element-Finite Element technique (DEM-FEM) for transient coupled-field analysis is proposed. The method combines the standard finite element method and a diffuse element technique (also called Element-Free Galerkin Method). The resulting approach takes advantage of the capabilities of both of these numerical techniques. For instance, different approximations can very easily be introduced for different fields. Moreover, the finite element mesh provides the cells for numerical integration of the DEM equations. The matrix formulation is derived from the variational formulation of the coupled equation system. The case of the coupled hydromechnical formulation of two-phase porous media is studied as an applied example. It is shown that, as only few pore-pressure nodes are necessary, the stability requirements for almost impervious porous media are satisfied. The precision and stability of the obtained formulation was studied, and using several examples, we investigated the role of different parameters on the accuracy of results, such as the influence domain, the weighting function type, or the number of nodes.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 3867-3887 
    ISSN: 0029-5981
    Keywords: discrete Kirchhoff theory ; shell element ; semiloof element ; non-linear shell analysis ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the formulation of flat shell elements it is difficult to achieve inter-element compatibility between membrane and transverse displacements for non-coplanar elements. Many elements lack proper nodal degrees of freedom to model intersections making the assembly of elements troublesome. A flat triangular shell element is established by a combination of a new plate bending element DKTL and the well-known linear membrane strain element LST, and for this element the above-mentioned deficiencies are avoided. The plate bending element DKTL is based on Discrete Kirchhoff Theory and Loof nodes. The nodal configuration of the element is similar to the SemiLoof element, and the formulation is an improvement of a previous formulation. The element is used for both linear statics, linear buckling and geometrical non-linear analysis, and numerical examples are presented to show the robustness, accuracy and quick convergence of the element.
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    International Journal for Numerical Methods in Engineering 39 (1996) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 4243-4258 
    ISSN: 0029-5981
    Keywords: distributed computing ; heterogeneous workstations ; incompressible Navier-Stokes ; FEM ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The potential for using a network of workstations for solving the incompressible Navier-Stokes equations using a finite element formulation is investigated. A programming paradigm suitable for a heterogeneous distributed workstation environment is developed and compared to the traditional paradigm employed for distributed memory parallel computers. In particular, the issues of load balancing and fault recovery are explored. Numerical results are presented for two computer configurations: (1) a homogeneous network of workstations and (2) a heterogeneous network of workstations. The superiority of the developed paradigm over the traditional paradigm employed for distributed memory parallel computers is shown in cases where a heterogeneous network of workstations is employed or when one of the workstations of the cluster is loaded by other users.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 2531-2554 
    ISSN: 0029-5981
    Keywords: boundary element method ; elastohydrodynamic lubrication ; layered contact ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a numerical routine to compute the contact characteristics of elastomer layered cylinders lubricated by isoviscous liquids. The indentation of the elastic layer is calculated from boundary integral equations which are solved by linear and quadratic boundary element methods for a finite plane model and a circular representation of the junction. The hydrodynamic equation is also transformed into a boundary integral equation and solved by Simpson's rule. Some factors which possibly affect numerical accuracy are examined. Examples for finite plane and circular layer are analysed with reference to parameters for printing press roller contact, in which results are obtained for the indentation, film thickness and liquid pressure, as well as internal stresses through the simultaneous solution of the elasticity and hydrodynamic equations. The results show that high precision is easily achieved and the method is efficient for such layered problems.
    Additional Material: 10 Ill.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 2575-2591 
    ISSN: 0029-5981
    Keywords: finite element method ; numerical analysis ; numerical method ; groundwater modelling ; subsurface modelling ; groundwater pollution modelling ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Real world ground water pollution modelling deals with solute transport through anisotropic, heterogeneous media. The applicability of analytical solutions for such a real world system is extremely limited. As an effective tool, numerical models, such as finite difference and finite element methods, are usually employed to model field scenarios. Nevertheless, ground water pollution modelling is a hallenging task and frequently ends up with misleading results. Most of the time insufficient data are blamed for such erratic results. A recent investigation shows that the shortcomings of numerical formulations may be the major cause for many disputes and confusions in numerical analyses. In reality, a point injection of water in a static, homogeneous and isotropic groundwater system shows a radial dissipation of water forming a sphere; and a full-depth line injection shows a radial dissipation forming a cylinder. The finite difference method completely ignores this fundamental flow principles and allows water only to flow along orthogonal directions. To overcome this limitation, the finite element method was developed as a flexible approach in order to connect a node with the neighbouring nodes in various directions where water is assumed to flow in any directions along node connections. In a recent investigation, it has been found that the conventional finite element method does not keep the commitments; and its formulation techniques lead to a global matrix where a solution domain is not connected with all the neighbouring nodes and does not comply with the control-volume mass balance concept. A consistent finite element formulation approach which does not need imaginary mathematical formulation and overcomes the limitations of both the conventional finite difference and finite element methods has been developed. This method allows fluid flow and solute transport in a porous medium in radial directions. The global matrices for flow and transport obtained from this technique are field representative, diagonally dominant and easily convergent. The new method is robust, needs less mathematical computation and has many advantages over the conventional finite difference and finite element methods.
    Additional Material: 6 Ill.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 2647-2671 
    ISSN: 0029-5981
    Keywords: hierarchic models ; laminated composites ; stress-based formulation ; complementary energy ; finite element method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A hierarchic sequence of equilibrium models in terms of stresses assumed to be not a priori symmetric is derived for cylindrical bending of laminated composites, using first-order stress functions. The stress field of each hierarchic model satisfies a priori (i) the translational equilibrium equations and the stress boundary conditions of two-dimensional elasticity, and (ii) the continuity requirement for the transverse shear and normal stresses at the lamina interfaces. The levels of hierarchy correspond to the degree to which the two first-order compatibility equations and the rotational equilibrium equation of two-dimensional elasticity are satisfied. The numerical solution is based on Fraeijs de Veubeke's dual mixed variational principle, employing the p-version of the finite element method. The number of degrees of freedom is independent of the number of the layers in the laminate. Results are obtained directly for the stresses and rotations; the displacement field is obtained in the post-processing phase by integration. Numerical results with comparisons show the capability of the mathematical and numerical models proposed.
    Additional Material: 14 Ill.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 2695-2723 
    ISSN: 0029-5981
    Keywords: virtual work ; a priori unknown large and rapid rigid-body motion ; non-linear strain measure ; large deflections and rotations ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This study presents a transient non-linear finite element analysis within the realm of a multibody dynamics formalism. The governing equations are derived using the concept of virtual work. Unlike others, this analysis includes the non-linear strain measure and rotation explicitly in order to capture the correct dynamic stiffening in anisotropic shells. The finite element analysis invokes the co-rotational form of the updated Lagrangian formulation and utilizes a flat shell element.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 2769-2787 
    ISSN: 0029-5981
    Keywords: free-surface wave ; boundary element method ; r-method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An adaptive meshing based on the r-method is developed for two-dimensional unsteady non-linear flows with a free surface. Coupling of a boundary element equation and a weighted residual formulation of the pressure equation on the free surface is employed in solving the wave problems. A mesh optimization scheme is constructed for these two matrix equations. The final mesh distribution on the free surface is determined from the weighted average of these two adaptive meshes. Through numerical analyses of a non-linear sloshing problem and solitary waves in a tank, the influence of time interval of the remeshing and the weight factor for two adaptive meshes on the accuracy and efficiency of the proposed approach is investigated.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 2743-2767 
    ISSN: 0029-5981
    Keywords: structural mechanics ; voxel conversion ; largeFEM applications ; iterative solving ; element-by-element ; row-by-row ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: FE-models for structural solid mechanics analyses can be readily generated from computer images via a ‘voxel conversion’ method, whereby voxels in a two- or three-dimensional computer image are directly translated to elements in a FE-model. The fact that all elements thus generated are the same creates the possibilities for fast solution algorithms that can compensate for a large number of elements. The solving methods described in this paper are based on an iterative solving algorithm in combination with a unique-element Element-by-Element (EBE) or with a newly developed Row-by-Row (RBR) matrix-vector multiplication strategy. With these methods it is possible to solve FE-models on the order of 105 3-D brick elements on a workstation and on the order of 106 elements on a Cray computer.The methods are demonstrated for the Boussinesq problem and for FE-models that represent a porous trabecular bone structure. The results show that the RBR method can be 3.2 times faster than the EBE method. It was concluded that the voxel conversion method in combination with these solving methods not only provides a powerful tool to analyse structures that can not be analysed in another way, but also that this approach can be competitive with traditional meshing and solving techniques.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 2789-2802 
    ISSN: 0029-5981
    Keywords: finite elements ; three-dimensional elasticity ; equilibrium formulations ; hybrid finite elements ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper an approach to the formulation of equilibrium elements for the analysis of three-dimensional elasticity problems is presented.This formulation is an extension of the approach previously proposed for the analysis of two-dimensional elasticity problems. The general aspects of the formulation remain unchanged when applied to the new problem, but new points are considered, namely the way to perform volume integrations for general elements and the techniques used to obtain the self-equilibrated three-dimensional stress approximation functions.The numerical behaviour of such elements is presented and discussed.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 2821-2835 
    ISSN: 0029-5981
    Keywords: asymptotic solution ; natural frequency ; solid vibration ; finite element analysis ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In order to assess the discretization error of a finite element solution, asymptotic solutions for predicted natural frequencies of two-dimensional elastic solid vibration problems in the finite element analysis are presented in this paper. Since the asymptotic solution is more accurate than the original finite element solution, it can be viewed as an alternative solution against which the original finite element solution can be compared. Consequently, the discretization error of the finite element solution can be evaluated. Due to the existence of two kinds of two-dimensional problems in engineering practice, both the plane stress problem and the plane strain problem have been considered and the corresponding asymptotic formulae for predicted natural frequencies of two-dimensional solids by the finite element method have been derived from the fact that a discretized finite element system approaches a continuous one if the finite element size approaches zero. It has been demonstrated, from the related numerical results of three examples, that the present asymptotic solution, which can be obtained by simply using the corresponding formula without any further finite element calculation, is indeed more accurate than the original finite element solution so that it can be considered as a kind of corrected solution for the discretization error estimation of a finite element solution.
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  • 295
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    International Journal for Numerical Methods in Engineering 39 (1996) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 296
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 2863-2864 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 2865-2887 
    ISSN: 0029-5981
    Keywords: variable-order ; spectral element method ; localp-refinement ; incompressible viscous flow ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new variable-order spectral element scheme is proposed in this work for the numerical solution of the steady incompressible Navier-Stokes equations in primitive variables. The spectral orders of polynomial expansion in each spatial direction for each element are specified by the user in advance. Next, an interface-nodes-replacement procedure is initialized to recover the conformity of the mesh. The interpolation functions are modified to accommodate the new sets of nodes. The present formulation does not require any interface iteration scheme; in addition, any complicated data structure is also avoided. Implementation of this strategy toward the existing spectral element framework is direct and simple. Additionally, the performance of the method is examined by many numerical experiments. Improved flexibility and efficiency of the accurate spectral element method make it a highly promising candidate for solving practical fluid dynamics problems.
    Additional Material: 12 Ill.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 2907-2920 
    ISSN: 0029-5981
    Keywords: sensitivity analysis ; error estimates ; mesh refinement ; hypersingular integrals ; boundary element method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The subject of this paper is the sensitivity analysis of approximate boundary element solutions with respect to the positions of the collocation points. The direct differentiation approach is considered here and the analysis is performed analytically. Since only the collocation points are perturbed, the shape of the body and the corresponding discretization remain unaltered. This aspect makes the present work quite different in spirit with respect to earlier analyses on shape sensitivities. Sensitivities of approximate BEM solutions with respect to the positions of collocation points are shown to be related to the residual of hypersingular integral equations. Numerical results confirm that the present approach can be seen as the analytical counterpart of an adaptive scheme for mesh refinement presented by the same author in some recent papers. Some other advantages of the present approach over the former one are also outlined.
    Additional Material: 9 Ill.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 2921-2944 
    ISSN: 0029-5981
    Keywords: wavelet orthogonal bases ; wavelet-Galerkin method ; Burgers' equation ; numerical method ; approximation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes exact evaluations of various finite integrals whose integrands involve products of Daubechies' compactly supported wavelets and their derivatives and/or integrals. These finite integrals play an essential role in the wavelet-Galerkin approximation of differential or integral equations on a bounded interval.
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    International Journal for Numerical Methods in Engineering 39 (1996), S. 2945-2971 
    ISSN: 0029-5981
    Keywords: object oriented framework ; interactive numerical analysis ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A simple object-oriented framework is presented for computer programs which require interactive numerical analysis in a Graphical User Interface environment. The work attempts to bridge the current gap between purely analytical programs and interactive programs developed solely for graphics. Our proposed scheme is based on user interaction through a three-dimensional view, a menu system, a control bar, a tool box and a status bar. Displayed objects are derived from a common parent object class Element, while objects encapsulating user interactions are derived from a common parent class Tool. A class Framework holds Element and Tool objects, as well as a view object, a control bar object, a tool box object and a status bar object. Examples involving interactive finite element beam analysis and interactive finite difference bearing pressure analysis are given. The paper argues that programming interactive analyses need not be difficult if an object-oriented approach is adopted.
    Additional Material: 17 Ill.
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