bluuebunny/crossref_metadata_2025_split huggingface dataset:
Internally discontinuous finite elements for moving interface problems
Authors: Steven Grant P. 
Published: August 2005

AbstractAll physical process change with time and although physicists and engineers often freeze them to simplify their model studies, this is not always possible. Add to this the existence of several subregions within the modelling domain with different physical properties, the size and number of which change with time, and one has produced what might appear to be an intractable problem. Previous studies have shown that adaptive grids are an inconvenient way of modelling such moving interface problems and suggested that the use of a fixed grid with special discontinuous elements affords an efficient solution technique.This work presents and develops the characteristic matrices for two such elements, namely a quadratic triangle with an internal interface modelled by two straight lines and a quadratic isoparametric element. Both these elements are tested against an analytical solution to a simple Poisson equation. Such tests reveal the performance of the proposed elements to be satisfactory except for the definition of gradients near the interface.
Semi‐implicit transient analysis procedures for structural dynamics analysis
Authors: Park K. C. , Housner J. M. 
Published: August 2005

AbstractA semi‐implicit direct time integration procedure is presented which avoids factorization of the implicit difference solution matrix. The procedure, if properly implemented, requires only vectorial calculations and hence needs the same computer core space as explicit integration procedures. Guidelines for splitting the stiffness matrix into upper and lower matrices are established, which among other things are designed to satisfy a correct transmission of rigid‐body motions from element (or grid) to its adjacent elements.
A rational function approximation for the integration point in exponentially weighted finite element methods
Authors: Flaherty Joseph E. 
Published: August 2005

AbstractA rational function is presented for approximating the function f(z)=coth z‐1/z that appears in several exponentially fitted or weighted finite difference and finite element methods for convection‐diffusion problems. The approximation is less expensive to evaluate than f(z) and provides greater accuracy than the doubly asymptotic approximation when z = O(n1).
Automatic constraining of linear dependencies
Authors: Kark S. K. , Scholes A. 
Published: August 2005

AbstractA common cause of costly abortive computer structural analysis runs is the failure to identify and constrain linear dependencies inthe stiffness matrix, most of which results from axis transformation. This paper describes a very simple and economical method for automatic constraining the linear dependencies in structure made up of plates and beams. It can be easily installed in general‐purpose finite element programs.
A seventh‐order numerical method for solving boundary value nonlinear ordinary differential equations
Authors: Tewarson R. P. 
Published: August 2005

AbstractA numerical method for solving two‐point boundary value problems associated with systems of first‐order nonlinear ordinary differential equations is described. It needs three function evaluations for each sub‐interval and is of order O(h7), where h is the space chop. Results of computational experiments comparing this method with other known methods are given.
Time domain approximations in the solution of fields by time domain diakoptics
Authors: Johns P. B. , Akhtarzad K. 
Published: August 2005

AbstractThe numerical solution of field substructures in time domain diakoptics requires an interation time consistent with the numerical accuracy required. When storing and reconnecting the substructures, the information required can be obtained from considerably fewer samples. This paper shows how time domain approximations can further reduce the storage and computing time in space approximated time domain diakoptics.
Swirl flow studies in diffusers using the flux analysis method with orthogonal curvilinear coordinates
Authors: Uchida S. , Nakamura Y. , Kondo T. 
Published: August 2005

AbstractA computational method of flux analysis is applied to the study of the swirling flow of different regimes through a diffuser pipe. The flux analysis method is an iterative procedure to construct a system of orthogonal curvilinear co‐ordinates consisting of stream‐surface and normals following the flow. Examples of the inviscid swirling flow of an incompressible fluid are calculated, and deformations of vortices in a diffuser pipe are studied. For a simple vortex with rigid rotation the deceleration of flow is remarkable on the axis, where the total energy has the lowest level. For a Burgers type vortex, provided the circulation number exceeds a critical value, the rate of deceleration of flow along the axis become more pronounced for only a slight increase of swirl strength, and ultimately a stagnation point appears on the axis. The present method, however, may not be applied to the flow with stagnation point.
Control of spurious modes in the nine‐node quadrilateral element
Authors: Cook Robert D. , Zhao‐Hua Feng 
Published: August 2005

AbstractThe nine‐node quadrilateral is much more accurate than its eight‐node relative if elements are non‐rectangular. However, the nine‐node element may display spurious low‐energy modes under 2 × 2 Gauss quadrature. These modes can be controlled by using the 3 × 3 quadrature rule, but at added cost. This paper investigates two inexpensive control devices that can be used with 2 × 2 Gauss quadrature.
A partitioned frontal solver for finite element analysis
Authors: Beer G. , Haas W. 
Published: August 2005

AbstractA frontal solution program is presented, based on the original work of Irons, published in 1970. The main drawback of the original frontal solution program that the complete front matrix has to reside in core has been overcome by ‘partitioning’ the front matrix. The programming strategy has been optimized to (a) minimize the number of I/O operations on the partitioned front‐matrix (b) optimize the speed of I/O transfer between high speed memory and slow peripheral (or secondary) storage media, and (c) make the program transportable and easily implementable on different types of computers, including mini‐ and micro‐computers.
An implementation of the boundary element method for zoned media with stress discontinuities
Authors: Rudolphi Thomas J. 
Published: August 2005

AbstractThe boundary element method as it applies to two‐dimensional elastostatic problems is implemented with quadratic variation in boundary variables and geometry. Additional parameters are associated with nodes at segment intersections to allow for discontinuous tractions. Supplementary equations consistent with linear elasticity are used to augment the regular boundary integral equations for certain mixed and displacement boundary conditions. Zoning or subregionalization capabilities are included to provide solutions to piecewise nonhomogeneous problems or problems on regions of irregular shape. Example problems are given to demonstrate the accuracy of the technique.
A relaxation technique for evaluating stress intensity factors by the finite element method
Authors: Theocaris P. S. , Theotokoglou E. E. , Tsamasphyros G. 
Published: August 2005

AbstractA simple two‐step corrective technique is presented in this paper for evaluating stress intensity factors in crack problems. In the first step an approximate evaluation of the stress intensity factor was made by considering the cracked plate to be of infinite size. The stresses of the problem were relaxed by the stresses of the infinite body which corresponds to the approximate value of the stress intensity factor. The expected discrepancy in the value of SIF by the infinite plate approximation was corrected in the second step where the existing residual stresses are equilibrated at the cracked plate by using any of the conventional finite element techniques and the corrective value of the stress intensity factor is calculated by using an appropriate collocation formula. The method was applied to three typical plane problems of cracked plates with satisfactory results.
On the problem of two coplanar cracks inside an infinite isotropic elastic solid
Authors: Mastrojannis E. N. , Mura Toshio 
Published: August 2005

AbstractA method is proposed for the approximate evaluation of normal displacements and normal stresses on the plane of two coplanar cracks located inside an infinite isotropic elastic solid and subjected to normal internal pressure. The formulation results in a single integral equation for the unknown normal stresses on the plane of the cracks. Numerical results are given for the stress intensity factor KI of two coplanar circular cracks and two coplanar elliptical cracks opened up under a uniform internal pressure.
Development of mixed time partition procedures for thermal analysis of structures
Authors: Liu Wing Kam 
Published: August 2005

AbstractThe computational methods used to predict and optimize the thermal‐structural behaviour of aerospace vehicle structures are reviewed. In general, two classes of algorithms, implicit and explicit, are used in transient thermal analysis of structures. Each of these two methods has its own merits. Due to the different time scales of the mechanical and thermal responses, the selection of a time integration method can be a difficult yet critical factor in the efficient solution of such problems.Therefore mixed time integration methods for transient thermal analysis of structures are being developed. This proposed methodology would be readily adaptable to existing computer programs for structural thermal analysis.
Computations in limit analysis for plastic plates
Authors: Christiansen Edmund , Larsen Søren 
Published: August 2005

AbstractA class of mixed finite element discretizations of the problem of limit analysis for plastic plates is analysed. For the discrete problem we discuss a linear programming approach based on linearization of the yield condition and a convex programming approach based on the exact Mises condition. Applying the method to rectangular plates with uniform load and concentrated loads we get improved and new results partly in disagreement with one of our references.
Finite element iterative techniques for determining the interface boundary between Laplace and Poisson domains—characteristic analysis of a field effect transistor
Authors: Kagawa Yukio , Murai Tadakuni , Matsumoto Osamu 
Published: August 2005

AbstractTwo kinds of techniques for solving a shape determination problem are proposed. The determination of the interface boundary between two domains governed by Poisson and Laplace equations under the compatible and constraint condition is considered. Influence coefficient and inverse variational approaches are examined by using the iterative finite element procedure. A two‐dimensional model of a junction‐type field effect transistor is a test example. The determination of its interface boundary and the prediction of the potential distribution and static characteristic are demonstrated.
A numerical solution of singular integral equations without using special collocation points
Authors: Tsamasphyros G. , Theocaris P. S. , Stassinakis C. A. 
Published: August 2005

AbstractA new technique for the solution of singular integral equations is proposed, where the unknown function may have a particular singular behaviour, different from the one defined by the dominant part of the singular integral equation. In this case the integral equation may be discretized by two different quadratures defined in such a way that the collocation points of the one correspond to the integration points of the other. In this manner the system is reduced to a n × n system of discrete equations and the method preserves, for the same number of equations, the same polynomial accuracy. The main advantage of the method is that it can proceed without using special collocation points. This new technique was tested in a series of typical examples and yielded results which are in good agreement with already existing solutions.
Determination of the meridian and stresses of the drop‐shaped tank
Authors: Sofoluwe A. B. 
Published: August 2005

AbstractAn algorithm based on a new formulation of problem is used in generating the co‐ordinates of the meridian of the drop‐shaped tank. The stresses and moments of this form, due to the varying hydrostatic pressure head, are obtained by a finite element simulation and the usefulness of this approach is assessed.
Universal serendipity elements
Authors: Çitipitioǧlu Ergin 
Published: August 2005

AbstractUniversal serendipity elements (USE) are defined as isoparametric elements having linear, quadratic and cubic node configurations at their edges in an arbitrary manner. Formulation of shape functions and their derivatives for USE is presented. A computer algorithm which allows the efficient application of USE is explained. Only corner nodes are kept transparent to the user. Changing the order of USE is fully automated. It is concluded that the USE concept allows interactive mesh refinement in an efficient manner and eliminates the difficulties encountered in the use of higher order isoparametric serendipity elements.
An algorithm for engineering design optimization
Authors: Belsare Sharad V. , Arora Jasbir S. 
Published: August 2005

AbstractIn this paper a new concept for development of algorithms for optimal design of engineering systems is presented. The basic idea is to use upper and lower bounds on optimum cost to develop iterative search strategies. The main feature of the concept is that it does not rely on one‐dimensional search to compute a step size at any design iteration. Implication of the feature is that the algorithms based on this concept require evaluation of constraint functions only once at any design iteration. This is highly desirable for optimal design of engineering systems because evaluation of functions for such systems is very expensive due to their implicit dependence on design variables. An algorithm based on the new concept is derived in the paper. Several new step sizes are introduced and their relation to proper reduced optimal design problems are presented. A new step size based on the constant cost requirement at some design iterations is introduced. Numerical aspects for the algorithm are also presented. Based on the new algorithm, a general‐purpose computer code GRP2 is developed. The code is used to solve several problems to gain experience and insight for the algorithm. Numerical experience with examples is discussed. It is concluded that algorithms based on bounding optimum cost have substantial potential for applications in optimal design of engineering systems.
An alternative high‐order finite element formulation for cylindrical field problems
Authors: Daly P. 
Published: August 2005

AbstractEarlier formulations of the finite element approach to cylindrical (rz) field problems led initially to variational expressions containing a simple term in 1/r and consequent attempts to remove it by appropriate choice of interpolation functions. The present paper uses new interpolation functions which ensure that the field behaviour near the axis is correctly modelled. High‐order finite elements up to order four are derived and tested on a special cylindrical geometry to confirm, in a practical case, the theoretical claims of improved rates of convergence in solving problems of engineering significance.
On the performance of the enthalpy method in the region of a singularity
Authors: Bell G. E. , Wood A. S. 
Published: August 2005

AbstractA test problem is presented which provides a realistic challenge for computational techniques designed for the prediction of temperature distributions in melting/freezing processes. It is shown that a suitably modified finite difference implementation of the enthalpy method produces results that are perhaps adequate for practical purposes. However, the best approach to problems typified by the test problem remains to be found.
Finite elements for the dynamic analysis of fluid‐solid systems
Authors: Wilson Edward L. , Khalvati Mehdi 
Published: August 2005

AbstractSeveral new finite elements are presented for the idealization of two‐ and three‐dimensional coupled fluid‐solid systems subjected to static and dynamic loading. The elements are based on a displacement formulation in terms of the displacement degrees‐of‐freedom at the nodes of the element. The formulation includes the effects of compressible wave propagation and surface sloshing motion.The use of reduced integration techniques and the introduction of rotational constraints in the formulation of the element stiffness eliminates all unnecessary zero‐energy modes. A simple method is given which allows the stability of a finite element mesh of fluid elements to be investigated prior to analysis. Hence, the previously encountered problems of ‘element locking’ and ‘hour glass’ modes have been eliminated and a condition of optimum constraint is obtained.Numerical examples are presented which illustrate the accuracy of the element. It is shown that the element behaves very well for non‐rectangular geometry. The optimum constraint condition is clearly illustrated by the static solution of a rigid block floating on a mesh of fluid elements.
Stabilization of partitioned solution procedure for pore fluid‐soil interaction analysis
Authors: Park K. C. 
Published: August 2005

AbstractThe conventional staggered solution of pore fluid‐soil interaction problems is shown to suffer from stability restriction. This paper presents a stabilized form of the staggered solution procedure of the problem. Computational overhead for this stabilization is shown to be modest and hence this stabilized procedure is recommended for production implementation for pore fluid‐soil interaction analysis.
Analysis of free surface flows using isoparametric finite elements
Authors: Bettess Peter , Bettess Jacqueline A. 
Published: August 2005

AbstractA theory for free surface flow using variable geometry finite elements is numerically modelled using isoparametric finite elements, for the first time. The resulting nonlinear equations are solved using the Newton‐Raphson method. Because a functional is used as the basis of the formulation, the resulting equations are symmetrical. The realistic problem of flow over a Crump weir is solved for a large range of discharges.
A substructuring application of the virtual crack extension method
Authors: Hellen T. K. 
Published: August 2005

AbstractThe virtual crack extension method (VCE) is a very effective tool with finite elements for the accurate evaluation of stress intensity factors in two‐ or three‐dimensional structures. The method utilizes the concept of extending any node on the crack profile in any required direction and by any required amount. A new facility stores a relevant substructure of crack tip stiffnesses so that any number of restarts, each with a new set of extensions, can be performed. Different nodes around three‐dimensional crack profiles can be considered, either at vertex or midside node positions. The extension of the vertex nodes, in particular, also involves moving adjacent midside nodes along the profile, and different ways of effecting this, together with the calculation of the relevant area change, have been introduced and are described along with illustrative examples.
On the importance of the discrete maximum principle in transient analysis using finite element methods
Authors: Rank Ernst , Katz Casimir , Werner Heinrich 
Published: August 2005

AbstractIn transient analysis it is generally thought that small time steps can only improve the accuracy, because standard stability theorems limit the maximum time step for a given mesh size. In finite element approximations, however, small time steps may cause stability problems which lead to physically unreasonable results. It is shown that this is due to the violation of a discrete maximum principle. The influence of lumped and consistent mass matrices on a stable discretization of time and space is presented.
Anisotropic cylindrical shell element based on discrete Kirchhoff theory
Authors: Murthy S. Sridhara , Gallagher Richard H. 
Published: August 2005

AbstractA triangular cylindrical shell element based on discrete Kirchhoff theory is developed. It is a three‐node, 27‐degrees‐of‐freedom element using cubic polynomials for the tangential and normal displacement interpolations. The normal rotations are independently interpolated by quadratic polynomials. The formulation is capable of modelling general anisotropy representative of multi‐layered, multi‐directionally oriented composite construction. The numerical results indicate that the solution for displacements and stresses of cylindrical shells converge monotonically and rapidly to those based on deep shell theory.
Boundary integral equation method for linear porous‐elasticity with applications to soil consolidation
Authors: Cheng Alexander H‐D. , Liggett James A. 
Published: August 2005

AbstractFor 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.
On quadrature and singular finite elements
Authors: Solecki J. S. , Swedlow J. L. 
Published: August 2005

AbstractSpecial quadrature rules are described for elastic finite elements that haverqbehaviour (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.
A note on discontinuous numerical solutions of the kinematic wave motion
Authors: Lewis R. W. , Morgan K. , Pugh E. D. L. , Smith T. J. 
Published: August 2005

AbstractThis note discusses the numerical solution of the kinematic wave equation under those conditions when the solution contains a discontinuous shock. A finite element solution is described in which shocks are represented by discrete nodal discontinuities. The implementation of the method follows conventional finite element practice over the shockless regions of the solution domain which are coupled by frontal constraints. The basis of the method and examples of its application to the solution of the kinematic wave equation in one and two dimensions are presented.