bluuebunny/crossref_metadata_2025_split huggingface dataset:
Numerical formulation for a higher order plane finite dynamic element
Authors: Gupta K. K. 
Published: August 2005

AbstractThe 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.
A consistent and accurate procedure for obtaining difference equations from differential equations
Authors: Lick Wilbert , Gaskins Tom 
Published: August 2005

AbstractA 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.
The self‐equilibration of residuals and complementary a posteriori error estimates in the finite element method
Authors: Kelly D. W. 
Published: August 2005

AbstractIt 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.
Numerical laplace transformation and inversion in the analysis of physical systems
Authors: Wilcox D. J. , Gibson I. S. 
Published: August 2005

AbstractThe paper develops a new discrete transform pair which economizes on the number of samples of F(s) and f(t) compared with the standard pair. Whereas the standard pair used uniform sampling along the Bromwich contour, the new method allows a progressive increase in the sampling interval, thereby reducing the number of samples required to meet a specified bandwidth requirement. In the case of the computation of transient responses of physical systems, a reduction by a factor of 10 is not unrealistic. The new transform pair is based on the generalization of fundamental sampling principles. In particular, this leads to an integration contour different from the Bromwich contour.
Evaluation of a new method for numerical laplace transformation and inversion
Authors: Wilcox D. J. , Gibson I. S. 
Published: August 2005

AbstractThe paper presents results obtained by the implementation of a new method of Laplace transformation and inversion developed by the authors. Test functions are used to show that basic accuracy is comparable to that obtainable by uniform sampling along the Bromwich contour. The advantage of the new method is seen to be that it generally requires far fewer samples of F(s). It is clarified that the new method does have certain limitations so far as general application is concerned. However, given results indicate that very satisfactory performance may be expected whenever the method is specifically applied to the calculation of transient responses of damped physical systems.
A solution technique for indefinite systems of mixed finite elements
Authors: Mirza F. A. 
Published: August 2005

AbstractA solution technique for indefinite systems of symmetric linear, simultaneous equations, via the Hellinger–Reissner variational principle, is presented. The method utilizes symmetry of the global matrix and its expected real eigenvalues. Premultiplication of the global matrix with itself renders a positive definite matrix, hence enabling the use of any standard equation solver for a positive definite system and requiring only about twice the memory requirement for the original set of equations. Two subroutines, MULT and MULTIP, which are compatible with the sky‐line technique, are also listed.
Automatic three‐dimensional mesh generation by the modified‐octree technique
Authors: Yerry Mark A. , Shephard Mark S. 
Published: August 2005

AbstractAn approach for the fully automatic generation of three‐dimensional finite element meshes is presented. The method is specifically designed for use with solid modelling systems which provide a complete and unique definition of the geometry of a part. The method follows from the basic concepts of the octree encoding technique with specific modifications made to produce valid, user controllable finite element meshes. Example problems are included to demonstrate the technique.
On the convergence rate of the boundary penalty method
Authors: Shi Zhong‐Ci 
Published: August 2005

AbstractThe convergence rate of the boundary penalty finite element method is discussed for the Poisson equation with inhomogeneous Dirichlet boundary conditions on a polygonal domain. It is proved that, under certain circumstances, an optimal convergence rate may be achieved which agrees with the rate obtained recently in the numerical experiments by Utku and Carey.
Plastic straining, unstressing and branching in large displacement perturbation analysis
Authors: de Freitas J. A. Teixeira , Smith David Lloyd 
Published: August 2005

AbstractThe 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.
A new 48 d.o.f. quadrilateral shell element with variable‐order polynomial and rational B‐spline geometries with rigid body modes
Authors: Moore Carleton J. , Yang T. Y. , Anderson David C. 
Published: August 2005

AbstractA 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.
Development of a solid hexahedron finite dynamic element
Authors: Gupta K. K. 
Published: August 2005

AbstractThis paper presents the pertinent details of a newly developed solid rectangular hexahedron finite dynamic element, involving the derivation of the higher order stiffness and inertia dynamic correction matrices. Numerical results of a test case are also presented which indicate that adoption of the dynamic elements significantly improves the solution convergence, when compared with the related performance of the corresponding finite elements.
Potential integrals associated with quadratic distributions in a triangular domain
Authors: Okon E. E. 
Published: August 2005

AbstractExact expressions are presented for the potentials, at an arbitrary point in space, due to two quadratic distributions in a triangular disc. These expressions are obtained by means of extensions of the analytical techniques previously developed for evaluating the potential integrals for constant and linear distributions. It is shown that the potential due to any quadratic distribution in a triangle may be obtained by using the two expressions derived here, together with an expression for the potential corresponding to a linear distribution. This latter expression was presented in an earlier paper.1 Numerical values obtained through the use of the two expressions are compared with those which result from the numerical evaluation of the potential integrals by triangle quadratures.
Accurate numerical integration of singular boundary element kernels over boundaries with curvature
Authors: Lean Meng H. , Wexler A. 
Published: August 2005

AbstractUse of the Green function, for the solution of boundary‐value problems, frequently results in singular integral equations. Algorithms are presented for the accurate and efficient treatment of singular kernels frequently encountered in the boundary element method (BEM). They are based upon the use of appropriately weighted Gaussian quadrature formulae, together with numerical geometrical transformations of the region of integration. The use of high‐order subdomain expansion functions, for interpolation over nonplanar elements, allows boundary curvature to be accommodated. In particular, the handling of Green functions with logarithmic and r−1 behaviour are detailed. Volume integrals, with r−2 singularity, are outlined. Operations are performed on a simplex, thus resulting in generality and ease of automation. This scheme has been incorporated into boundary element method software and successfully applied to a variety of problems.
Analysis of laminated bimodulus composite thin shells of revolution using a doubly curved quadrilateral finite element
Authors: Murthy P. V. Ramana , Rao K. P. 
Published: August 2005

AbstractThis paper presents a finite element analysis of laminated bimodulus composite thin shells of revolution using a 48 d.o.f. doubly curved quadrilateral finite element. All the three displacements of the shell element reference surface are expressed as products of one‐dimensional first‐order Hermite interpolation polynomials. The constitutive relationship for a bimodulus composite is assumed to depend on the fibre‐direction strain experienced by each orthotropic layer. Consequently the true state of strain and the corresponding constitutive relationship in a bimodulus composite structure are to be determined iteratively. The true state of stress/strain is obtained by specifying a maximum error in the locations of the two neutral surfaces (one along each of the orthogonal reference axes) in the shell. The use of the quadrilateral shell finite element is validated by solving the problem of (i) a freely supported single layer (0°) bimodulus composite square plate and (ii) a freely supported single layer (0°) cylindrical panel, which are subjected to sinusoidal transverse loading and for which analytical solutions are available. Next, the problems of a single layer (90°) pinched cylindrical shell and a single layer (0°) open crown hemispherical shell are solved to show the ability of the present program.
Geometrically nonlinear formulation of a 48 D.O.F. quadrilateral shell element with rational B‐spline geometry
Authors: Yang T. Y. , Moore Carleton J. , Anderson David C. 
Published: August 2005

AbstractA geometrically nonlinear formulation for a 48 degrees‐of‐freedom (d.o.f.) quadrilateral shell element is presented. Each of the three displacement functions of u, v and w is based on the bicubic Hermitian polynomial. The surface of the element is modelled using linearized ratronal B‐spline functions which may be linked to the geometric data bases generated by the computer‐aided design system. The displacement functions and the 48 d.o.f. are expressed in both curvilinear and Cartesian forms, whereas the strain‐displacement equations are expressed in curvilinear co‐ordinates. The use of Cartesian displacement functions and degrees‐of‐freedom allow for the proper representation of the six rigid body motions even for the element with nonzero Gaussian curvature, such as a bellows. Two examples are demonstrated: snap‐through buckling of a spherical cap and large deflection of a semi‐toroidal bellows shell. Results compare well with alternative solutions.
Stability and convergence of some finite element algorithms for nonlinear elastodynamics
Authors: Hamdan S. M. , Patamapongs N. 
Published: August 2005

AbstractA series of direct‐integration and model‐expansion finite element algorithms for a geometrically and materially nonlinear elastodynamic problem are constructed and analysed. The algorithms are constructed by temporally approximating the individual nonlinear stiffness terms such that discrete conservation laws are obtained. This conservative property has a positive effect in providing a stable appromixation, and in addition allows the stability properties of the algorithms to be easily assessed. Stability and convergence criteria for the algorithms are rigorously established using an energy method.
A procedure to debug computer programs
Authors: Shih T. M. 
Published: August 2005

AbstractThis analysis presents a procedure that can reliably debug computer programs. The central idea lies in creating a fictitious problem whose exact solution exists and is known, and in obtaining the numerical solution for comparison with the exact solution. If the two solutions are found identical, it is safe to assume that the computer program computing the fictitious problem is free of bugs. Then, conversion of the program computing the ficititious problem to that computing the real problem generally involves changing only one single statement. This procedure may be jointly used with all the existing numerical schemes.
Finite element hourglassing control
Authors: Schulz J. C. 
Published: August 2005

AbstractA new hourglassing control technique for quadrilateral and hexahedral elements used in dynamic finite element codes is presented. Based on expansion of the strees in a Taylor series and retention of additional terms beyond the usual constant stress term, this technique has the advantage that actual rather than artificial material properties are used. Simplifications that render this technique competitive with artificial viscosity and stiffness procedures in terms of additional storage and computation requirements are described.
A CAD approach to the minimum weight design problem
Authors: Esping Björn J. D. 
Published: August 2005

AbstractA structure is defined by a set of governing points. These points can be used to define lines, surfaces and solids. A governing point can be connected to a design variable. The values of the design variables are determined in order to minimize the weight of the structure subject to a number of stress constraints. Three simple structures are then designed.
High degree efficient symmetrical Gaussian quadrature rules for the triangle
Authors: Dunavant D. A. 
Published: August 2005

AbstractGaussian quadrature is required for the computation of matrices based on the isoparametric formulztion of the finite element method. A brief review of existing quadrature rules for the triangle is given, and the method for the determination of high degree efficient symmetrical rules for the triangle is discussed. New quadrature rules of degree 12–20 are presented, and a short FORTRAN program is included.
Evaluation of added mass by a cloning algorithm
Authors: Dasgupta Gautam 
Published: August 2005

AbstractIn problems of structure interaction with infinite surrounding of incompressible, inviscid fluid media, added mass matrices on wet surfaces have been considered for modelling the effects of outgoing waves. For an arbitrary geometry of the wet surface, an expression for the added mass matrix is derived according to a finite element procedure which utilizes the force‐displacement relations of representative elements on the boundary. In the element mass matrix a certain symmetry, which characterizes interactions between the interior and exterior surfaces, helps reduce the quadratic matrix equation of the cloning algorithm to a linear eigenvalue problem. A benchmark example is included to establish the numerical accuracy of the proposed formulation.
Beam element matrices derived from Vlasov's theory of open thin‐walled elastic beams
Authors: Friberg P. O. 
Published: August 2005

AbstractA uniform beam element of open thin‐walled cross‐section is studied under stationary harmonic end excitation. An exact dynamic (transcendentally frequency‐dependent) 14 × 14 element stiffness matrix is derived from Vlasov's coupled differential equations. Special attention is paid to the computational problems arising when coefficients vanish in these equations because of symmetric cross‐section, zero warping stiffness, etc. The dynamic element stiffness matrix is established via a generalized linear eigenvalue problem and a system of linear algebraic equations with complex matrices. A static stiffness matrix is also derived and the associated consistent mass and geometric stiffness matrices are given. Modal masses are evaluated. A FORTRAN program and a numerical example are included.
Mapped infinite elements for exterior wave problems
Authors: Zienkiewicz O. C. , Bando K. , Bettess P. , Emson C. , Chiam T. C. 
Published: August 2005

AbstractRecently, a new type of infinite elements which uses r−1 decay was proposed. They were applied to exterior wave problems and good results were obtained. In two‐dimensional problems, however, it was necessary to move the origin of the r−1 decay in order to model the outgoing wave more accurately, because it decays roughly as r−1/2. In this paper, the mapped infinite elements with r−1/2 decay and the necessary numerical integration procedure are presented. These elements do not require any artificial movement of the origin. Several example problems are solved. The results show that the infinite elements with r−1/2 decay here give much more accurate values than the infinite elements with exponential decay and any damper elements.
Evaluation of ‘specia’ finite elements with non‐conventional Gaussian quadratures
Authors: Bernhard Robert J. , Holger David K. 
Published: August 2005

AbstractFinite elements with ‘Special’ basis functions have been proposed to develop better approximations for problems where the behaviour is known to be non‐polynomial. This paper discusses extension of Gaussian quadrature integration procedures of non‐conventional form to the evaluation of the finite element matrices for ‘Special’ elements. Algorithms for general ‘Special’ elements are discussed. The techniques are applied to ‘Special’ one‐ and two‐dimensional elements for spherically symmetric potential flow. The accuracy of the new ‘Special’ element is shown to be superior to linear and quadratic elements for spherically symmetric potential flow problems.
A numerical study of various algorithms related to the preconditioned conjugate gradient method
Authors: Jackson C. P. , Robinson P. C. 
Published: August 2005

AbstractWe present the results of a numerical study of the preconditioned conjugate gradient algorithm, the minimal residual algorithm, the biconjugate gradient algorithm and the bi‐minimal residual algorithm using both simple test matrices and more realistic test matrices derived from physical problems. The application of the methods to unsymmetric matrices is considered. We emphasize the importance of a good preconditioning, look at various methods including ICGG(n) and incomplete block factorization, and make some practical recommendations. Some of the folk‐lore surrounding the semi‐iterative methods is dispelled.
A unified set of single step algorithms part 3: The beta‐m method, a generalization of the Newmark scheme
Authors: Katona Michael C. , Zienkiewicz O. C. 
Published: August 2005

AbstractIntroduced herein is a generalization of Newmark's time marching integration scheme, called the β‐m method. Like the SSpj method (introduced in Parts 1 and 2 of this series), the β‐m method provides a gcneral single‐step scheme applicable to any set of initial value problems. The method is specialized by specifying the method order m along with rn integration parameters, β0, β1, …, βm−1. For a particular choice of m, the integration parameters provide a subfamily of methods which control accuracy and stability, as well as offering options for explicit or implicit algorithms. For the most part, attention is focused on the application to structural dynamic equations. Most well‐known methods (e.g. Newmark, Wilson, Houbolt, etc.) are shown to be special cases within the β‐m family. Hence, one computationally efficient and surprisingly simple algorithm unifies old and new methods. Stability and accuracy analyses are presented for method orders m = 2, 3 and 4 to determine optimal parameters for implicit and explicit schemes, along with numerical verification.
Necessary convergence conditions for upwind schemes in the two‐dimensional case
Authors: Roos H. ‐G. 
Published: August 2005

AbstractThis paper considers nine‐point difference schemes for a two‐dimensional boundary value singular perturbation problem without turning points and parabolic boundary layers. Necessary conditions are given for the uniform convergence (in the sense of the maximum norm) of a scheme. Using these conditions, several widely used schemes are analysed. It is shown that some common schemes are not uniformly convergent in ϵ. and that in some cases we are able to compute uniquely free parameters in the scheme. Some remarks on the treatment of a problem with a parabolic boundary layer are given.
Finite element method for in‐plane vibrations of rotating Timoshenko rings and sectors
Authors: Singh Kultar , Singh Bhupinder Pal 
Published: August 2005

AbstractA simple and logical finite element formulation is presented for the analysis of rings and sectors, with Timoshenko effects. The elemental properties are derived from the governing differential equation of motion using the Galerkin method. A quintic polynomial, satisfying the compatibility of derivatives up to second order, has been used for the ring finite element. The interpolating function is the same as for a thin ring. The efficiency of the formulation has been illustrated by the numerical results presented.