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  • 1980-1984  (1,378)
  • Engineering General  (1,377)
  • Nuclear reactions
  • 101
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 4 (1984), S. 1043-1063 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The difficulties experienced in the treatment of hyperbolic systems of equations by the finite element method (or other) spatial discretization procedures are well known. In this paper a temporal discretization precedes the spatial one which in principle is considered along the characteristics to achieve a self adjoint form. By a suitable expansion, the original co-ordinates are preserved and combined with the use of a standard Galerkin process to achieve an accurate discretization. It is shown that the process is equivalent to the Taylor-Galerkin methods of Donea.17Several examples illustrate the accuracy and efficiency attainable in such problems as transport, shallow water equations, transonic flow etc.
    Additional Material: 13 Ill.
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  • 102
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 1131-1151 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Rigid-plastic theory is used to predict the failure load of connections made up of groups of fasteners which are subjected to a force applied in the plane of the connection. The failure mechanism consists of one of the plates making up the connection rotating relative to the other about a point in the plane of the connection. This point may coincide with the position of a fastener in which case it is shown that difficulties arise in the computation. Conditions are given for predicting whether this situation will arise and methods are developed for overcoming these and other difficulties that are encountered in the computation. Two computer programs which were developed to do the calculations are described.
    Additional Material: 14 Ill.
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  • 103
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 1153-1163 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Exact and approximate analytical expressions can be derived for integrals arising in finite element methods, employing isoparametric linear quadrilaterals in two space dimensions with bilinear basis functions. The formulae associated with rectangular elements, arbitrarily oriented in space, can be shown to be a special case. The proposed method provides considerable savings in computational effort, in comparison with a numerical method that employs Gaussian quadrature procedures. In addition, the method, when applied to a quadrilateral inscribable in a circle, can be shown to produce better accuracy than the associated (2 × 2) Gaussian quadrature formulae.
    Additional Material: 2 Ill.
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  • 104
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 297-304 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A non-iterative method is presented for solving a system of algebraic equations forming a banded matrix with each diagonal submatrix being tridiagonal and all other submatrices being diagonal. A recursion relation is assumed between successive elements of the solution vector. This relation is determined by equating a linearly combined form of it with the original set of equations also being linearly combined. The solution vector is determined by back-substitution of elements in the recursion relation. Since the method takes advantage of the banded structure of the matrix, it is more efficient than the conventional methods. A FORTRAN program that incorporates the present method is included.
    Additional Material: 1 Ill.
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  • 105
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 315-319 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Viscoplastic constitutive models typically lead to compliance (strain-stress) relationships, which must be inverted for use in the finite element displacement method. Computational requirements can be increased significantly for models of practical size due to the large number of matrix inversions which are necessary. This paper describes a method of obtaining the required stress-strain relations analytically, thus eliminating the need for numerous matrix inversions in the solution. The technique is applicable to a number of commonly-used viscoplastic models, as demonstrated in the examples.
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  • 106
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 339-351 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Higher order implicit integration techniques for solving dynamic response equations are derived utilizing Padé approximations. In an effort to minimize the disadvantages of using these higher order formulae to obtain solutions to systems with large numbers of degrees-of-freedom, the conjugate gradient method is employed to solve for the displacements. The accuracy and efficiency of the techniques are evaluated by making comparisons between known analytical and calculated results.
    Additional Material: 9 Ill.
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  • 107
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 409-421 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 9 Ill.
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  • 108
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 395-408 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Special quadrature rules are described for elastic finite elements that have rq behaviour (0 〈 q 〈 1) directly induced in natural element co-ordinates. In general, the quadrature points and weights can vary with the exponent q. For two-dimensional problems with a square-root singularity (q = 1/2), the use of special quadrature results in significant improvements over regular Gauss quadrature. The development of special quadrature rules for three-dimensional elements is shown to be a difficult task. Several special case rules are developed and tested for a line-type singular element, and a precise rule is given for a point-type singular element in three dimensions.
    Additional Material: 11 Ill.
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  • 109
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 423-445 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 26 Ill.
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  • 110
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 529-548 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An assumed stress hybrid curvilinear triangular finite element is described which is based upon the Kirchhoff theory of plate bending. The derivation extends the assumed stress hybrid technique to curvilinear boundaries where the twelve connectors are related to those of an equilibrium rectilinear element and to Semiloof. The solution process demands only first derivatives of the shape functions.The element is subjected to various patch tests for constant bending, e.g. where the central element is in close approximation to a circle. All tests are passed for stress couples and vertex displacements, but values of the remaining connectors do not resemble exact results. Patch tests for rigid-body movements are passed exactly in every respect.
    Additional Material: 7 Ill.
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  • 111
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 549-553 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: It is demonstrated that finite element discretizations may not, in general, satisfy the maximum principle; and sufficient conditions are presented to guarantee that solutions based on bilinear elements do satisfy the maximum principle.
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  • 112
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 565-572 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The BEM is shown to be superior to FEM with respect to economy (man hour and data processing) and convergence (with increasing number of boundary nodes) in the elasic notch stress analysis of compact components.
    Additional Material: 6 Ill.
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  • 113
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 114
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 583-587 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Analysis of multi-layer composite laminates using three-dimensional finite element models often results in high computational cost. This communication reports a three-dimensional super-element scheme which can reduce the computational cost.
    Additional Material: 3 Ill.
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  • 115
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 783-786 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 116
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 803-816 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Recursive quadratic programming methods have become popular in the field of mathematical programming owing to their excellent convergence characteristics. There are two recursive quadratic programming methods that have been published in the literature. One is by Han and the other is by Pshenichny, published in 1977 and 1970, respectively. The algorithm of Pshenichny had been undiscovered until now, and is examined here for the first time. It is found that the proof of global convergence by Han requires computing sensitivity coefficients (derivatives) of all constraint functions of the problem at every iteration. This is prohibitively expensive for large-scale applications in optimal design. In contrast, Pshenichny has proved global convergence of his algorithm using only an active-set strategy. This is clearly preferable for large-scale applications. The method of Pshenichny has been coded into a FORTRAN program. Applications of this method to four example problems are presented. The method is found to be very reliable. However, the method is found to be very sensitive to local minima, i.e. it converges to a local minimum nearest to the starting design. Thus, for optimal design problems (which usually possess multiple local minima) it is suggested that Pshenichny's method be used as part of a hybrid method.
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  • 117
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 851-867 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A unified simple 6 degrees-of-freedom beam finite element and the associated computational procedures have been developed for the fast and efficient solution of a wide class of static and dynamic response problems of the beam type with material and/or geometrical nonlinearities.The material nonlinearity is treated by including its effect in the governing equations by forming the stiffness matrix of each element using a two-dimensional grid of Gauss points and using the material properties at each point corresponding to the uniaxial strain at that point. Examples are provided for metal and reinforced concrete beams.A powerful yet straightforward method for the solution of elastica problems of beams and frames, using the beam element developed by the senior author, has been extended for determining the dynamic response of beams undergoing large displacements, including large rotations.The solution procedure involves piecewise linearization of response equations and iterations at each incremental step to achieve equilibrium. The solution procedure is simple and easy to apply. A variety of problems is solved to determine the applicability of the proposed simple formulations. Excellent agreement with existing analytical solutions which employ higher order elements demonstrates the efficiency and versatility of the present simple beam element in nonlinear analysis.
    Additional Material: 10 Ill.
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  • 118
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 1164-1166 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Least square strain smoothing is applied to the popular eight-node serendipity quadrilateral plane stress element. Substitute shape functions, derived from the least squares principle, are provided explicitly for smoothing the strain matrix. It is found that the spurious shear straining modes appearing in the unsmoothed formulation are now completely eliminated. The nodal stress values can thus be computed directly without any smoothed extrapolation from the Gauss-point stresses.
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  • 119
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 1167-1168 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 120
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 1169-1174 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 121
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 1175-1175 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 122
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 1175-1175 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 123
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    International Journal for Numerical Methods in Engineering 20 (1984) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 124
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 125
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 1372-1372 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 126
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 1373-1376 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Formulae are derived for exact inextensional bending solutions for arbitrary quadrilateral shell finite elements of bilinear parametric representation. It is found that the polynomial degree of parametric representation of the rectangular components of displacement requires to be at least cubic in order to describe any inextensional bending modes.
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  • 127
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 1399-1405 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A simply-supported rhombic plate with obtuse angle equal to 150 degrees is analysed by the finite element method, using both the h-version and the newer p-version. Results obtained using the computer code CONE (C1-continuity) for plate bending problems are compared with theoretical predictions and with computational results reported in the literature. If accuracy in terms of the number of degrees-of-freedom is used as a criterion, the solutions presented here are the most efficient that have been published to date.
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  • 128
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 1415-1431 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A computational strategy for the evaluation of delamination stresses in multilayered fibre-reinforced composites is presented. The approach uses special inter-laminar shear elements and an iterative procedure in the calculation of out-of-plane stresses. Both regular and singular elements for the free edge are presented. The solutions are carried on by switching between direct matrix solution methods of small systems of equations and an iterative conjugate gradient method. The proposed discretization avoids ill-conditioning problems, modelling difficulties and large computational cost associated with three-dimensional analysis of delamination of holes, cut-outs, joints and areas of complex stress states.
    Additional Material: 9 Ill.
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  • 129
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 1407-1414 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper describes the development of an eight-node plane rectangular finite dynamic element and presents detailed descriptions of the associated numerical formulation involving the higher order dynamic correction terms pertaining to the related stiffness and inertia matrices. Numerical test results of free vibration analyses are presented in detail for the newly developed eight-node element and also the corresponding four-node element in order to make a clear comparison of the relative efficiencies of the corresponding finite element and dynamic element procedures. Such results indicate a superior pattern of solution convergence of the presently developed dynamic element.
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  • 130
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 1377-1398 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Stiffness matrices for three-dimensional beam elements that include the effect of warping restraint on elastic torsional response have been derived by various investigators. Using one of the available stiffness matrices and assuming that the warping boundary conditions can be specified on a member-by-member basis, an elastic ‘warping’ support is introduced to represent conditions of partial warping restraint at the member ends. The concept of a ‘warping indicator’ is then introduced to facilitate use of warping springs. Following this, static condensation is used to eliminate the restrained warping degrees-of-freedom. The condensed stiffness matrices for the elements can then be assembled to yield a global stiffness matrix. In the global matrix, continuous warping degrees-of-freedom, that is, those internal to a member represented by several elements, are expressed in local co-ordinates. The remainder are expressed in global co-ordinates. In the force recovery phase, it is shown that an ‘indirect’ method yields most accurate results for the bimoment and warping torsion when the twist function is represented by a cubic polynomial. Solutions to examples of linear elastic analysis are compared with well-known analytical solutions to demonstrate the application of the method.
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  • 131
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 1433-1441 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A general, consistent and accurate procedure for obtaining difference equations from differential equations is presented and illustrated by several examples. The procedure is an extension of the integral method and incorporates what is known of the solution to the differential equation in the formation of the corresponding difference equation. For the same accuracy, large increases in grid size over that obtained by standard Taylor's series approximations are possible. Both boundary-value and initial-value problems are treated.
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  • 132
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 1443-1459 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The standard isoparametric transformation for finite element analysis is shown to be only a special case of a more general transformation which allows for flexibility in locating side and interior element nodes. Side nodes positioned at the same relative distance from corner nodes in both local and global space, and interior nodes positioned such that they do not affect the Jacobian of the co-ordinate transformation, provide improved accuracy over nodes positioned locally without regard for the global configuration. This concept is demonstrated in the context of two-dimensional quadratic quadrilateral isoparametrics, but is also applicable to higher orders and dimensions. In the test cases examined, the new formulation provides a reduction in error of up to three orders of magnitude and also provides accurate solutions for nodal placements which are not allowed using the standard transformations.
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  • 133
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 1461-1475 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A weighting function by which the mass matrix is made to be diagonal is deduced on the two-dimensional simplex element. Adopting the weighted residual method with the deduced weighting function for spatial domain and the two-step Lax-Wendroff method for time differentiation, the two-dimensinoal tidal flow in a model basin is calculated by means of the explicit finite element method. The water mass transport integrated over one tidal period at some cross-sections of the basin is also estimated, in order to verify the water mass conservation. It is found that the water mass is nearly conserved in the present method, although the usual lumped mass matrix technique fails to conserve.The present explicit finite element method with the conservative form of governing equations is also investigated and the water mass conservation is found to be a little more improved in this case than in the case of non-conservative forms. Application to a real bay indicates that the method with the conservative form of equations could be used for the estimation of tidal residual flow.
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  • 134
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 1477-1489 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this work, the plastic stress-strain relation and the incremental elastoplastic stiffness matrix for materials obeying the principal stress yield criterion are derived in the context of the associated theory of plasticity. Particular attention is paid to the treatment of the singularity conditions associated with this yield criterion.
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  • 135
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 1491-1506 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: It is demonstrated that the residual in a compatible (displacement) finite element solution can be partitioned into local self-equilibrating systems on each element. An a posteriori error analysis is then based on a complementary approach and examples indicate that the guaranteed upper bound on the energy of the error is preserved.
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  • 136
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 1567-1573 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new method of performing the shakedown analysis of structures subjected to variable repeated loads and temperature fields is presented. The method employs the standard incremental elastic-plastic finite element algorithm and is based upon a cyclic repetition of piecewise-proportional paths that contain all the vertices of the load-temperature variation domain. A numerical example illustrates the approach.
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  • 137
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 1575-1580 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The receptance matrix of a system after a modification of rank k 〈 n to system matrices (of ordern) may be derived from the receptance matrix of the original system by solution of a system of linear equations of order k. In this paper it is shown that it is desirable to impose a much more conservative condition on the system of equations than simple solvability. The possible consequences of breaching this conservative condition are developed and discussed.
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 1581-1597 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A new family of coupled time integration operators of different orders is developed. It permits different time integration operators to be used simultaneously in various regions of the model. This approach has the advantage of applying a very accurate time integrator, such as Runge Kutta method of order two to four, to the local nonlinear region of interest and a simple time integrator, such as the implicit-explicit or mixed time implicit-explicit method of order one, for the remaining region. The computer implementation aspects, stability analysis as well as the numerical evaluations of these new methods are presented. This is another attractive addition to the repertoire of time integration methods.
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 1599-1612 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A local interpolation method for an irregular mesh of nodal points is proposed. The method is based on a Taylor expansion of the unknown function combined with the minimization of errors. Some numerical tests as well as a computer program are presented. Applicability and stability of the method are shown. By the appropirate definition of weighting coefficients, this method may be viewed as an interpolation or approximation in the sense of minimum deviation from given values. Applications in finite element and finite difference methods are shown.
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  • 140
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 1613-1628 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A finite element formulation for elastoviscoplasticity problems in the presence of large strains and deformations is presented in this paper. The formulation is capable of using any of a class of combined creep-plasticity constitutive models with state variables for the description of material behaviour. The specific problem considered is plane strain extrusion using the constitutive model originally proposed by Hart. Numerical results are presented for sample problems and the important effects of extrusion speed and friction (at the die-workpiece interface) on the residual stresses in an extruded sample are investigated. The computer program developed here is quite general and can be modified to solve problems for other manufacturing processes like rolling, sheet forming, etc.
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 1629-1641 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: This paper attempts to answer two commonly raised questions during the preparation of a finite element mesh, for the linear elastic fracture analysis of cracked structure: how to set up the finite element mesh around the crack tip, and what level of accuracy is to be expected from such a modelling.Two test problems, with known analytical expressions for their stress intensity factors, are analysed by the finite element method using the isoparametric quadratic singular element. The modified parameters were the order of integration, aspect ratio, number of elements surrounding the crack tip, use of transition elements, the singular element length over the total crack length, the symmetry of the mesh around the crack tip. Based on these analyses, a data base is created and various plots produced. The results are interpreted, the accuracy evaluated and recommendations drawn.Contrary to previous reports, it is found that the computed stress intensity factor (SIF) remains within engineering accuracy (10 per cent) throughout a large range of l/a (singular element length over crack length) for problems with a uniform non-singular stress distribution ahead of the crack tip (i.e. double edge notch), and l/a should be less than 0·1 for problems with a non-singular stress gradient (i.e three-point bend). Also, it is found that the best results are achieved by using at least four singular elements around the crack tip, with their internal angles around 45 degrees, and a reduced (2 × 2) numerical integration.
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  • 142
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 1643-1660 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new direct search package is presented. Typical test functions solved establish the robustness and efficiency of the package. The most significant features of the package are that it works satisfactorily even in single precision and requires much less memory. It needs only the function values and the unidimensional search is totally dispensed with. Methods such as different descent techniques, the RMS procedure, the co-ordinate movement technique and the gallop-canter equalization scheme form the sequence of strategies.
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 1685-1695 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new method for the formulation of hybrid elements by the Hellinger-Reissner principle is established by expanding the essential terms of the assumed stresses as complete polynomials in the natural coordinates of the element. The equilibrium conditions are imposed in a variational sense through the internal displacements which are also expanded in the natural co-ordinates. The resulting element possesses all the ideal qualities, i.e. it is invariant, it is less sensitive to geometric distortion, it contains a minimum number of stress parameters and it provides accurate stress calculations. For the formulation of a 4-node plane stress element, a small perturbation method is used to determine the equilibrium constraint equations. The element has been proved to be always rank sufficient.
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 1697-1702 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: An inversion formula based on expansion in a Fourier sine series, proposed by Koizumi in 1935, is examined. It is found to give results of moderate accuracy with relatively little work.
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 1745-1749 
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    Notes: Using the partial-boundary element approach, in which only a part of the boundary in problem is discretized, the elastic torsion problem of a prismatic beam of a cracked rectangular cross-section has been solved in this brief paper, together with a numerical example to show the accuracy and versatility of the approach.
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 1751-1755 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The radial symmetry of the cable results in circular finite elements to evaluate the potential distribution in a multi-dielectric cable. Owing to this, a two dimensional analysis used in conjunction with triangular finite elements is reduced to one-dimensional analysis. This method therefore suggests an alternative proposal to calculate the potential distribution in a multi-dielectric cable with better accuracy.
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 1756-1756 
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 1757-1757 
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 2051-2064 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A conceptually simple, general method is described for the finite element simulation of multi-stage construction and excavation processes, including recognition of nonlinear material behaviour. Anomalous results reported in the literature for simulation of excavation of elastic media are examined, and shown to result from the inconsistent determination of nodal excavation forces from element boundary stresses.
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 2065-2075 
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    Notes: A method which combines the finite element technique and the singular-integral equation method is presented. The association of the two methods is obtained with the help of Schwarz's alternating method (SAM). The method was applied with satisfactory results to the solution of a series of problems of a circular arc crack lying inside a finite thin plate for various lengths of the circular arc and for various dimensions of the rectangular cracked sheet.
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 2077-2092 
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    Notes: The nonlinear system of equations and inequalities relating to the large displacement behaviour of elasto-plastic structures can be transformed by the method of perturbations into an infinite sequence of recursive linear complementarity problems (LCP). Each such LCP can be solved by a simple variant of the simplex algorithm of linear programming. Special consideration is given to describing those steps of the algorithm that are needed for detecting and controlling the phenomena of plastic straining, unstressing and branching.
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 2121-2141 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A 48 degrees-of-freedom (d.o.f.) quadrilateral thin elastic shell finite element using variable-order polynomial functions, B-spline functions and rational B-spline functions to model the shell surface is developed. This development may allow the stiffness formulation of the shell element to be linked to the geometry data bases created by computer aided design systems. The displacement functions are that of bicubic Hermitian polynomials. The displacement functions and d.o.f. are expressed and investigated in both the curvilinear and Cartesian forms. The cuivilinear form is simpler and can provide the proper solution for a certain class of shell problems. For certain highly curved shells such as bellows, however, the curvilinear form fails to properly model some rigid body modes even with either the explicit inclusion of rigid body terms or the high order displacement functions. It is suggested in this study that such difficulty can be circumvented and the rigid body modes can be properly included if a Cartesian form is used for displacement functions. The strain-displacement equations are expressed in curvilinear co-ordinates. Thus, the Cartesian displacement functions require a transformation to curvilinear displacement at each numerical integration point. Examples include a pinched cylinder, a translational shell under central load, a uniformly loaded hypar shell, a pressurized ovel shell, a semi-toroidal bellows and a U-shaped bellows. For the first four examples, geometric modellings consist of polynomials of second-order (subparametric), third-order (isoparametric), and fourth and fifth-order (both superparametric) as well as B-spline functions of fourth- and fifth-order. The geometries of the pinched cylinder, the semi-toroidal bellows, and the U-shaped bellows were modelled exactly using rational B-spline functions. All the results obtained are in good agreement with alternative existing solutions.
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 2152-2153 
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    International Journal for Numerical Methods in Engineering 20 (1984) 
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 2155-2174 
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    Notes: A finite element model for the elastic-plastic analysis of plane frames is proposed. The formulation is based on the independent modelling of the displacement and plastic strain fields; the latter is modelled both over the cross-section and along the element length as function of a finite number of parameters, which are considered as an extra set of independent variables, in addition to nodal displacements. Stress redistribution is allowed for over the cross-section, but not over the element length, where the distribution of stress resultants (axial forces and bending moments) is imposed consistently with the assumed displacement model; stress redistribution in terms of stress resultants becomes possible only because of the finite number of redundancies introduced when assembling. It is shown that the model can be formulated in such a way that not only compatibility and elasticity, but also equilibrium (in the sense of beam theory), are fully complied with and only the plastic portion of the constitutive relationship is approximately fulfilled, even if, in principle, to any desired level of accuracy. The model produces accurate results, including a detailed representation of the spreading of plastic zones, with a fairly limited number of elements.
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 2175-2195 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A finite element method for contact problems in crack mechanics is developed on the basis of the penalty function method. The method is successfully applied to three important problems in fracture mechanics: a crack propagated from a pin hole, a two-point supported specimen with an edge crack loaded by a stamp, and a thick plate with a through-wall crack under bending force.
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 2213-2220 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The transmission-line-matrix (t.l.m.) numerical analysis technique is used in this paper to evaluate resonant frequencies and field parameters of the generated modes in microwave ovens loaded with lossy process materials. Analysis is made for the variation of resonant frequencies with the loss factor of the loading material. Temperature rise profile through the load is predicted from the calculated results of field parameters of sustained modes. The demonstrated data are for the dimensional parameters of a rectangular cavity of a commercial microwave oven operating at the standard heating frequency 915 MHz.
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 2221-2234 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The present paper is concerned with the nonlinear finite solution of the postbuckling instability behaviour of thin shell structures in resonance regions of vibration. The development of reliable and efficient techniques for handling the dynamic postbuckling behaviour is emphasized. An illustrative solution associated with the postbuckling resonance response of thin shells is presented.
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 2235-2252 
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    Notes: An isoparametric shell element has been developed capable of linear response to the imposed loads. The original formulation, which was written for static and dynamic analyses, was extended to embrace linear buckling problems. A variety of numerical examples were attempted in order to assess the adaptability of the element to different geometrical representations. Despite serious size limitations of the computer, the accuracy of the predicted buckling loads was found to be satisfactory.
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 2253-2281 
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    Notes: A total Lagrangian finite element formulation for the geometrically nonlinear analysis (large displacement/large rotations) of shells is presented. Explicit expressions of all relevant finite element matrices are obtained by means of the definition of a local co-ordinate system, based on the shell principal curvature directions, for the evaluation of strains and stresses. A series of examples of nonlinear analysis of shell and plate structures is given.
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 2303-2309 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Part 1 of this paper1 presents a very general single step algorithm SSpj for the numerical integration of first and second order time dependent differential equations. In Part 2 we present and discuss results of the accuracy and stability analysis for SS11, SS21, SS31, SS22 and SS32. There is also a detailed comparison of SS22 and the Newmark algorithm.
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 2311-2324 
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    Notes: This paper is the final in a series of three in which we have discussed a finite element post-processing technique. Here we shall deal with the questions of adaptive mesh selection and a posteriori error estimation. Some numerical examples computed by the FEARS program will be used to illustrate the approaches taken.
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 2325-2325 
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 2325-2325 
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 2326-2329 
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 2330-2331 
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 1-14 
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    Notes: The solution of dynamic contact (elastic impact) problems is complicated by the changing nature of the contact area. If a finite element approach is used, the system matrices vary with the contact area. If the problem is properly formulated, such changes are rank one. Rank one changes produce easily determinable changes in the LDLT decompositions of the system matrices. This renders a class of dynamic contact problems soluble with the same accuracy and computational effort as is associated with the solution of any dynamic problem using finite element procedures. Consideration of an example problem involving the impact of spring-mass systems confirms this claim.
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 25-37 
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    Notes: A generalized boundary integral equation method for the solution of the Laplace equation is developed based on the Cauchy integral theorem for analytical complex variable functions. Although the approach is complicated by the utilization of complex variable theory, the resulting model involves direct integration along straight-line boundary segments (elements) rather than using quadrature formulae that are required in current real variable boundary element formulations. Previously published boundary integral equation methods based on the Cauchy integral theorem are shown to be a subset of the generalized model theory developed in this paper.
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 15-24 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The present paper attempts to evaluate the fracture mechanics parameters, the stress intensity factor (K) and Rice's energy integral (J) in plane strain conditions for three-point bend specimens. Both the parameters have been evaluated by the FEM using higher order isoparametric elements (i.e. quadratic elements). The crack tip elastic singularity (1/√r) has been taken into account by the use of the special crack tip elements of degenerate triangular element type as well as the fine eight-noded isoparametric plane elements. The stress distribution has been compared with the Westergaard solution in the vicinity of the crack. The K and J values have also been-compared with the theoretical results.
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 39-75 
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    Keywords: Engineering ; Engineering General
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    Notes: An optimum design sensitivity analysis capability is reported which exploits the approximation concepts-dual method formulation of the minimum weight structural sizing problem. An efficient iterative solution technique is used to facilitate determination of sensitivity derivatives for both primal and dual variables. Estimates on the useful range of parameter perturbations, over which the optimum design sensitivity projections can be expected to yield satisfactory revised optimum designs, are also obtained. Numerical results for several example problems will be presented to illustrate the effectiveness of the capability reported.
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 77-84 
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    Notes: We present numerical solutions for the following Stefan problems. The half-space z 〉 0 is initially filled with liquid at its fusion temperature. The boundary z = 0, taken to be the x axis, is maintained at a constant temperature, less than the fusion temperature, for x 〈 0. For x 〉 0, the first problem considers the case of an insulated boundary, and the second problem considers the case of the boundary maintained at the fusion temperature. This gives rise to a solid-liquid interface curved in the (x, z) plane.
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  • 173
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 85-100 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An optimal control finite element approximation of the penalization type for the solution of incompressible viscous Navier-Stokes equations is presented. This paper has proved the convergence of its minimizing sequence and the existence of the solution for the optimal control problem corresponding to the penalty variational problem of the Navier-Stokes equations. Based on this method and the conjugate gradient algorithm, the program for solving the three-dimensional Navier-Stokes problem has been developed, and some numerical results have also been provided.
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  • 174
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 121-130 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper a straightforward derivation of one- and two-dimensional finite difference forms for general cartesian networks is given. General analytic compact expressions up to third order for first derivatives are specifically derived. General cartesian networks with locally telescoping subnetworks are also introduced and the basic problem of approximating derivative boundary conditions is clarified. The applicability of these general finite difference forms is shown by solving numerically the Laplace problem with mixed Dirichlet-Neumann boundary conditions for an elliptic domain.
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  • 175
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 101-119 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method is described to derive finite element schemes for the scalar convection equation in one or more space dimensions. To produce accurate temporal differencing, the method employs forward-time Taylor series expansions including time derivatives of second- and third-order which are evaluated from the governing partial differential equation. This yields a generalized time-discretized equation which is successively discretized in space by means of the standard Bubnov-Galerkin finite element method. The technique is illustrated first in one space dimension. With linear elements and Euler, leap-frog and Crank-Nicolson time stepping, several interesting relations with standard Galerkin and recently developed Petrov-Galerkin methods emerge and the new Taylor-Galerkin schemes are found to exhibit particularly high phase-accuracy with minimal numerical damping. The method is successively extended to deal with variable coefficient problems and multi-dimensional situations.
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  • 176
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 131-141 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The aim of the work reported in this paper is to present the new formulation of the integral equation method for non-self-adjoint problems and to apply the method to stability problems of elastic continua subjected to non-conservative loadings. A general non-self-adjoint eigenvalue problem stated in terms of differential operators is transformed into a set of coupled integral equations. Our derivation of integral equations is based on an inverse formulation of a canonical form for the original problem and the corresponding fundamental solution pair. Three well-known non-conservative stability problems in elasticity are examined by this integral equation method as illustrative examples. The approximate values of the critical parameters of sample problems demonstrate a sufficient accuracy through a comparison of other values.
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  • 177
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 169-173 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A two-noded, straight element with one-point quadrature is introduced for the unsymmetrical bending of orthotropic axisymmetric shells. The numerical results indicate that the present simple element performs accurately for both thick and thin shell applications.
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  • 178
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 175-181 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 4 Ill.
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  • 179
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 143-167 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Steady-state, free surface seepage through a heterogeneous porous medium underlain by a drain at a finite depth is solved using a fixed domain solution technique. The problems investigated are axisymmetric seepage from a circular pond and plane seepage from a symmetric channel. These ponds and channels may have variable shaped bottoms. Since the Baiocchi transformation was used to define a new dependent variable, the form of the permeability function was restricted to a product of functions of the independent variables. Herein the permeability was chosen to be a function of the depth only. For certain forms of this function, namely those having negative gradients, part of the flowfield becomes unsaturated and this violates the assumed saturation of the flowfield in the flow theory. The governing differential equation, which holds in the sense of distributions, is derived for a fixed solution domain and a simple algorithm (a finite difference successive over-relaxation scheme with projection) is given to obtain the solution to these free surface problems. Numerous comparisons are made with published results. Rigorous mathematical justification of the methods used herein can be found in the references cited.
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  • 180
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    International Journal for Numerical Methods in Engineering 20 (1984) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 181
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 182-186 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Bathe's basic algorithm of subspace iteration for the solution of the symmetric eigenvalue problem is improved by including a Chebyshev filtering mechanism. To obtain satisfactory convergence for the largest eigenvalues, a shifting strategy is adopted. The shift factor is approximately computed by the Lanczos process.
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  • 182
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 187-194 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Numerical results using uniform h-refinement approaches to the solution of a pair of elasticity problems with singularities are presented and compared to recently published results based on the uniform p-refinement approaches.
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  • 183
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 195-195 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 184
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 197-216 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper develops the theory of reparametrization within the context of computer-aided geometric design. It is established that the parametrization plays a positive role in the numerical description of curves and surfaces and it is proposed that the parametrization should be controlled, independently from the shape, via reparametrization. A general approach to reparametrization is adopted in which a function to change the parametrization is modelled in addition to the basic parametric equation. Examples are given for parametric polynomial curves, probably the most commonly used curve segments in computer-aided geometric design. Finally it is shown how reparametrization might be applied to enhance existing surface definition procedures. A surface equation is developed based on the parametric cubic segment that can define shapes virtually independent of the parametrization.
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  • 185
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 217-225 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents an efficient algorithm to solve phase change problems. The first part gives the definition of the problem and mentions some practical applications. The second part analyses how to deal with phase changes by means of concentrated fictitious heat flows. The principles of the method are described and compared to those of other methods. The concept of ‘the area associated with a node’ is developed and some practical values for the weight coefficients are recommended. Conclusions are given about the convergence and the stability of the algorithm, and about the improvements obtained by prescribing the temperatures and using relaxation techniques. Theoretical and practical examples illustrate the validity and efficiency of the proposed method.
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  • 186
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 227-240 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: For the two most common rotor types-the cylindrical rotor with an arbitrarily shaped cross-section and the axially symmetrical rotor with an arbitrary contour of the longitudinal section-algorithms for the computation of the moments of inertia with respect to the major axes are developed, which are particularly suitable for digital computer programming. In both cases the volume integrals can be reduced to area integrals which in turn can be reduced to contour integrals along the boundary of the generating area. The boundary can be approximated as accurately as desired by a polygonal course. For the area moments of any order of the resulting polygonal bounded domain, an analytical solution is presented, for whose numerical calculation only the co-ordinates of the corner points are required. Hence the preparations for data processing are reduced to the absolutely necessary minimum.
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  • 187
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 241-253 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Recently developed computer aided design systems for the design and modification of complex physical solids using interactive computer graphics offer the exciting possibility of an integrated design/analysis system. Called geometric modellers, these systems build complex solids from primitive solids (cubes, cylinders, spheres, etc.) and macro solids (combinations of primitives). To provide an effective finite element analysis capability for these systems, methods must be devised to ease the burden of discretizing the solid geometry into a user controlled finite element mesh. In this paper we describe a new class of transitional blended finite elements which make substantially simpler the task of finite element mesh generation and local mesh refinement. Computational experience indicates that numerical accuracy is not compromised by use of these flexible elements.
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  • 188
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 255-278 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: For physical phenomena governed by the Biot model of porous-elasticity, a reciprocal relation, similar to the Betti's recoprocal theorem in elasticity, is constructed in Laplace transformed space. Integrating the reciprocal relation enables one to formulate boundary integral equations. The fundamental kernels for the integral equations are solved in closed forms for the case of isotropic material. Numerical implementation of two-dimensional problems includes finite element ideas of discretization and polynomial interpolation, and numerical inversion of a Laplace transform. Practical applications of the method are found in consolidation problems in soils which contain compressible as well as incompressible pore fluids. Also, as a numerical experiment, consolidation of partially saturated soil is simulated and interesting phenomena are observed. The currently developed boundary integral equation method (BIEM) for porous-elasticity may be viewed as an efficient and accurate alternative of existing finite element and finite difference methods. For linear consolidation problems, application of BIEM is always preferred to the other numerical methods whenever possible.
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  • 189
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 279-296 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: For the semi-infinite crack propagating quasi-statically in a porous-elastic medium, the boundary integral equation method (BIEM), based on a reciprocal principle, is formulated for the governing equations of the Biot model of linear porous-elasticity. The resulting numerical scheme is efficient since the discretization of the solution unknowns is required only along the axis of symmetry of a fracture. Fracture propagation criteria based on both elastic and plastic constitutive relations are investigated. Practical applications of the model are expected in the failure of overconsolidated clay, earthquake prediction and underground hydraulic fracturing for energy exploration.
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 447-464 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 9 Ill.
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  • 191
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 465-477 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A lowest order difference scheme has been developed for a spatially non-uniform grid such that the integrated square error is a minimum. This algorithm accommodates grid asymmetry and maintains reasonable accuracy without recourse to higher order approximations. Numerical experiments and computations of the Fourier response factor confirm the performance of the optimized asymmetric algorithm.
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  • 192
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 479-503 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A transfer-matrix analysis is presented for determining the static behaviour of thick beams of ‘multimodular materials’ (i.e. materials which have different elastic behaviour in tension and compression, with nonlinear stress-strain curves approximated as piecewise linear, with four or more segments). To validate the transfer-matrix method results, a closed-form solution is also presented for cases in which the neutral-surface location is constant along the beam axis. Numerical results for axial displacement, transverse deflection, bending slope, bending moment, transverse shear, axial force and location of neutral surface are presented for multimodular and bimodular models of unidirectional aramid cordrubber. The transfer-matrix method results agree very well with the closed-form solutions.
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  • 193
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 505-514 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical technique has been developed to solve a system that consists of m linear parabolic differential equations with coupled nonlinear boundary conditions. Such a system may represent chemical reactions, chemical lasers and diffusion problems. An implicit finite difference scheme is adopted to discretize the problem, and the resulting system of equations is solved by a novel technique that is a modification of the cyclic odd-even reduction and factorization (CORF) algorithm. At each time level, the system of equations is first reduced to m nonlinear algebraic equations that involve only the m unknown grid points on the nonlinear boundary. Newton's method is used to determine these m unknowns, and the corresponding Jacobian matrix can be computed and updated easily. After convergence is achieved, the remaining unknowns are solved directly. The efficiency of this technique is illustrated by the numerical computations of two examples previously solved by the cubic spline Galerkin method.
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  • 194
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 515-522 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The efficiency and computational accuracy of the boundary element and finite element methods are compared in this paper. This comparison is carried out by employing different degrees of mesh refinement to solve a specific illustrative problem by the two methods.
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  • 195
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 523-528 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An 8-node brick element based on the assumed stress hybrid formulation is described. With three additional stress fields, the element stiffness matrix now has the required rank of 18, and the ‘bending’ response is exact with rectangular elements. Surprisingly, the 2 × 2 × 2 Gauss rule suffices for all numerical integrations, to satisfy the constant stress patch test.
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 715-732 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 733-743 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A simple element numbering algorithm is described which yields near-minimal frontwidths for two- and three-dimensional finite element assemblies. Renumbering of E elements requires an immediate-access computer memory size which is proportional to the square root of E in two-dimensional problems, and to the two-thirds power of E in three dimensions. This very small memory requirement allows processing of large problems in minicomputers. When used in large computers, page-swapping operations are minimized.
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 757-771 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 773-777 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The Hellinger-Reissner generalized variational principle is used to deduce further principles directed especially towards formulation of high integrity finite elements for plates and curved shells in polynomial parametric representation. Assumed stresses in these principles are derived from displacements and supplemented with stresses derived from stress functions.
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    International Journal for Numerical Methods in Engineering 20 (1984), S. 745-756 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Two general algorithms for refining triangular computational meshes based on the bisection of triangles by the longest side are presented and discussed. The algorithms can be applied globally or locally for selective refinement of any conforming triangulation and always generate a new conforming triangulation after a finite number of interactions even when locally used. The algorithms also ensure that all angles in subsequent refined triangulations are greater than or equal to half the smallest angle in the original triangulation; the shape regularity of all triangles is maintained and the transition between small and large triangles is smooth in a natural way. Proofs of the above properties are presented. The second algorithm is a simpler, improved version of the first which retains most of the properties of the latter. The algorithms can be used either for constructing irregular computational meshes or for locally refining any given triangulation. In this sense they can be adequately combined with adaptive and/or multigrid techniques for solving finite element systems. Examples of the application of the algorithms are given and two possible generalizations are pointed out.
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