bluuebunny/crossref_metadata_2025_split huggingface dataset:
An application of global approximations in the finite element method
Authors: Allen E. J. 
Published: August 2005

AbstractA technique is described in which global approximations are used to improve the accuracy of the finite element method. The technique is theoretically based on two corollaries to the Lax–Milgram lemma which are presented in this paper. Basically, the technique consists of factoring the unknown function for which an approximation is desired into the product of a global approximation and a second unknown function. Finite element methods are appropriately applied to obtain an approximation to the second unknown function. The approximation to the original function then consists of the product of the specified global approximation and the approximation to the second unknown function. The advantage that finite element methods possess with respect to obtaining banded matrices is preserved in this technique. In addition, numerical examples indicate that the technique's accuracy is as much as a factor of fifty better than the accuracy obtained by directly applying a finite element method to approximate the original function.
Economical symmetrical quadrature rules for complete polynomials over a square domain
Authors: Dunavant D. A. 
Published: August 2005

AbstractIt is of interest in numerical analysis to develop symmetrical quadrature rules for integration of complete polynomial functions over a square domain with minimum computational effort. Gaussian product quadrature rules integrate such functions with maximum effort. Symmetrical quadrature rules are developed and presented for integration of complete polynomial functions up to 21st order with minimum computational effort.
Vibration analysis of rotating turbomachinery blades by an improved finite difference method
Authors: Subrahmanyam K. B. , Kaza K. R. V. 
Published: August 2005

AbstractThe problem of calculating the natural frequencies and mode shapes of rotating blades is solved by an improved finite difference procedure based on second‐order central differences. Lead‐lag, flapping and coupled bending–torsional vibration cases of untwisted blades are considered. Results obtained by using the present improved theory have been observed to be close lower bound solutions. The convergence has been found to be rapid in comparison with the classical first‐order finite difference method. While the computational space and time required by the present approach is observed to be almost the same as that required by the first‐order theory for a given mesh size, accuracies of practical interest can be obtained by using the improved finite difference procedure with a relatively smaller matrix size, in contrast to the classical finite difference procedure which requires either a larger matrix or an extrapolation procedure for improvement in accuracy.
On the effect of quarter‐point element size on fracture criteria
Authors: Yehia Nabil A. B. , Shephard Mark S. 
Published: August 2005

AbstractThe effect of the quarter‐point element size on the solution parameters of fracture criteria is investigated in view of its effect on the computed stress intensity factors. An analytical relationship between the error in calculating crack propagation increment and stress intensity for single mode problems is obtained while, for mixed mode problems, the investigation is based on numerical experimentation. The singular element size is found to have a substantial effect on both crack propagation angle and increment for the geometries considered.
Material modelling for accurate stresses in involute composites
Authors: Stanton Edward L. 
Published: August 2005

AbstractMaterial modelling requirements for accurate stress fields in a nonuniform anisotropic composite are established for all six components of stress at a material point. The gauge section from a conical involute structure tested in an earlier investigation provides the case data for this modelling study. Stress results from a tricubic Hermite finite element model are shown to be in agreement with another computational analysis by Pagano using a Reissner energy formulation. Comparisons are made in the interior and at a corner with high interlaminar stress gradients. The small, but critical, matrix dominated stress components are shown to be very sensitive to modelling material orientation changes within each finite element. Uniform stress accuracy was obtained using distribution functions for material orientation of the same degree as the displacement functions, an isoparametric material geometry model.
Collocation time finite element procedures for integration of strongly nonlinear initial value problems
Authors: Kujawski Jerzy 
Published: August 2005

AbstractBy use of a collocation time finite element formulation a modification of the well‐known generalized midpoint method is derived. The new family possesses an additional free parameter. This allows for significant improvement of the numerical solution in strongly nonlinear situations. Numerical results show the accuracy of the proposed algorithm in comparison to the midpoint method.
The hybrid‐Trefftz finite element model and its application to plate bending
Authors: Jirouseka J. , Guex Lan 
Published: August 2005

AbstractThis paper presents a new hybrid element approach and applies it to plate bending. In contrast to more conventional models, the formulation is based on displacement fields which fulfil a priori the non‐homogeneous Lagrange equation (Trefftz method). The interelement continuity is enforced by using a stationary principle together with an independent interelement displacement. The final unknowns are the nodal displacements and the elements may be implemented without any difficulty in finite element libraries of standard finite element programs. The formulation only calls for integration along the element boundaries which enables arbitrary polygonal or even curve‐sided elements to be generated. Where relevant, known local solutions in the vicinity of a singularity or stress concentration may be used as an optional expansion basis to obtain, for example, particular singular corner elements, elements presenting circular holes, etc. Thus a high degree of accuracy may be achieved without a troublesome mesh refinement. Another important advantage of the formulation is the possibility of generating by a single element subroutine a large number of various elements (triangles, quadrilaterals, etc.), presenting an increasing degree of accuracy. The paper summarizes the results of numerical studies and shows the excellent accuracy and efficiency of the new elements. The conclusions present some ideas concerning the adaptive version of the new elements, extension to nonlinear problems and some other developments.
Effectiveness of linear bifurcation analysis for predicting the nonlinear stability limits of structures
Authors: Chang S.‐C. , Chen J.‐J. 
Published: August 2005

AbstractAs an effort to predict effectively the actual collapse load of a structure, a series of numerical studies on the stability of shell structures are made. The difference in formulation between the two types of linear buckling loads, the classical and the fully linearized, is first demonstrated. Their correlations with respect to the actual stability limit of the structure are compared, and finally the two types of critical load approximations are obtained at various stages of a nonlinear analysis to study the pattern of convergence to the actual collapse load. It is found that the fully linearized buckling analysis, when combined with nonlinear analysis, can serve as a useful tool for prediction of the stability limit of a structure. While for most types of structures the approximation is within engineering accuracy, the rate of convergence of the extrapolated critical load also gives some insight to the accuracy of the approximation.
DEM: A new computational approach to sheet metal forming problems
Authors: Cavendish James C. , Wenner Michael L. , Burkhardt John , Hall Charles A. , Rheinboldt Werner C. 
Published: August 2005

AbstractMany current approaches to finite element modelling of large deformation elastic—plastic forming problems use a rate form of the virtual work (equilibrium) equations, and a finite element representation of the displacement components. Called the incremental method, this approach produces a three‐field formulation in which displacements, stresses and effective strain are dependent variables. Next, the formulation is converted to a one‐field displacement formulation by an algebraic time discretization which uses a low order explicit time‐stepping procedure to integrate the equations. This approach does not produce approximations which satisfy the discrete equilibrium equations at all times and, moreover, the advantage of the single‐field algebraic formulation is realized at the expense of very small time steps needed to produce stability and accuracy in the numerical calculations.This paper describes a variant of the mixed method in which all three field variables (displacements, stresses and effective strain) are given finite element representations. The discrete equilibrium equations then generate a nonlinear system of algebraic equations whose solutions represent a manifold, while the constitutive equations form a system of ordinary differential equations. A commercially available, variable time step/variable order code is then used to integrate this differential/algebraic system. When applied to the problem of hydrostatic bulging of a membrane, the new approach requires far less computer time than the incremental method.
Control of zero‐energy modes in 9‐node plane element
Authors: Verhegghe Benedict , Powell Graham H. 
Published: August 2005

AbstractFor plane stress/plane strain analysis, the 9‐node quadrilateral element performs better than the corresponding 8‐node element, especially for non‐rectangular shapes. For improved element flexibility and lower computer cost, 2 × 2 quadrature is generally preferable to 3 × 3 quadrature. Unfortunately the 9‐node element contains spurious zero‐energy modes when under‐integrated. A method is proposed to restrain these modes without significant loss of accuracy or added cost.
Predicted axial temperature gradient in a viscoplastic uniaxial bar due to thermomechanical coupling
Authors: Allen D. H. 
Published: August 2005

AbstractThe thermomechanical response of a uniaxial bar with thermoviscoplastic constitution is predicted herein using the finite element method. After a brief review of the governing field equations, variational principles are constructed for the one‐dimensional conservation of momentum and energy equations. These equations are coupled in that the temperature field affects the displacements and vice versa. Due to the differing physical nature of the temperature and displacements, first‐order and second‐order elements are utilized for these variables, respectively. The resulting semi‐discretized equations are then discretized in time using finite differencing. This is accomplished by Euler's method, which is utilized due to the stiff nature of the constitutive equations. The model is utilized in conjunction with stress‐strain relations developed by Bodner and Partom to predict the axial temperature field in a bar subjected to cyclic mechanical end displacements and temperature boundary conditions. It is found that spacial and time variation of the temperature field is significantly affected by the boundary conditions. The nomenclature used is given in an Appendix.
Computer evaluation of singular integrals and their applications
Authors: Fabrikant V. I. 
Published: August 2005

AbstractAn algorithm and a standard subroutine are developed for the evaluation of singular integrals over arbitrary two‐dimensional domains. The integrand is a product of a Green's function with another function having a weak singularity at the boundary of the domain. Formulae are derived for an accurate estimation of the integral in the neighbourhood of the singularities. The integral over the rest of the domain is evaluated by a library subroutine. The software developed is applied to a study of some contact problems of the theory of elasticity for non‐classical domains.
Numerical solution of constrained non‐linear algebraic equations
Authors: Shacham Mordechai 
Published: August 2005

AbstractThe numerical solution of n non‐linear algebraic equations with n unknowns, when any or all of the variables are subjected to constraints, is discussed. Distinction is made between physical and absolute constraints. It is shown, using a set of test problems, that solution of constrained equations does require a special approach. It is found that the step length restricted Newton's method performs best for problems with absolute constraints. Physical constraints can be best handled using a continuation method or penalty functions.
Improved co‐ordinate transformations for finite elements: The Lagrange cubic case
Authors: Celia Michael A. , Gray William G. 
Published: August 2005

AbstractA modified isoparametric co‐ordinate transformation is developed for the case of Lagrange cubic finite elements. This modified transformation produces significant improvements in solution accuracy while eliminating troublesome aspects of the standard isoparametric mapping. In particular, zero Jacobians in the standard transformation, which can occur in elements having non‐uniform node spacing, are completely eliminated with the new transformation. Within the analysis, the range of node locations for which the standard transformation is valid (the Jacobian does not vanish) is determined. The treatment of curved sides is discussed and illustrated. Example calculations using two‐dimensional serendipity elements show that the new transformation provides solutions that are as much as several orders of magnitude more accurate than those computed using the standard formulation.
A weak variational formulation for the propagation of Love waves
Authors: Serón F. J. , Badal J. 
Published: August 2005

AbstractThis paper describes the fundamental principles of the mathematical method used by the authors in discussing the direct geophysical problem of analysing the behaviour of the Atlantic continental margin of the Iberian Peninsula as a transmission medium of seismic energy.In order to resolve this problem, a weak variational formulation is proposed, building up an approximate solution by means of a semidiscrete treatment with the finite element method.The excitation of that non‐subductive ocean‐continent transition zone is supposed to be caused by Love waves normally incident at the continental boundary. The physical and geometrical parameters describing the model are obtained using as a starting point the experimental data known for this zone.The work shows the main results that we have obtained, the geophysical interpretation of which can be seen in Reference 1. Finally we proposed a large variety of open problems to which analogous techniques can be applied, owing to the extended validity of the proposed method.
Surfaces of minimum area by FEM
Authors: Pramila A. , Virtanen S. 
Published: August 2005

AbstractIn many practical applications it is desired to describe a surface enclosing a given volume which has to possess a minimum area. Moreover, there are engineering criteria, e.g. the requirement of minimum resistance, which cannot be involved in the present interpolation algorithms of the existing CAD systems. The present paper describes an approach where the surface creation task is formulated as a constrained minimization problem. The pointwise specified co‐ordinates are used as boundary conditions. The volume enclosed is a constraint, and the functional under minimization is the surface area. Thus, as the viscous resistance is roughly proportional to the area of the wetted surface, the result approximates the form having minimum viscous resistance. The finite element method is employed and the elements used are C1 continuous isoparametric elements to be able to represent infinite slopes. In the light of applications studied thus far it can be said that the method converges and is thus capable of creating surfaces of minimum area enclosing a given volume.
Minimum weight design of cylindrical water tanks
Authors: Thevendran V. , Thambiratnam David P. 
Published: August 2005

AbstractThe paper deals with the minimum weight design of cylindrical water tanks. The design is to conform to BS5337. The design procedure used is a combination of the finite element analysis of structures and a numerical method of optimization. In the design, the internal radius and the height of the tank are fixed and the variation of wall thickness is treated as the unknown of the design. Only piecewise linear variations of thickness are considered. Results of some examples are presented and discussed.
A new mode renumbering algorithm for bandwidth reduction
Authors: Burgess I. W. , Lai P. K. F. 
Published: August 2005

AbstractA new algorithm is presented for automatic renumbering of systems of interconnected nodes so as to minimize the bandwidth of the connectivity matrix. This is necessary to reduce storage requirements for banded matrix solution techniques. The method is based on those due to Cuthill and McKee1 and Gibbs, Poole and Stockmeyer.2 Under test against several other algorithms on a range of 20 examples of various types it always performed at least as well as, and in most cases better than, the best of the other methods. Seven examples are given in the paper, comparing final bandwidths with those produced by seven other algorithms.
Vibration and buckling of beam‐columns subjected to non‐uniform axial loads
Authors: Coulter Brett A. , Miller Robert E. 
Published: August 2005

AbstractThe small‐displacement free vibration of elastic Euler‐Bernoulli beams subjected to non‐uniform axial forces and the buckling of elastic columns are both analysed by means of various types of beam finite elements. The procedure incorporates beams and columns of varying cross‐sections, such as linear tapers, inhomogeneous beams and columns, distributed axial forces, elastic end and interior restraints and point masses with linear and rotary inertias. All of these topics individually or in some combinations have been analysed by others. The purpose of this paper is to bring together under a single umbrella the various problems studied by others, and to provide the solution to one problem apparently not yet solved—the buckling and vibration of tapered columns under non‐uniform axial thrust. The mass, stiffness and geometric stiffness matrices for the standard beam element are fully written out for direct incorporation into existing finite element programs. A FORTRAN subroutine for generating these matrices, and those for various higher‐order beam elements, is also provided.
An efficient finite‐difference scheme for multidimensional Stefan problems
Authors: Wood A. S. 
Published: August 2005

AbstractIn this paper the enthalpy approach for solving Stefan problems is applied to a three‐dimensional situation. A novel and particularly efficient finite‐difference scheme is then used to solve the resulting equations. As a starting solution for the numerical algorithm, a three‐dimensional result using the heat‐balance integral method is obtained for the case of heat flow in two phases with, possibly, different thermal properties.
The patch test for mixed formulations
Authors: Zienkiewicz O. C. , Qu S. , Taylor R. L. , Nakazawa S. 
Published: August 2005

AbstractThis paper presents a simple extension of the patch test to mixed formulations to provide the necessary and sufficient conditions for convergence. The general algebraic conditions of Babuska and Brezzi are given a simple form and a conceptual application of the patch tests serves to point out the instability of several well known formulations for incompressible problems. The test is also applied to mixed displacement—strain formulations of elasticity, and limiting formulations are noted.
Hybrid element method for unbounded electromagnetic problems in hyperthermia
Authors: Lynch Daniel R. , Paulsen Keith D. , Strohbehn John W. 
Published: August 2005

AbstractFinite element and boundary element methods are described for predicting high‐frequency electromagnetic heating of tissue as a cancer therapy. For the class of clinical problems of interest, the patient is electrically inhomogeneous and best discretized by finite elements, but the unbounded nature of practical source configurations calls for a boundary element approach. A hybrid is introduced which couples the two methods and is superior in algebraic requirements to either method alone. The formulation is three‐dimensional and allows exact satisfaction of the electromagnetic jump conditions at interfaces separating distinct tissue types. Test cases show its validity for transverse magnetic and electric situations with known solutions. Examples of clinical applications are shown.
Derivation of Lagrangian and Hermitian shape functions for quadrilateral elements
Authors: El‐Zafrany A. , Cookson R. A. 
Published: August 2005

AbstractThis paper introduces a general theory for the derivation of the shape functions for the quadrilateral family of finite elements. The first section deals with the Lagrangian shape functions for the cases of uniform and boundary‐described elements. Two basic procedures are introduced; the first by linear combinations of side‐interpolations and the second by superposition. The remainder of the paper introduces a theory for the general uniform Hermitian element of any order. Details for quadrilateral elements, with first order derivatives are explained. All of the shape functions presented here were derived in the interval [0,1].The shape functions, developed by such an engineering approach, have been used successfully in the ABSEA Finite Element System of Cranfield Institute of Technology.
A mechanical dynamic programming algorithm for structure optimization
Authors: Schnack Eckart , Spörl Uwe 
Published: August 2005

AbstractStructure optimization for problems of solid mechanics is gaining in importance. Of special interest to the ship and aeroplane designer is optimizing changes in sections and hols in such a way that the largest value of the von Mises stress becomes as small as possible, to optimize the use of material. Also, the temporal beginning of crack propagation should be delayed as long as possible. A dynamic programming formulation for structure optimization is presented and mechanical theorems fix an iterative solution process.
Triangular and tetrahedral space‐time finite elements in vibration analysis
Authors: Bajer Czesław I. 
Published: August 2005

AbstractRecently, several methods of time integration of the equations of motion have been proposed. Many of them result in square mass, damping and stiffness matrices. The space–time finite element method is an extension of the FEM, familiar to most engineers, over the time domain. A special approach enables the use of triangular, tetrahedral and hyper‐tetrahedral elements in time and space. By special division of the space–time layer the triangular matrix of coefficients in the system of equations can be obtained. A simple algorithm enables the storage of non‐zero coefficients only. Dynamic solution requires a small amount of the memory compared to other methods, and ensures considerable reduction of arithmetic operations. The method presented is also efficient in solving both linear and non‐linear problems. Matrices for a beam and plane stress/strain element are derived. Exemplary problems solved by the method described have proved the effectiveness of the application of triangular and tetrahedral space–time elements in vibration analysis.