bluuebunny/crossref_metadata_2025_split huggingface dataset:
Solution of a free boundary problem by finite elements: Numerical considerations and results
Authors: Caprili M. 
Published: August 2005

AbstractThis paper contains numerical considerations on, and the results of the problem of a fluid filtering through a porous, isotropic, homogeneous, three‐dimensional dam with variable cross‐section. The numerical solution is obtained by the finite element method using cylindrical elements that exactly match the curved part of the boundary.Furthermore, a lower and an upper numerical enclosure of the free boundary are considered, together with a description of the procedure of calculations performed by an IBM 370/158 computer.
A novel boundary infinite element
Authors: Zienkiewicz O. C. , Emson C. , Bettess P. 
Published: August 2005

AbstractA new, improved infinite element based on mapping is proposed for modelling unbounded domain problems. Mapping has previously been used in such problems, not only for the entire domain, but also for the infinite element itself. The novelty of the present approach is the simplicity of the mapping, and the retention of standard integration abscissae and weights. The implementation of these elements is very straightforward, and they are ideally suited for the analysis of infinite domain static problems in two and three dimensions.
A stabilization procedure for the quadrilateral plate element with one‐point quadrature
Authors: Belytschko Ted , Tsay Chen‐Shyh 
Published: August 2005

AbstractA stabilization procedure is developed for controlling the kinematic modes of the four‐node, bilinear quadrilateral element when single‐point quadrature is used. These kinematic modes manifest themselves by spatial oscillations or singularity of the total stiffness. In this stabilization procedure, additional generalized strains are defined which are activated by the kinematic modes; these generalized modes are furthermore not activated by rigid body motions regardless of the shape of the quadrilateral. By using a scaling law developed in an earlier paper, the stabilization parameters are defined so they do not adversely affect the element's performance. Several problems which are subject to kinematic modes are presented to illustrate the performance of this stabilization procedure for linear problems.
Fortran computer program for inextensional bending of a doubly curved shell triangular element
Authors: Morley L. S. D. 
Published: August 2005

AbstractA Fortran computer program is described which calculates physical quantities for a class of shell triangular elements undergoing inextensional bending. These elements are in quadratic parametric representation and may have positive, zero or negative Gaussian curvature.The exact inextensional bending solutions for the rectangular displacement components are cubic in the surface co‐ordinates and the curvature changes are relatively slowly varying.
Performance evaluation of algorithms for mildly nonlinear elliptic problems
Authors: Houstis E. N. , Mitchell W. F. , Papatheodorou T. S. 
Published: August 2005

AbstractA number of numerical methods for mildly nonlinear elliptic boundary value problems on general domains is presented. The discretization procedures considered are: a fourth‐order FFT‐type method, collocation using Hermite bicubic splines and Galerkin with linear triangular as well as quadratic quadrilateral isoparametric elements. The linearized collocation and Galerkin equations are solved by various direct methods available in the ELLPACK system. A comparative study of the above equation solvers is presented for different domain geometries and compilers. The evaluation of software for the general mildly nonlinear elliptic equations is performed over 36 instances from a population of 16 parametrized problems with ‘real world’ and ‘mathematical’ behaviour. The performance data suggests that collocation is an effective method for such general problems, while Galerkin with quadratic quadrilateral isoparametric elements is uniformly superior to the one with linear elements.
Nonlinear programming on a microcomputer
Authors: Rangaiah V. P. , Sadasivan S. 
Published: August 2005

AbstractThe Davidon‐Fletcher‐Powell (DFP) algorithm for multivariable unconstrained nonlinear function minimization is implemented on a desk microcomputer—the Hindustan Computers MICRO‐2200—with a floppy disk memory extension peripheral. The program is developed using the programming keys of the system. The program is closely based on FMFP, a well‐known FORTRAN subroutine of the algorithm. Among the exercises performed are two standard nonlinear programming (NLP) test problems, namely the Rosenbrock and Wood function minimization and two SUMT (Sequential Unconstrained Minimization Technique) illustration problems in structural optimization, i.e. two‐bar and three‐bar truss weight minimization examples. Experience bears out the potential of desk calculating systems as tools in nonlinear programming algorithm research. Also, the small‐scale structural optimization capability afforded by such systems is expected to be of significance in teaching and preliminary design contexts.
A predictor‐corrector contouring algorithm for isoparametric 3D elements
Authors: Kontopidis George D. , Limbert David E. 
Published: August 2005

AbstractThis paper describes a new contouring algorithm for isoparametric elements which can be used to map three‐dimensional scalar fields. The contours are generated on arbitrary planes intersecting finite element structures. Tracing element contour lines is accomplished by an accurate predictor‐corrector technique. A method of finding starting points for the algorithm on the boundary of the elements is also given.
An arc‐length method including line searches and accelerations
Authors: Crisfield M. A. 
Published: August 2005

AbstractThis paper describes a method for introducing line searches into the arc‐length solution procedure. Such line searches may be used at each iteration to calculate an optimum scalar step‐length which scales the normal iterative vector. In practice, a loose tolerance is provided so that on many iterations the line searches are avoided. However on ‘difficult iterations’, the line searches are shown to lead to a substantial improvement in the convergence characteristics. A simple single‐parameter acceleration is also developed using line search concepts. The new arc‐length method is applied to both the geometrically nonlinear analysis of shallow shells and the materially nonlinear analysis of reinforced concrete beams and slabs. Significant improvements are demonstrated in relation to the standard arc‐length method.
A solution to the C1 continuity problem in plate bending
Authors: Caramanlian C. 
Published: August 2005

AbstractA family of high‐order, conforming triangles for the finite element analysis of plate bending problems is developed, using the displacement method of formulation.The development proceeds in two steps. A family of non‐conforming triangles, based on polynomial expansions of order >4 is first generated, and its performance found to be unacceptable. Nodal variables for the non‐conforming family are selected from the set w, wx, wy, wn. The elements are then made to conform, by adding a twist nodal variable wnt at the mid‐side nodes. Rational functions define the three additional degrees‐of‐freedom. Simple and very accurate procedures solve the problems associated with the use of such functions.Numerical results are presented for the conforming triangles of order 4 and 7, following a brief description of the two elements. A listing of the explicit shape functions for the quartic triangle is included.The numerical results are very good. In particular, they are superior per degree‐of‐freedom to the results predicted by the various non‐conforming and conforming, cubic and related elements at present used in computer packages. Together with a similar performance by the quintic member10 of the family, they validate the proposed theoretical solution.
Minimum weight design using finite elements
Authors: Kark S. K. , Scholes A. 
Published: August 2005

AbstractThe authors' aim was the development of a suitable procedure for the structural design of railway vehicles within an existing general purpose finite element package. A previous application to railway vehicles was based on the use of a sequence of linear programming steps incorporating move limits on the design variables. This approach was slow and in other fields mathematical programming techniques tended to give way to methods based on optimality criteria.Nevertheless because of its simplicity of concept, and because some apparently successful alternatives to the move limit idea were available, the use of linear programming was returned to and the method is now incorporated in the British Rail finite element program NEWPAC. Couched in terms of inverse variables and using linearized forms of the stress constraints, the linear programming approach converges with the optimality criteria method. Details of the implementation and of some standard examples are given.
Analysis of steel frames under fire environment
Authors: Jain P. C. , Rao M. N. G. 
Published: August 2005

AbstractA numerical technique is developed using an implicit time‐marching scheme to study the deformation history of steel building frames in fire, by considering the change in the material properties due to rise of temperature, effect of creep and large deformations. A computer program has been developed for the analysis of plane frames based on the above algorithm using incremental and iterative procedures. Based on such a study, the length of time for which the structure can perform its function without either local or overall failure can be predicted.
Asymptotic rates of convergence of iterative methods applied to finite difference calculations on non‐uniform grids
Authors: Jones I. P. 
Published: August 2005

AbstractIn this paper the use of strongly stretched finite difference grids is examined in detail for a simple model equation. Numerical solutions of this equation demonstrate the overall second‐order accuracy of the difference approximations. The behaviour of two simple iterative methods, S.O.R. and stationary A.D.I. is discussed for several cases with strong grid stretching and with variable diffusion coefficients. The results show that grid compression near to boundaries can greatly enhance the rates of convergence of these iterative methods, whereas with grid compression in the centre the rate of convergence can be extremely slow. The case of a diffusion coefficient which increases away from the boundaries of a region is analogous to grid compression in the centre and again the convergence rates can degrade considerably.
On computing the inverse of a sparse matrix
Authors: Niessner H. , Reichert K. 
Published: August 2005

AbstractThe Gauss‐Jordan inversion algorithm requires 0(n3) arithmetic operations. In some practical applications, like state estimation or short‐circuit calculation in power systems, the given matrix is sparse and only part of the inverse is needed. Most frequently in the diagonal dominant case this is the diagonal. There are two ways to exploit sparsity to determine elements of the inverse:

Columnwise inversion via the solution of sparse linear systems with columns of the unit matrix as right‐hand sides.
Application of the algorithm of Takahashi et al6
.The latter algorithm arises very naturally from multiplying the left‐ and right‐hand factors of the Zollenkopf bifactorization in reverse order. We indicate how computing time can be gained in the important symmetric diagonal dominant case if only part of the diagonal is needed and compare computing times of the method of Takahasi et al.6 with several variants of columnwise inversion. Whereas most of the theory holds for general matrices, experiments are performed on the symmetric diagonal dominant case. For band matrices the operation count is 0(n) both for computing a column of the inverse by columnwise inversion and the diagonal by the algorithm of Takahashi et al6.
On the suppression of zero energy deformation modes
Authors: Pian Theodore H. H. , Chen Dapeng 
Published: August 2005

AbstractBased on the Hellinger‐Reissner principle and the deformation energy due to assumed stresses and displacements, the problem of the kinematic deformation modes in assumed stress hybrid/mixed finite elements has been examined. Basic schemes are developed for the choice of assumed stress terms that will suppress all kinematic deformation modes. Quadrilateral membrane and axisymmetric elements, and three‐dimensional hexahedral elements, are used to illustrate the suggested procedure.
Multiple‐parameter reduced basis technique for bifurcation and post‐buckling analyses of composite plates
Authors: Noor Ahmed K. , Peters Jeanne M. 
Published: August 2005

AbstractA multiple‐parameter reduced basis technique and a problem‐adaptive computational algorithm are presented for the bifurcation and post‐buckling analyses of composite plates subjected to combined loadings. The computational algorithm can be conveniently divided into three distinct stages. The first stage is that of determining the stability boundary. The plate is discretized by using displacement finite element models and the analysis region is reduced by exploiting the special symmetries exhibited by the response of the plate. The vector of unknown nodal displacements is expressed as a linear combination of a small number of path derivatives (derivatives of the nodal displacements with respect to path parameters), and a Rayleigh‐Ritz technique is used to approximate the finite element equations by a small system of algebraic equations. The reduced equations are used to determine the stability boundary of the plate.In the second stage, a nonllnear solution in the vicinity of the stability boundary is obtained by using a bifurcation buckling mode as a predictor, and a set of reduced equations is generated. In the third stage, the reduced equations are used to trace post‐buckling paths corresponding to various combinations of the load parameters.The potential of the proposed approach is discussed and its effectiveness is demonstrated by means of a numerical example of laminated composite plate subjected to combined compressive and shear loadings.
Heat diffusion with time‐dependent convective boundary conditions
Authors: Becker N. M. , Bivins R. L. , Hsu Y. C. , Murphy H. D. , White A. B. , Wing G. M. 
Published: August 2005

AbstractThe heating (or cooling) of the rock adjacent to water flowing through a crevice is of interest in certain geothermal studies. For many purposes, only the rock temperature at the rock‐water interface is needed. The fact that the convective heat transfer coefficient is a function of time in the case of unsteady flow takes this problem out of the strictly classical domain.Several methods of solution are described. An approach in which the heat equation is solved, under appropriate side conditions, by standard finite difference techniques is shown to be satisfactory but rather wasteful because much unneeded information concerning internal rock temperatures must be obtained. Several integral equations of Volterra type are derived that provide the temperature only at the interface. Two numerical approaches to their solution are described: one quite classical and only partially effective; the other an apparently new algorithm that is fast and efficient. Analytical upper and lower bounds on the temperature are obtained and serve to demonstrate that this numerical device is also very accurate.The algorithm is applicable to a wide class of Volterra integral equations of the second kind. A brief discussion of the possible future uses of this scheme and the need for additional research is given.
Numerical evaluation of stress intensity factor and J integral in three‐point bend specimen
Authors: Pratap C. R. , Pandey R. K. , Natarajan R. , Gupta K. N. 
Published: August 2005

AbstractThe 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.
A Taylor–Galerkin method for convective transport problems
Authors: Donea Jean 
Published: August 2005

AbstractA 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.
An integral equation method for non‐self‐adjoint eigenvalue problems and its applications to non‐conservative stability problems
Authors: Tosaka Nobuyoshi , Kakuda Kazuhiko 
Published: August 2005

AbstractThe 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.
Comparative study of six explicit and two implicit finite difference schemes for solving one‐dimensional parabolic partial differential equations
Authors: Roberts David L. , Selim M. Sami 
Published: August 2005

AbstractEight finite difference schemes used in solving parabolic partial differential equations are compared with respect to accuracy, execution time and programming effort. The analysis presented is useful in selecting the appropriate numerical scheme depending on the emphasis placed upon accuracy, execution time or programming effort.
Two high‐order numerical methods for solving boundary‐value nonlinear ordinary differential equations
Authors: Tewarson R. P. 
Published: August 2005

AbstractTwo numerical methods for solving two‐point boundary‐value problems associated with systems of first‐order nonlinear ordinary differential equations are described. The first method, which is based on Lobatto quadrature, requires four internal function evaluations for each subinterval. It does not need derivatives and is of order h7, where h is the space chop. The second method, which is similar to the first but is based on Lobatto–Hermite quadrature, makes the additional use of derivatives to achieve O(h9) accuracy. Results of computational experiments comparing these methods with other known methods are given.
A simple element for static and dynamic response of beams with material and geometric nonlinearities
Authors: Yang T. Y. , Saigal Sunil 
Published: August 2005

AbstractA 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.
Formulation methods of geometric and material nonlinearity problems
Authors: Gadala M. S. , Dokainish M. A. , Oravas G. Ae 
Published: August 2005

AbstractA concise survey of formulation methods of geometric and material nonlinearity problems is given. Differences between existing formulations in the literature are discussed. A consistent Lagrangian and updated Lagrangian formulations are derived from the energy balance equation transformed to the proper reference configuration. Differences between the existing formulations and similar ones in the literature are found to be in specific geometric nonlinear terms in the final incremental equation as well as in the definition of the load increment vector. Specific forms of constitutive equations for elastic and elastoplastic materials are presented. Some of the forms used by other authors in application to elastoplastic materials are shown to be inconsistent. Sample numerical examples intended for checking some particular points in the formulation are presented.
Efficient linear and nonlinear heat conduction with a quadrilateral element
Authors: Liu Wing Kam , Belytschko Ted 
Published: August 2005

AbstractA method is presented for performing efficient and stable finite element calculations of heat conduction with quadrilaterals using one‐point quadrature. The stability in space is obtained by using a stabilization matrix which is orthogonal to all linear fields and its magnitude is determined by a stabilization parameter. It is shown that the accuracy is almost independent of the value of the stabilization parameter over a wide range of values; in fact, the values 3, 2 and 1 for the normalized stabilization parameter lead to the 5‐point finite difference, 9‐point finite difference and fully integrated finite element operators, respectively, for rectangular meshes; numerical experiments reported here show that the three have identical rates of convergence in the L2 norm. Eigenvalues of the element matrices, which are needed for stability limits, are also given. Numerical applications are used to show that the method yields accurate solutions with large increases in efficiency, particularly in nonlinear problems.