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  • 1993  (629)
  • Engineering General  (629)
  • 101
    Electronic Resource
    Electronic Resource
    Neural networks for computing in structural analysis: Methods and prospects of applicationsCertain results of this paper were obtained in the framework of a STRIDE-programme of the EEC concerning the ‘applications of the neural networks in engineering and medicine’, The programme, for which the second author is the scientific co-ordinator, takes place in the Aristotle University of Thessaloniki and the Democritus University of Xanthi in Greece. (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 2305-2318 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A neural network model is proposed and studied for the treatment of structural analysis problems. Both the cases of bilateral and unilateral constraints are considered and Hopfield-like neural models are proposed. Moreover, new results, generalizing the results of Hopfield and Tank,10 are obtained.Numerical applications illustrate the theory and show clearly the advantages of the neural network approach. Finally, the parameter identification problem is formulated and solved as a ‘learning’ problem for a neural network.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620361310
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  • 102
    Electronic Resource
    Electronic Resource
    Adaptively shifted integration technique for finite element collapse analysis of framed structures (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 2323-2339 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The present study is concerned with the improvement of the previously proposed ‘shifted integration technique’ for the plastic collapse analysis of framed structures using the linear Timoshenko beam element or the cubic beam element based on the Bernoulli-Euler hypothesis. In the newly proposed ‘adaptively shifted integration technique’, the numerical integration points for the evaluation of the stiffness matrices are automatically shifted immediately after. the occurrence of plastic hinges according to the previously established relations between the locations of numerical integration points and those of plastic hinges. By using the adaptively shifted integration technique, sufficiently accurate solutions can be obtained in the non-linear frame analysis by two-linear-element or only one-cubic-element idealization for each structural member. The present technique can easily be implemented in the existing finite element codes utilizing the linear or the cubic beam element.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620361402
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  • 103
    Electronic Resource
    Electronic Resource
    A Hermite interpolation algorithm for hypersingular boundary integrals (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 2357-2367 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a conforming C1 boundary integral algorithm based on Hermite interpolation. This work is motivated by the requirement that the surface function multiplying a hypersingular kernel be differentiable at the collocation nodes. The unknown surface derivatives utilized by the Hermite approximation are determined, consistent with other boundary values, by writing a tangential hypersingular equation. Hypersingular equations are primarily invoked for solving crack problems, and the focus herein is on developing a suitable approximation for this geometry. Test calculations for the Laplace equation in two dimensions indicate that the algorithm is a promising technique for three-dimensional problems.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620361404
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  • 104
    Electronic Resource
    Electronic Resource
    Fundamental frequency analysis of laminated rectangular plates by differential quadrature method (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 2341-2356 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper a differential quadrature method is presented for computation of the fundamental frequency of a thin laminated rectangular plate. The partial differential equations of motion for free vibration are solved for the boundary conditions by approximating them by substituting weighted polynomials functions for the differential operator. By doing this, the coupled partial differential equations of motion are reduced to sets of homogeneous algebraic equations. These sets of homogeneous algebraic equations are combined to give a set of general eigenvalue equations for the problem. Three types of laminated plate problems, which include symmetric, antisymmetric cross-ply, and symmetric, balanced angle-ply laminates, are analysed by the method and the results obtained are compared with solutions reported in the literature for other numerical methods. The effects of the level of discretization on the accuracy and rate of convergence of the results are also discussed. The method presented gives accurate results and is found to use not much computer time.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620361403
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  • 105
    Electronic Resource
    Electronic Resource
    Numerical simulation of ultrasonic transmission through curved interface (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 2369-2393 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The direct boundary integral equation formalism is used to model reflected and transmitted wave fields due to a bounded ultrasonic beam incident upon an arbitrarily curved interface separating a fluid and a solid media. The numerical procedure involves application of point collocation with quadratic isoparametric approximation that reduce the integral equations to a discrete set of linear algebraic equations. Numerical results are provided for plane, concave and convex interfaces for incident beam profiles which are Gaussian or approximately rectangular. The case of surface wave excitation on a plane interface is considered and features of their numerical solution are discussed. Constraints on the various parameters of the numerical model and their effects on the accuracy of the solution are investigated in detail.
    Additional Material: 24 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620361405
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  • 106
    Electronic Resource
    Electronic Resource
    A numerical investigation of the effect of boundary motion on viscous channel flow (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 2395-2413 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The steady, laminar, incompressible flow past a moving boundary in the entry region of a two-dimensional channel is considered in this study. The formation of a separated region during the upstream motion of a section of the lower boundary is of particular interest. The size of the separated region depends on the Reynolds number, and on the velocity and length of the moving boundary as well. A numerical solution is obtained from the continuity and the complete Navier-Stokes equations, subject to the appropriate boundary conditions. The describing equations are expressed in terms of the vorticity and the stream function. The alternating-direction implicit method is used to solve the vorticity equation while the successive over-relaxation method is used to solve, the stream function equation. The present numerical scheme is second-order-accurate since both the finite-difference equations and boundary conditions have second-order accuracy.
    Additional Material: 20 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620361406
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  • 107
    Electronic Resource
    Electronic Resource
    A boundary element analysis of metal matrix composite materials (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 2415-2433 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The numerical modelling of metal matrix composites is an important part of the research now being conducted on these materials. Due to the numerical complexity of a fully three-dimensional analysis, two-dimensional approximations are normally used with finite element methods. While these analyses are informative, they cannot treat complex particle shapes or examine three-dimensional effects in the composite. The use of boundary element methods in place of the more widely used finite element methods significantly reduces the computing power necessary to obtain a solution to a given problem, making it possible to simulate fully three-dimensional geometries. In the present paper a two-dimensional form of the BEM is applied to the study of metal matrix composite materials, and its performance compared with that of similar FEM stadies. We also compare the predicted composite properties with existing and new experimental results. We conclude that the BEM is an effective tool for the analysis of this class of problems.
    Additional Material: 15 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620361407
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  • 108
    Electronic Resource
    Electronic Resource
    Shape optimization using adaptive shape refinement (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 2435-2451 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A large part of the computational effort in shape optimization problems is expended in the numerical computation of the gradients for sensitivity information. This effort increases dramatically with an increase in the number of variables used to represent the shape. An adaptation of the gradient projection algorithm for shape optimization problems is described here along with a method to reduce the intermediate size of the optimization problem by allowing adaptive refinement of the shape. The method is demonstrated with a simple representative test case.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620361408
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  • 109
    Electronic Resource
    Electronic Resource
    A novel isoparametric finite element displacement formulation for axisymmetric analysis of nearly incompressible materials (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 2453-2472 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: It is well accepted that severe numerical difficulties arise when using the conventional displacement method to analyse incompressible or nearly incompressible solids. These effects are caused by the kinematic constraints imposed on the nodal velocities by the constant volume condition. In elastic-plastic analysis, these effects are due to a conflict between the plastic flow rule and the finite element discretization. Although several methods have been proposed to cope with this problem, none has been based on the appropriate choice of displacement interpolation functions to minimize the constraints. The theoretical formulation of a new six-noded isoparametric displacement finite element, which is well suited for elastic-plastic analysis of axisymmetric constrained solids by using a rational displacement interpolation function, is presented in this paper. The proposed displacement interpolation function implies that the displacement in the axial direction and the product of the displacement in the radial direction and the radius should be treated as two independent basic variables. Alternatively, the proposed displacement interpolation function can also be implemented in a conventional displacement formulation simply by using a modified shape function matrix. The suitability of the proposed formulations is first studied theoretically by assessing the number of degrees of freedom per constraint and then verified by performing numerical experiments on typical boundary value problems which involve incompressible behaviour.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620361409
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  • 110
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    Conference diary (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 2501-2501 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620361411
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  • 111
    Electronic Resource
    Electronic Resource
    Masthead (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993) 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620361501
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  • 112
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    Electronic Resource
    Application of singular quadratic distorted isoparametric elements in linear fracture mechanics (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 2473-2499 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The understanding of the performance of the quarter-point and transition elements is of considerable importance as these singular elements are widely used in linear elastic fracture mechanics (LEFM) analyses. However, a number of issues remain unresolved although numerous investigations into their performance have been conducted. In particular is the question of optimum quarter-point element and transition element size. This study examines several aspects in relation to the size effect by performing a large number of numerical analyses on several standard problems. Interpretation of the numerical results was aided by the use of two concepts, the ‘zones of dominance’ and ‘zones of representation’. This study proposes a means of explaining the errors in stress intensity factor computation through the interaction between both types of zones. Consequently, a number of new and significant observations were made regarding the singular elements' performance. This study concludes with some recommendations for the application of these elements.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620361410
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  • 113
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    Electronic Resource
    Exact integration of constitutive equations in elasto-plasticity (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 2525-2544 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A unified approach is presented for establishing exact integration of the constitutive equations in elastoplasticity, assuming the total strain-rate direction to be constant. This unified approach includes all previous exact integration procedures as special cases and, in addition, some new closed-form solutions are derived for combined kinematic and isotropic hardening. Special emphasis is laid on combined kinematic and isotropic hardening for von Mises' material and on isotropic hardening for Mohr-Coulomb and Tresca materials.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620361503
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  • 114
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    Electronic Resource
    Performance of the h-p version of the finite element method with various elements (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 2503-2523 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper addresses the performance of square elements of type Q(p) and Q′(p). (Q(p) and Q′(p) are elements of degree p, analogous to the well-known 9- and 8-noded elements for p = 2.) The performance is analysed theoretically for the class of analytic functions. Numerical experiments confirm the conclusions drawn from the theory. The computational complexity of a solution algorithm is studied using timings of the computation on an Alliant FX/8 computer. The data show that high-order elements are very effective for the considered class of solutions.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620361502
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  • 115
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    Electronic Resource
    A two-dimensional frost-heave model for buried pipelines (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 2545-2566 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The rigid-ice model of frost heave is one of the most comprehensive frost-heave models but is restricted to one-dimensional cases in its present form. In this paper, the model is extended to two-dimensional problems. The complete formulation of the partial differential equations governing heat, moisture and ice transport in freezing soils is provided. The equations are subsequently solved using the Galerkin finite element method in space and the finite difference method in time. A computer program is developed for the two-dimensional rigid-ice model. A case of freezing around chilled gas pipeline is solved and the numerical results are compared with experimental values, with good agreement between the two sets of results.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620361504
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  • 116
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    Electronic Resource
    Quickly convergent integration methods for plane stress plasticity (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 293-305 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Explicit finite-element programs, such as DYNA3D, are frequently used to solve large structural problems, such as automobile impacts, that involve tens of thousands of shell elements. Since the explicit finite-element programs do not use a stiffness matrix, the major cost of the calculation is the evaluation of the force vector. A significant part of that cost is the evaluation of the constitutive models. The standard algorithm for integrating J2 plasticity at the stress points is the radial return method. An iterative variation of radial return is commonly used to impose the zero normal stress condition within the shell elements. In this paper we explore several different non-iterative methods that impose the zero normal stress condition in an approximate manner. We show that the cost of the constitutive evaluation can be reduced by 25 per cent without introducing significant errors.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090403
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  • 117
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    Electronic Resource
    On bicubic transformation for the numerical evaluation of Cauchy principal value integrals (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 307-311 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Recently a bicubic transformation was introduced to numerically compute the Cauchy principal value (CPV) integrals. Numerical results show that this new method converges faster than the conventional Gauss-Legendre quadrature rule when the integrand contains different types of singularity. Assume η is the singular point of a CPV integral. The point η divides the interval [-1, 1] into two parts: [-1, η] and [η, 1]. The bicubic transformation maps the intervals [-1, η] and [η, 1] to the interval [-1, 1] with the following constraints: it maps the point η - ∊ to μn, and η + ∊ to -μn, where μn is the largest Gaussian point of an n-point Gauss-Legendre quadrature rule, and ∊ is a user-supplied constant. The n-point Gauss-Legendre quadruture rule is then applied. In contrast to ordinary expectation, further numerical experiment shows that smaller ∊ does not always produce better results. In this paper we are concerned with the selection of ∊ to yield rapid convergence of numerical integration when the bicubic transformation method is applied.
    Additional Material: 3 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090404
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  • 118
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    Suitability of three-dimensional finite elements for modelling material incompressibility using exact integration (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 313-329 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper examines the suitability of three-dimensional finite elements to model accurately problems involving material incompressibility, using the displacement finite element method and exact numerical integration. The previously used method for classification of element suitability is presented and extended to the three-dimensional case. However, an alternative approach for examining suitability, quantified in terms of free degrees of freedom (equal to the degrees of freedom minus the incompressibility constraints), is introduced. This is used to examine Lagrangian cubic, serendipity cubic and tetrahedral three-dimensional elements configured in a regular cubic arrangement. The findings of this paper are substantiated by a number of three-dimensional numerical experiments and comparison with a separate two-dimensional study.All serendipity cubic elements are found to be unsuitable. The linear strain tetrahedron is on the borderline of suitability in a 6-tetrahedra-per-cube arrangement, and is thought to be only suitable if the mesh boundary nodes are not over-constrained. The same element in a 5-tetrahedra-per-cube arrangement, and higher order tetrahedra (quadratic strain etc), are suitable. The Lagrangian cube elements of higher order than the 27-node cube are suitable, but are probably not as efficient computationally as the tetrahedral elements of the same order.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090405
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  • 119
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    On the accuracy of time-stepping schemes for dynamic problems with negative stiffness (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 131-137 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper examines the behaviour of various time-stepping schemes used in structural dynamic analysis when applied to models with negative stiffness. It is found that under such circumstances the accuracy of the numerical solution is greatly affected by the choice of integration parameters of the scheme. Optimal parameters for the Newmark family and the SS32 family have been investigated.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090206
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  • 120
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    A comparison of TVD Lax-Wendroff methods (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 147-155 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper compares two formulations of Lax-Wendroff TVD methods. The basis of comparison is to the results of several test problems providing both qualitative and quantitative results. Results show that using an upwind biased limiter provides higher resolution of both smooth and discontinuous solutions from a lower amount of induced numerical viscosity. The conclusion is that a limiter should have as small a support as possible in order to limit its effects if high resolution is the object.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090208
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  • 121
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    Use of a p-version finite-element formulation for compressible lubrication calculations (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 139-145 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: To obtain accurate gas-bearing lifts and moments, finite-difference and conventional finite-element techniques often require excessively large degrees of freedom. In this paper we avoid this problem by solving the compressible gas-bearing solution by the p-version finite-element method. The lubrication finite-element equation is formulated based on the weighted residual approach, and the resulting nonlinear equations are solved iteratively by the Newton-Raphson procedure. To achieve higher-order solutions the formulation utilizes the C0 hierarchical shape functions to describe the element pressure field. A numerical example is included to demonstrate the simplicity of modelling and the rapid convergence characteristics of the present p-formulation. An efficient numerical strategy, which utilizes the most recent polynomial pressure solution available as an estimate for the next higher polynomial level calculations, shows a 50 per cent reduction in the required computational effort for the low-flying Winchester air-bearing slider presented here. When compared against results obtained from conventional h-version finite-element models, the p-formulation yields better accuracy with fewer degrees of freedom required.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090207
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  • 122
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    Generalized conforming quadrilateral plate element by using semi-loof constraints (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 417-426 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A 12-DOF quadrilateral element for plate bending is formulated based on the concept of generalized compatibility and semi-Loof constraints. The element DOFs are defined with the conventional displacements at corner nodes and the semi-Loof constraints are used in the formulation. This element is a generalized conforming one which passes Irons' patch test and can be used to solve problems with complicated boundaries. When overall considerations of simplicity, accuracy and reliability are taken into account, this new element is one of the best 12-DOF quadrilateral plate-bending elements currently available.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090507
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  • 123
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    The Gauss-Laguerre quadrature rule for finite-part integrals (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 439-450 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The classical Gauss-Laguerre quadrature rule for the semi-infinite integration interval [0,∞] is modified and applied to the case of the weight function exp(-x)/x corresponding to finite-part (or, equivalently, hypersingular) integrals. The new set of orthogonal polynomials is constructed and it is seen to consist of linear combinations of the classical Laguerre polynomials with appropriately determined coefficients. The zeros of these modified Laguerre polynomials are seen to be distinct, but one of these lies outside the integration interval. Formulae for the corresponding weights are also given and numerical values and results are presented. The present results generalize the corresponding results for the finite interval [0,1] to semi-infinite intervals and they are applicable to a variety of applied mechanics and related problems, where finite-part integrals appear in a natural way.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090509
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  • 124
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    Conference diary (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 451-453 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090510
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    Perturbation analysis of vibration modes with close frequencies (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 427-438 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper focuses on how parameter changes in a vibration system expressed by a discrete eigenvalue problem affect vibration modes in the special case of closely spaced eigenvalues, i.e. ‘eigenvalue clusters’. For this class of problems, a perturbation analysis is developed that can be used to compute changes in eigenvalues and eigenvectors in response to small parameter changes. The analysis is applied to a 6-degree-of-freedom spring-mass system containing a single pair of closely spaced eigenvalues.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640090508
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  • 126
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    A posteriori error bounds for numerical solutions of regularized compressible flow problems (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 511-523 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We give a posteriori error bounds for numerical solutions of regularized compressible flow problems. To verify the efficiency of our method, numerical experiments are performed.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640090609
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    Iterative method of integral relations scheme for wake flows (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 525-531 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The orthonormal method of integral relations (MIR) is extended to calculate wake flow problems. Two previous difficulties are overcome: (1) the non-constant integral domain is eliminated by introducing a linear transformation in the formulation; (2) the difficulty associated with determining unique orthonormal weighting functions is overcome by an iterative scheme. The new formulation is applied to calculate a wake flow. A high-order solution for N up to 4 is obtained with relative ease.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640090610
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  • 128
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    Multi-level iterative technique and aggregation concept with semi-analytical preconditioning for solving boundary-value problems (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 649-657 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Some iterative multi-level approaches for solving large-scale finite-element elliptic problems are proposed. It is suggested that these approaches be used in combination with an aggregation technique. On the basis of the aggregation concept a new efficient preconditioning procedure in the inner iterative scheme of the algorithm is developed. This procedure is derived from the fundamental solution of a corresponding elliptic problem. The efficiency of the approaches is demonstrated by numerical examples.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640090804
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  • 129
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    Simple curved shear beam elements (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 659-669 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We have developed two curved beam elements with two nodes, CSCC and CSLC, based on Timoshenko's beam theory and the curvilinear co-ordinate system. These curved beam elements have been modified from the conventional strain element, which has been applied only to Euler beam analysis. Therefore they do not have any spurious constraints and locking characteristics. They also show rapid and stable convergence on the wide ranges of beam length to height ratio for linear and non-linear analyses.
    Additional Material: 12 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640090805
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  • 130
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    Explicit formulas for correcting finite-element predictions of natural frequencies (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 671-680 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Explicit formulas for correcting finite-element predictions of natural frequencies are presented for longitudinal, torsional and bending vibrations of beams. By employing these simple explicit formulas the finite-element discretization error in the natural frequency predictions can be effectively reduced at almost no computational cost. For longitudinal and torsional vibrations the frequency correction always yields the exact solution, while for the bending vibration it gives a significant improvement over the uncorrected frequencies. This method is also applied to two- and three-dimensional frames, and it is found that the errors in the original finite-element predictions of natural frequencies are reduced by about 50 per cent after such a correction.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090806
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  • 131
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    Some aspects in the calculation of transverse shear stresses in Mindlin plates (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 681-685 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Calculation of transverse shear stresses in Mindlin plates by the use of the equilibrium equations and the displacement solutions from either finite-strip or finite-element analyses is considered. It is shown that at least quadratic interpolation of displacements should be used for this purpose. Also, a difference in the shear stress distributions obtainable across the plate thickness under linear and geometrically nonlinear analyses is explained.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640090807
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  • 132
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    Editorial (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. i 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090102
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  • 133
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    A new plate shell element of 16 nodes and 40 degrees of freedom by relative displacement method (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 15-20 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An isoparametric plate shell element of 16 nodes and 40 degrees of freedom is developed in this paper directly from 3-D elastic theories. In order to overcome the difficulties caused by straightforward use of a 3-D formulation, the relative displacement method is introduced. For curved shell elements, the use of the orthogonal curvilinear co-ordinate system greatly reduces the computer effort. The new element can conveniently solve shell problems with variable thicknesses and also easily link with other finite elements using displacement d.o.f. such as 8-node to 21-node 3-D elements. Numerical examples demonstrate the efficiency of the element.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090105
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  • 134
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    Performance of a Hermitian element for a beam with rotational constraints (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 27-34 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The behaviour of a Hermitian two-node element based on the Bernoulli beam equation is examined. The assumed constraints generate rotation-dependent distributed moments. It is shown that for these moments a potential exists, and that a rigid translation is the only rigid body mode of the element. The analysis of the Bernoulli equation demonstrates that very large values of α= e/EI enforce the condition w,x = 0, resulting in displacements equal to zero. The element is examined for two types of constraints. The first type of constraint, diminishing rotations of a beam (α 〈 0), yields regular solutions which, however, seem to have a non-differentiality near the end of the beam. A special procedure is developed to evaluate analytical solutions for long beams or stiff constraints, for which computer accuracy is exceeded. For the second type of constraint, enlarging rotations of a beam (α 〉 0), a highly oscillatory nature of the solution is proven.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640090107
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  • 135
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    Perturbation based on boundary-element technique in structural vibration analysis (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 45-52 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper, based on the boundary-element technique, presents a perturbation method which can be applied to reanalysis of the eigenvalues and eigenvectors in an elastic structure. Regarding the shape changes of a structure as the perturbation of its surface nodes within the neighbourhood of the given values, this method uses the perturbation formula to obtain the eigensolutions of the modified system without solving the generalized eigenvalue problem. Finally, the authors give some sample examples to demonstrate the validity of the method.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640090109
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    A numerical method for predicting the motion of a bubble close to a moving rigid structure (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 81-86 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090112
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  • 137
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    Modified Lanczos method for solving large sparse linear systems (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 67-79 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Generalized conjugate gradient methods are often used to solve large sparse non-symmetric linear systems. Such systems often arise in the numerical solution of convection-diffusion problems. The Lanczos/Orthodir method proposed by Jea and Young suffers the roundoff error problem. In this paper a modified Lanczos/Orthodir method is considered. The modifications are based on Paige's computational procedure and on the adaptive restarting procedure. Numerical results showed that the modified Lanczos/Orthodir method is more stable than the original version. Furthermore, with the adaptive restarting scheme the method performed much better than the Lanczos/Orthomin method.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090111
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    Masthead (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993) 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090201
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  • 139
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    A boundary-element method for the solution of a class of time-dependent problems for inhomogeneous media (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 111-119 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A boundary-element method is derived for determining the anti-plane displacement and stress in an inhomogeneous elastic material subjected to a time-dependent load.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640090204
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  • 140
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    The application of a numerical model of heat and mass transfer in unsaturated soil to the simulation of laboratory-based experiments (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 91-102 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical model of coupled heat and mass transfer in unsaturated soil, recently proposed by the authors, is used to simulate a laboratory-based experimental test. The modelling approach adopted is based on the use of the capillary potential and the temperature as independent variables. The experimental results have recently been presented in the literature by other workers. Very good correlations are obtained of both steady-state values of variables and the times required to reach steady-state conditions. The results achieved lend confidence to the numerical modelling approach proposed and extend the range of applications of the model hitherto achieved to that of a further generic soil type, namely a silt.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640090202
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  • 141
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    Adaptive mesh generation and transformation of triangular to quadrilateral meshes (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 121-129 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper an algorithm for generating pure triangular or pure quadrilateral meshes for arbitrary polygonal domains is presented. The first part shows a triangulation procedure being as suitable for local mesh refinement as for local mesh coarsening. In the second part an algorithm for transformation of triangular grids to quadrilateral meshes of the same relative mesh density is introduced. Two simple strategies are shown which can easily be implemented into any existing triangulation algorithm.
    Additional Material: 15 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640090205
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  • 142
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    Incorporation of strain-hardening in the implicit elasto-viscoplasticity algorithm (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 331-336 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An algorithm is presented for the inclusion of general strain-hardening/softening behaviour into the direct method of finite-element analysis of elasto-viscoplasticity using implicit time discretization.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090406
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  • 143
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    Evaluation of field singularities by an iterative boundary-element method (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 337-343 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical method is presented for the evaluation of field singularities of the type (1/r1-λ) using iterative solutions of standard boundary-element analyses in a region surrounding the origin of singularity. Results for λ are presented for both two and three-dimensional problems, and representative asymptotic fields for these examples are discussed.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090407
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  • 144
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    Variational validation of a membrane finite element with drilling rotations (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 345-351 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: It is shown that a triangular membrane finite element with vertex ‘drilling rotations’ which was developed in earlier publications is, in fact, a correct implementation of a variational principle. The existence of a variational principle is a crucial factor which places the earlier work on a secure theoretical foundation. It implies superior computational characteristics of the finite-element equations and provides valuable guidance on practical issues such as the consistent treatment of boundary conditions.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090408
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    Conference diary (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 361-363 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090410
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  • 146
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    Masthead (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993) 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090501
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    An algorithm for the numerical inversion of a tridiagonal matrix (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 353-359 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents an algorithm for obtaining the inverse of a tridiagonal matrix numerically. The algorithm does not require diagonal dominance in the matrix and is also computationally efficient.
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090409
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  • 148
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    Completed Richardson extrapolation (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 365-374 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The Richardson extrapolation method, which produces a 4th-order-accurate solution on a subgrid by combining 2nd-order solutions on the fine grid and the subgrid, is ‘completed’ - in the sense that a higher-order-accurate solution is produced on all the fine grid points.
    Additional Material: 4 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090502
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  • 149
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    Stream function vorticity solution using high-p element-by-element techniques (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 387-395 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A p-type finite-element scheme is introduced for Navier-Stokes problems in a fully coupled stream function/vorticity formulation. The resulting coupled non-linear system is solved using a Newton iteration with incremental continuation in the Reynold's number. A biconjugate gradient (BCG) scheme in an element-by-element setting is applied to solve the linearized system at each Newton iteration. Pseudo-element block preconditioners produce a practical PBCG method, even for ill-conditioned systems arising from high-p elements in the case of Stokes flow. The problem at higher Reynolds numbers further limits p.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640090504
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  • 150
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    A choice of interpolation schemes for the boundary-element method in elastodynamics (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 375-385 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: It is known that the boundary-element coefficient matrices in steady-state elastodynamics are frequency-dependent. For a multifrequency run, the coefficient matrices have to be reformed at each different frequency. This procedure usually involves heavy numerical integration, and hence is very time consuming. In this paper, two interpolation schemes are initially introduced to accelerate the process of matrix reformation without sacrificing the solution accuracy. In the first scheme, the coefficient matrices are first slightly transformed and then interpolated in the frequency domain. In the second scheme, the Green function is interpolated in the spatial domain. Comparison between these two schemes both in terms of accuracy and efficiency is presented. Finally, a hybrid scheme that takes advantage of the best of both interpolation schemes is proposed. Numerical examples are given to demonstrate the three different interpolation schemes.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640090503
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    Masthead (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993) 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090301
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    On a numerical solution of a class of partial differential equations of mixed type, not adding artificial terms (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 181-187 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A relaxation-like method for the numerical solution of a class of partial differential equations of mixed type is presented. The equations of this class have not yet been solved by functional outlines. The numerical method does not add artificial terms to the original equation.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090302
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  • 153
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    Wave distribution in fibre members subjected to kinematic forcing (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 189-196 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper is concerned with the solution of non-linear wave distribution in structural fibre members subjected to dynamic kinematic forcing. The development of reliable and efficient techniques for numerical handling of wave distribution based on the application of combined finite-element and transfer matrix approaches is emphasized. Illustrative numerical solutions are presented.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090303
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    Solution of the advection-diffusion equation using the spline function and finite elements (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 197-206 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper deals with the solution of the one-dimensional advection-diffusion equation. The method of solution is based on the process-splitting technique. The transport equation is split up into the advection part and the diffusion part at every time step. The advection transport equation is solved by a method of characteristics using a spline function for interpolation. This solution approach proves to be very effective because it reduces numerical dispersion and wiggles. The diffusion equation is solved by the standard Galerkin finite-element method. A comparison of calculations with the results of Holly and Preissmann and with analytical solutions demonstrates the great accuracy of the proposed method.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640090304
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    An element error indicator and a related stress-improvement procedure (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 207-217 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A posteriori error indicators for strain energy error in finite-element solutions have recently been shown to be effective. A popular error indicator, usually denoted by η, makes use of ‘error energy’, i.e. strain energy associated with the difference between the conventional element stresses σ and a smoothed stress field constructed from σ. It is intended that η be constructed by summing element contributions and that it be applied at the global level. The present study suggests that an error indicator applicable at the element level can be obtained by combining an element value of η with information about stress gradient and strain energy density. It is also shown how the stress gradient information can be used to obtain more accurate stresses at mesh boundaries.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640090305
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    Masthead (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993) 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090601
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    Validation of finite-element codes for prediction of machining distortions in forgings (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 463-473 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: When a forging is machined to its net shape, unacceptably large distortions can occur if the final part shape is complex. Such distortions can be predicted with the application of the finite-element method. However, numerical errors associated with the finite element technique can render such predictions unreliable. This paper presents benchmark problems for verifying the accuracy of machining distortions predicted by any prospective finite-element code. Also, a comparison between two industry-standard general-purpose codes, ANSYS and ABAQUS, is presented.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640090603
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    The virtual contact loading method for elastic contact problems (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 455-461 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The virtual contact loading method (VCLM), a highly efficient numerical method to solve elastic contact problems, is proposed in this paper. Having applied virtual loads on the possible contact region (PCR) of a structure system, we carried out the usual finite-element calculations only once and made a local iteration analysis in PCR then the contact region (shape and size), contact state (stick, slide or mixed), contact normal and shear stress distributions, and the stress and displacement fields in contact bodies were all obtained simultaneously. This method is very simple and easy to use.The elastic contact problems for cylinder-cylinder are solved in this paper and the results agree well with those in previous work.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640090602
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    Method to determine optimum number of knots for cubic splines (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 483-488 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper a new method has been presented to determine the optimum number of knots for cubic splines. The knot-finding process is based on the numerical integration of the input curve. The number and the location of the knots is determined automatically. The method has been applied to a test case and the performance has been compared with two other existing methods. It is shown that fewer knots are retained for the portions of the curve having small curvature whereas a larger number of knots is retained for highly curved portions. The computer time required by our method depends only upon the number of points in the input curve and does not depend upon the shape of the curve or the desired accuracy.
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640090605
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    Conference diary (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 269-271 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090311
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  • 161
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    Masthead (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993) 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090401
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    Bandwidth reduction of rectangular matrices (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 259-267 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Two graph-theoretical algorithms are developed for bandwidth reduction of rectangular matrices. A K-total graph is defined for a selected cycle basis, generalized cycle basis and cut set basis of a graph. This transforms a simultaneous ordering of the elements of a basis and members of a graph into that of a nodal numbering of its K-total graph.The first algorithm uses the K-total graph and results in banded equilibrium and self-stress matrices. The second employs a nodal ordering algorithm followed by a member ordering process. This algorithm can be used for optimizing the bandwidth of member-cocycle incidence matrices, resulting in banded equilibrium matrices.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640090310
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    A simple local error estimator and an adaptive time-stepping procedure for direct integration method in dynamic analysis (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 273-292 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A simple a posteriori local error estimator for time discretization in structural dynamic analysis is presented. It is derived from the difference of the solutions between an ordinary integration method (the Newmark scheme) and another higher-order one which assumes that the derivatives of accelerations vary linearly within each time step. It may be obtained directly without resolving new equations, so the additional computational cost is small and the implementation is convenient. Furthermore, it is shown that this error estimator may also be obtained by Taylor expansion or by a post-processing technique. Accordingly, an adaptive time-stepping procedure, which automatically adjusts the time-step size so that the local error at each time step is within a prescribed accuracy, is described. Numerical examples, including two single-DOF problems, a two-DOF problem and a multi-DOF model, are presented. The results show that the presented local error estimator is simple, reliable and accurate.
    Additional Material: 9 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640090402
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    Conference diary (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 543-545 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090612
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    Masthead (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993) 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090701
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    Corrective technique for numerical prediction of liquid flow rate in annular flow study (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 533-542 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The computer code FIDAS-3DT, developed by Power Reactor & Nuclear Fuel Development Corporation of Japan, has been used to solve by the finite-difference method an air-water horizontal annular flow problem based on two-phase, three-fluid and two-component velocity modelling. In an attempt to improve the water flow rate results, as compared with those of a reported experiment, several corrections applied to the code are investigated, and the recommended technique is presented.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640090611
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  • 167
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    Numerical solution of regularized long-wave equation (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 579-586 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A combination of the splitting method and the cubic spline technique has been used to solve a non-linear regularized long wave (RLW) equation. The accuracy and the stability of the proposed method are discussed. Then, two numerical examples are solved to illustrate the robustness of the algorithm. The results are in good agreement with the available results.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640090705
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  • 168
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    Iterative solution of the stream function-vorticity equations using a multigrid solver with finite elements (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 587-594 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The solution of the stream function-vorticity equations is developed using a multigrid method to improve efficiency in a finite-element p-method. The equations are discretized using 2-D Lagrange finite elements (linear, quadratic and cubic) and solved in iteratively decoupled form using successive approximation and continuation methods. The comparative performance of several multigrid and direct matrix solvers is investigated with respect to convergence characteristics and time performance on the Cray Y-MP.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640090706
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    Masthead (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993) 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090801
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    Erratum (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. i 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090802
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    Optimum design of composite laminates with STROPT (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 863-871 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The design of a composite laminate involves the determination of layer thicknesses and orientation angles. The problem is posed as the optimum weight (or volume) design of composite laminates which withstand the specified loads without failure. The modified Hill-Mises or Tsai-Wu failure criterion is taken as a constraint, each layer being subjected to this criterion. The design variables considered are the layer thicknesses and orientation angles. Based on the finite-element analysis capability of composite laminates provided by NISA II, a composite laminate optimization procedure has been developed. Nonlinear optimization techniques are used to approach the optimum design of the composite laminates. Efficient design sensitivity analysis procedures are implemented based on the direct differentiation and adjoint variable methods. Example problems illustrate that the program offers an efficient and practical design tool for composite laminates.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640091102
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    A simple time-step control scheme (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 873-881 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A simple automatic time-step control procedure is devised for use in implicit one-step time-integration schemes. First- and second-order semi-discrete systems of equations emanating from finite-element spatial discretization are considered. The varying time-step interval is controlled by the relative distance between the solution in two consecutive time steps, using the solution update formula of the time integrator under consideration. A model problem involving the vibrations of a membrane is used to demonstrate the performance of the scheme.
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640091103
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  • 173
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    Analytic evaluation of singular boundary integrals without CPV (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 909-915 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Boundary integral equations are generally derived by employing a Cauchy Principal Value definition for the singular integral involving the derivative of the Green function. As a consequence, evaluation of this integral requires special attention, and computing the associated ‘solid angle coefficient’ can often pose difficulties. As discussed herein, these problems can be avoided by defining the integral directly, in terms of a limit to the boundary. This approach leads to a straightforward evaluation procedure.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640091107
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  • 174
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    BEM analysis of reduced dynamic stress concentration by multiple holes (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 917-924 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The reduction of stress concentration around a circular hole in a dynamically loaded plate by introducing auxiliary holes around the original hole is studied numerically. The solution of this plane stress problem is carried out in the Laplace transformed domain with the aid of the boundary-element method, and subsequently the time domain response is obtained by numerically inverting the transformed solution. Numerical examples are presented which demonstrate a stress reduction as high as 18 per pent by the introduction of two auxiliary holes in the loading direction for the uniaxial case.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640091108
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    Use of load-dependent vectors for dynamic analysis of large space structures (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 897-908 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Structural models of large space structures have a substantial number of degrees of freedom (DOF) and possess semi-positive-definite stiffness matrices. The paper presents an efficient co-ordinate reduction procedure for structural dynamic analysis of large space structures. The method is based on the superposition of load-dependent Ritz vectors, which are computed in block form using a shifted stiffness matrix. Comparative transient dynamic analyses are performed on a 2803 DOF model of the space station Freedom using the load-dependent method (LDM) and the mode-displacement method (MDM) based on the superposition of eigenvectors. It is shown that the LDM is able to provide convergence of displacements with a small number of vectors. The acceleration response is found to be more sensitive to vector truncation than the displacement response. Error norms based on the representation of the dynamic load by the vector basis are developed to provide an indication of the effect of vector truncation on the structural response.
    Additional Material: 8 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640091106
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    Comparison of strain recovery techniques for the mixed iterative method (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 925-932 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Three strain recovery techniques are investigated in the framework of the mixed iterative method. The need for appropriate strain recovery for low-order elements is shown. The three techniques compared are: C-lumping, strain-smoothing and a new technique called C-splitting. It is shown that the use of C-lumping has negative effects on the convergence of the mixed iterative method. Both strain-smoothing and C-splitting deliver convergent results, but the new technique converges faster.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640091109
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    Incompressible viscoplastic flow analysis using a quadrilateral 2-D element based on mixed interpolation of tensorial components (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 157-164 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the Eulerian description of metal forming operations usually rigid/incompressible viscoplastic material models are used. In this paper a quadrilateral 2-D finite-element formulation for incompressible viscoplastic flow analysis is developed. The element (QMITC) is based on mixed interpolation of tensorial components, and the incompressibility constraint is imposed via the penalty method. It is shown that the resulting element does not lock either in plane strain rate flows or in axisymmetric flows, that the oscillations in the pressure predictions (checkerboard) tend to zero when the mesh is refined and that the solutions for some typical benchmark problems are very accurate.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640090209
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    Conference diary (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 177-179 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090211
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    On perturbation behaviour in non-linear dynamics (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 165-175 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The static bifurcation criterion, i.e. singularity of the tangential stiffness matrix, is discussed in the sense of non-linear dynamics since it is sometimes used in the engineering literature. In this paper the connection between static stability, i.e. that the tangential stiffness matrix is positive-definite, and insensitivity, i.e. local damping of small perturbations, is proved. Since, in general, there is no connection between insensitivity and asymptotic stability, the concept of sensitivity cannot replace the classical stability theory of motion.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640090210
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  • 180
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    Numerical solution of Burger's equation (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 397-406 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the present paper numerical solutions of the one-dimensional Burger equation are obtained. The technique of finitely reproducing non-linearities introduced by Bazley is used. This technique when applied to Burger's equation gives a method where a system of non-linear ordinary differential equations is to be solved. The present method produces very accurate results in comparison to finite-difference of finite-element methods.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640090505
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    An efficient wave input procedure for infinite media (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 407-415 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An efficient wave input procedure in the finite and infinite element coupled model is presented in this paper. Compared to the previous wave input method, the main advantage of the present wave input procedure lies in its computational efficiency because only a small region of the medium needs to be modelled by finite elements. The equivalence between the present wave input procedure and the previous one has been theoretically proven when a harmonic wave propagates vertically in an isotropic homogeneous elastic half-space. In addition, the accuracy of the present wave input method has been evaluated based on the solutions obtained for SH-wave, SV-wave and P-wave scattering problems in a semicircular canyon for which analytical solutions are already available.
    Additional Material: 8 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640090506
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    Balancing domain decomposition (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 233-241 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The Neumann-Neumann algorithm is known to be an efficient domain decomposition preconditioner with unstructured subdomains for iterative solution of finite-element discretizations of difficult problems with strongly discontinuous coefficients (De Roeck and Le Tallec, 1991). However, this algorithm suffers from the need to solve in each iteration an inconsistent singular problem for every subdomain, and its convergence deteriorates with increasing number of subdomains due to the lack of a coarse problem to propagate the error globally. We show that the equilibrium conditions for the singular problems on subdomains lead to a simple and natural construction of a coarse problem. The construction is purely algebraic and applies also to systems such as those that arise in elasticity. A convergence bound independent of the number of subdomains is proved and results of computational tests are reported.
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    URL: http://dx.doi.org/10.1002/cnm.1640090307
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    How to deal with hypersingular integrals in the symmetric BEM (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 219-232 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The symmetric boundary-element method for mixed boundary-value problems is currently gaining increasing interest as it permits the derivation of symmetric matrices. It is even possible to obtain positive-definite finite-element stiffness matrices for BEM subregions, and therefore the method provides a very straightforward coupling to the finite-element method (FEM). The BEM subregions can be handled like FEM substructures in a domain decomposition context. The symmetric BEM uses the full set of integral representations for the 2n types of boundary data for self-adjoint problems of order 2n and solves them in a weighted residual (Galerkin) sense. The main difficulty of the method is caused by the need to compute hypersingular integrals arising from the integral representations of the Neumann boundary data. It is the object of the paper to show that, for 2-D problems on polygonal domains, these hypersingular integrands pose no problem at all, even for higher-order approximations. The present approach makes use of analytical integrations as far as possible. The integrals of the hypersingular expressions are derived completely within the framework of simple engineering mathematics. The problem is reduced to the computation of weakly singular integrals even for C0 continuous approximations.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090306
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    Self-adaptive finite-element simulation of bipolar, strongly reverse-biased pn-junctions (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 243-250 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The potential distribution of bipolar, strongly reverse-biased pn-junctions can be described by a double obstacle problem for the Laplacian. The problem is solved by a self-adaptive finite-element method involving automatic termination criteria for the iterative solver, local error estimation and local mesh refinement. Special attention is paid to the efficient resolution of the geometries typically arising in semiconductor device simulation. The algorithm is applied to a reverse-biased pn-junction with multistep field plate and stop electrode to illustrate its efficiency and reliability.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090308
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  • 185
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    Superconvergent patch recovery techniques - some further tests (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 251-258 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A modification has been introduced to the new superconvergent patch derivative recovery technique recently developed (Zienkiewicz and Zhu, 1991). By use of a locally normalized co-ordinate system, the application of this technique can now be applied to higher-order finite-element shape functions. Numerical studies are carried out for up to 6th-order elements in one dimension and for up to quartic elements in two dimensions, and superconvergent results are obtained for all examples tested.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090309
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  • 186
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    Error study on numerical approximation of radiation boundary condition for one-dimensional wave equation (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 475-482 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The radiation boundary condition is frequently used at the artificial outflow boundary created in the numerical computation of fluid flow problems to allow outgoing waves to leave the domain undisturbed. However, the numerical approximation of the radiation boundary condition will produce errors which will affect the interior solution. In this work the errors due to two different numerical approximations of the radiation boundary condition are studied, with the one-dimensional wave equation being used as the model equation. A theoretical analysis shows that: (a) if the numerical approximation of the boundary condition generates a celerity error, a reflected wave with amplitude proportional to the size of the celerity error is produced; (b) if the numerical approximation of the boundary condition generates a numerical diffusion and hence an amplitude damping error, a reflected wave with amplitude proportional to the magnitude of the numerical diffusion is produced. A modification of the Sommerfeld radiation boundary condition to account for the linear bottom friction effect is investigated. Numerical experiments show that the use of the backward characteristics scheme with quadratic interpolation is able to reduce significantly the reflection of the wave at the outflow boundary and that the scheme is unconditionally stable.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090604
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  • 187
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    Standard eigenvalue analysis by boundary-element method (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 489-495 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method for analysing eigenvalues of the Helmholtz equation using a standard existing subroutine for eigenvalue determination is developed in this paper. It is based on the boundary integral equation formulation known as the multiple reciprocity method (MRM). The above-mentioned formulation, having polynomial matrices in terms of the eigenvalue as the coefficient matrices, is transformed into the standard-type eigenvalue problem. The resulting formulation makes it possible to determine the required eigenvalues only by boundary discretisation without any initial rough estimation.
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090606
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  • 188
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    Flow development in entrance region of ducts (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 503-509 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The integral transform method is used to compute numerically the development of the velocity profile in the hydrodynamic entrance region for laminar flow inside a parallel plate channel. The results have user-prescribed accuracy and can be used to test other numerical methods.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090608
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  • 189
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    Appropriate boundary conditions for FE-modelled elastic half-plane (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 497-501 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The completely adhesive contact between an FE-modelled orthotropic half-plane and a vertically loaded rigid flat punch is studied. Interface normal and shear-stress distributions between the punch and half-plane are FE-calculated and compared for some sets of half-plane boundary conditions frequently used in the literature for contact problems with friction. These results are compared with analytical solutions, and appropriate half-plane boundary conditions are recommended for frictional contact problems.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090607
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  • 190
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    Mesh enrichment against mesh regeneration using quadrilateral elements (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 547-554 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An adaptive refinement procedure using a new automatic quadrilateral element mesh generator is presented. The performance of the adaptive procedure in achieving a given accuracy with different mesh refinement strategies is compared. It is found that when using bilinear or biquadratic quadrilateral elements refinement strategies of both mesh enrichment and mesh regeneration can lead to a prescribed accuracy being achieved by the Zienkiewicz-Zhu adaptive procedure1 with the optimal rate of convergence. However, fewer mesh refinement steps are needed if the strategy of mesh regeneration is employed with the newly developed automatic quadrilateral element mesh generator2.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090702
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  • 191
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    Geometrically based, automatic generator for irregular triangular networks (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 555-566 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The network generation method described herein produces two-dimensional irregular triangular grids in which element area is proportional to some scalar density function defined over the domain. This density function can reflect arbitrarily chosen properties of the geometry or flow. After the initial generation, various adjustment utilities and an interactive (graphic-based) editor ensures that the resultant triangular elements are well shaped. Some of these utilities can be used with adaptive refinement schemes.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090703
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  • 192
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    The construction of nearly orthogonal multiblock grids for compressible flow simulation (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 567-578 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method is described whereby structured multiblock meshes can be constructed from the solution of elliptic partial differential equations and which possess the property of orthogonality close to boundaries and near orthogonality within the domain. To construct grids for viscous flow simulations which have appropriate point distributions close to solid boundaries these grids are used with point redistribution formulations. The result is high-quality grids for use with both inviscid and viscous flow simulation algorithms. Examples using the approach are given, and these include grids for single and multicomponent aerofoils and bluff bodies.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090704
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    Masthead (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993) 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090101
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  • 194
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    Multi-rate numerical methods for diffusion problems (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 1-8 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The one-dimensional diffusion equation is solved using a recent class of multi-rate numerical algorithms collectively referred to as waveform relaxation methods. The methods enable different parts or blocks in the system to take widely different time steps by decoupling the blocks in the time domain. Significant speed-up is obtained over the results using a composite trapezoidal rule/second-order backward Euler time-stepping scheme without blocking. Possible implementation strategies for two-dimensional diffusion are briefly discussed.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090103
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  • 195
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    A note on multiple reciprocity integral formulation for the Helmholtz equation (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 9-13 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The multiple reciprocity method (MRM) is known as a method for elimination of domain integrals appearing in the integral equation in the framework of the direct-type boundary-element formulation. The method employs the fundamental solution of a part of the adjoint operator corresponding to the original differential equation. In this paper we discuss the relation between the conventional integral equation formulation of the Helmholtz equation and that derived by means of the MRM formulation. The latter, formulated in terms of real-valued variables, is proved to be a special case of the general complex-valued formulation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090104
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  • 196
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    Compressible duct flow of a real gas in a Lagrangian frame (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 21-26 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An approximate Riemann solver is presented for the compressible flow equations with a general (convex) equation of state in a duct of variable cross-section and within a Lagrangian frame of reference. The scheme is applied to a well-known shock tube problem.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090106
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  • 197
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    Consistent diagonal mass matrices for the isoparametric 4-node quadrilateral and 8-node hexahedron elements (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 35-43 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Diagonal mass matrices offer computational advantages in many applications. Their general use is confronted, however, with the fact that usual finite-element formulations generate consistent mass matrices. Some methods have been suggested to diagonalize these consistent matrices. These methods are largely founded on an intuitive basis. They abandon the classical way of calculating finite-element matrices. In an attempt to overcome this deficiency, a procedure is presented which enables direct calculation of consistent diagonal mass matrices for the isoparametric 4-node quadrilateral and 8-node hexahedron. This procedure is based on an expansion of the interpolation functions and the selection of an appropriate integration order. It is shown that the consistent diagonal mass and the associated stiffness matrices represent the dynamic structural properties with good accuracy.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090108
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  • 198
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    Generalized conforming triangular elements for plate bending (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 53-65 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Based on the modified principle of potential energy, three triangular thin-plate elements with nine degrees of freedom (LZ1, LZ2 and LZ3) are derived by using compatibility conditions for nodal deflection at each node and generalized compatibility conditions for average deflection and average normal slope along each side of the element. These generalized conforming elements are low-order and high-precision elements which pass the patch test. When overall considerations of accuracy, simplicity and reliability are taken into account, these new elements are the best 9-DOF triangular thin-plate elements currently available.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090110
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  • 199
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    Conference diary (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 87-89 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090113
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  • 200
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    Crack propagation in tooth root with variable loading (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 103-110 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper describes the numerical method for calculating the crack propagation in the tooth root of a case-hardened and hardened gear. The method is based on the linear elastic fracture mechanics taking into account the total values of loadings and properties of the individual layers of the gear material. The main points are the determination of the stress intensity factor and the numerical calculations of the crack propagation, crack speed and path1.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090203
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