bluuebunny/crossref_metadata_2025_split huggingface dataset:
Continuity conditions for finite element analysis of solids
Authors: De Almeida J. P. Moitinho , De Freitas J. A. Teixeira 
Published: August 2005

AbstractIn conventional finite element formulations the concept of node—a point where one of the shape functions is unitary and all others are nil—is used to advantage as it simplifies the definition of interelement continuity conditions.This constraint on the definition of the shape functions hinders the formulation of elements with complex shapes and, in particular, of equilibrium elements.In the approach presented herein linearly independent functions are defined within each element irrespectively of the location of the nodes. Interelement continuity conditions are imposed ‘a posteriori’, as in hybrid elements.The derivation of the element matrices is based upon the equations expressing equilibrium, compatibility and the constitutive relations without explicitly using variational principles.This results in a wider choice of available funciiuns ami in an easier way to formulate equilibrium elements and/or to use conforming or non‐conforming elements.As the approach used is independent of the choice of basic functions and of the shape of the elements, it is perfectly general. It allows the parallel analysis of kinematically and statically admissible formulations, as proposed by Fraeijs de Veubeke.1As the interelement continuity conditions are imposed ‘a posteriori’ new variables are used to express this condition.
Geometrically non‐linear enhanced strain mixed methods and the method of incompatible modes
Authors: Simo J. C. , Armero F. 
Published: August 2005

AbstractA class of ‘assumed strain’ mixed finite element methods for fully non‐linear problems in solid mechanics is presented which, when restricted to geometrically linear problems, encompasses the classical method of incompatible modes as a particular case. The method relies crucially on a local multiplicative decomposition of the deformation gradient into a conforming and an enhanced part, formulated in the context of a three‐field variational formulation. The resulting class of mixed methods provides a possible extension to the non‐linear regime of well‐known incompatible mode formulations. In addition, this class of methods includes non‐linear generalizations of recently proposed enhanced strain interpolations for axisymmetric problems which cannot be interpreted as incompatible modes elements. The good performance of the proposed methodology is illustrated in a number of simulations including 2‐D, 3‐D and axisymmetric finite deformation problems in elasticity and elastoplasticity. Remarkably, these methods appear to be specially well suited for problems involving localization of the deformation, as illustrated in several numerical examples.
A numerical model for determining the motion of a bubble close to a fixed rigid structure in a fluid
Authors: Harris P. J. 
Published: August 2005

AbstractThis paper is concerned with the problem of modelling the motion of a bubble close to a rigid structure in an infinite fluid. It is well known that the boundary integral method is a powerful technique for modelling the motion of a single bubble in a fluid. In this paper we shall present a modified boundary integral method for modelling the motion of a bubble close to a fixed finite rigid structure, and discuss a numerical scheme for solving the resulting integral equation for three‐dimensional problems. Finally, we illustrate our method with some typical numerical results.
Analysis of parameter estimation heat conduction problems with phase change using the finite element method
Authors: Ouyang Tianhong 
Published: August 2005

AbstractA solution to a parameter estimation problem in heat conduction with phase change is presented. Specifically, the thermophysical properties of the material are estimated by using the temperature measurements of several sensors located inside the fixed domain.In the parameter estimation problem the error is minimized between given and modelled temperatures at sensor locations over the time interval where the experiment involved variation of the material parameters. The methods are illustrated with several examples. The effects on the solution of the locations of the sensors, the number of the sensors, the time step and the number of time steps are examined.
Stress oscillations and spurious load mechanisms in variationally inconsistent assumed strain formulations
Authors: Prathap G. , Naganarayana B. P. 
Published: August 2005

AbstractAssumed field‐consistent strain formulations of the displacement finite element procedure can lead to poor convergence and spurious stress oscillations if the assumed strain fields are not variationally correct, i.e. they do not satisfy an important orthogonality condition emerging from the equivalence sought between assumed strain displacement procedures and mixed procedures based on the Hellinger–Reissner theorem. Failure to ensure variational correctness introduces errors which can be equated to the presence of spurious loading mechanisms that cause stress oscillations. In this paper, we use the Timoshenko beam element to demonstrate that field‐consistency and variational' consistency are two complementary but mutually exclusive principles—one does not imply the other and that both are necessary to successfully implement a displacement type finite element for constrained media.
A Laplace‐transform‐based three‐dimensional BEM for poroelasticity
Authors: Badmus T. , Cheng A. H‐D. , Grilli S. 
Published: August 2005

AbstractThis paper presents the formulation and the numerical implementation of a three‐dimensional direct boundary element method for the Biot theory of poroelasticity. To avoid the need of time‐stepping and volume integration, the solution is performed in the Laplace transform space. Solution in time is obtained via numerical inversion. Several examples, including the settlement of a rectangular footing and a modified Mandel problem, are examined.
Triangular C0 bending elements based on the Hu‐Washizu principle and orthogonality conditions
Authors: Karakostas C. , Talaslidis D. , Wempner G. 
Published: August 2005

AbstractThis paper deals with simple and effective C0 linear triangular bending elements based on the Hu‐Washizu variational principle. The following key features are inherent in the proposed formulation: extensional, flexural and transverse shear strains and the corresponding stresses are referred to the directions of the triangle sides. The independent variation of displacements, strains and stresses yields discrete approximations consistent with the continuum theory. Furthermore, a proper identification of the deformational modes and the orthogonality requirements between the assumed transverse shear forces and the undesirable strain fields lead to element formulations with important attributes: minimization of superfluous energy, properly justified assumptions, simplicity of formulation and straightforward extension to non‐linear problems. Alternative approximations of strains and stresses, also presented, enhance the element performance in the case of both thick and thin plates and shells. Test examples demonstrate the characteristic properties of the proposed element formulations.
On improved predictions for structural equilibrium path evaluations
Authors: Eriksson Anders 
Published: August 2005

AbstractThe paper describes how several procedures for higher‐order predictions have been introduced in order to improve the convergence speed in a general finite element program for non‐linear structural analysis. In addition to higher‐order Taylor expansions earlier discussed, Lagrangian extrapolations and some methods commonly used for the integration of initial value problems have been introduced. The methods are used for improved predictions in the stepwise solution of equilibrium states and for accurate descriptions of the initial post‐bifurcation behaviour. They are used in a general solution algorithm, based on a parameter formulation. The methods are discussed in the light of the strategies for re‐creation of the tangential stiffness matrix, used for equilibrium iterations.Numerical examples, exhibiting different limit and bifurcation behaviours for trusses, frames and shells, are used to evaluate the numerical properties and efficiencies of the methods.The paper concludes that the overall efficiency in the algorithm can be improved by introduction of more accurate predictions than the standard Euler prediction. In terms of reliability combined with efficiency, an implicit generalized Simpson method is the preferred method.
Generalized midpoint finite element dynamic analysis of elastoplastic systems
Authors: Corigliano A. , Perego U. 
Published: August 2005

AbstractThe application of a four‐parameter generalized midpoint integration method to small‐displacement elastoplastic dynamic problems is considered. The integration of the governing relations over a time step is formulated as a non‐linear algebraic problem (finite‐step problem) by making use of generalized variables finite element modelling. Uniqueness and an extremum characterization of the solution of the finite‐step problem are discussed. Sufficient conditions for convergence of various iterative algorithms, including Newton‐Raphson, are given. The B‐stability of the proposed procedure is assessed.
Numerical methods for second‐order shape sensitivity analysis with applications to heat conduction problems
Authors: Hou Gene J. ‐W. , Sheen Jeenson 
Published: August 2005

AbstractIn this paper, two finite‐element‐based schemes for second‐order shape sensitivity analysis are presented. In the first formulation, the AV‐DD method, the first‐order shape sensitivity equation is derived and expressed in terms of state and adjoint variables. The resultant equation is then directly differentiated to obtain the second‐order shape sensitivity equation. In the second formulation, the DD‐AV method, the functional of concern is differentiated twice to yield the second‐order sensitivity equation in which the second‐order shape derivatives can be eliminated by introducing a proper adjoint equation. A thermal fin problem and a thermal insulation layer problem have been studied to validate the proposed schemes. It is shown that both methods yield identical results, though the DD‐AV method is computationally more efficient.
Computation of heat conduction in materials with random variable thermophysical properties
Authors: Nicolaï Bart M. , De Baerdemaeker Josse 
Published: August 2005

AbstractA method for the direct computation of mean values and variances of the temperature in conduction‐heated objects with random variable thermophysical properties is presented. This method is based on a Taylor expansion of the finite element formulation of the heat conduction equation and offers a powerful alternative to the computationally expensive Monte Carlo method. Both steady‐state and transient problems are considered. Some example problems are solved and the results discussed. The simulations indicate that the variability of the thermophysical properties may cause a considerable variability of the temperature within the heated object. This may have important consequences on the design of heating operations in food process engineering.
Moving‐grid finite element modelling of thermal ablation and consolidation in porous media
Authors: Mackinnon R. J. , Carey G. F. 
Published: August 2005

AbstractA moving‐grid finite element model for the analysis of thermal ablation, fluid flow and deformation in elastic porous media is presented. The model is formulated in terms of temperatures, fluid pressures and solid displacements, and takes into account a moving phase boundary. Supporting algorithms for treating the moving phase boundary and solving the coupled equations are described. The model has application to several important moving‐boundary geotechnical problems. Numerical test cases are provided for model verification and example applications corresponding to thermal ablation, consolidation and underground coal gasification are given.
Automatic partitioning of unstructured meshes for the parallel solution of problems in computational mechanics
Authors: Farhat Charbel , Lesoinne Michel 
Published: August 2005

AbstractMost of the recently proposed computational methods for solving partial differential equations on multiprocessor architectures stem from the 'divide and conquer' paradigm and involve some form of domain decomposition. For those methods which also require grids of points or patches of elements, it is often necessary to explicitly partition the underlying mesh, especially when working with local memory parallel processors. In this paper, a family of cost‐effective algorithms for the automatic partitioning of arbitrary two‐ and three‐dimensional finite element and finite difference meshes is presented and discussed in view of a domain decomposed solution procedure and parallel processing. The influence of the algorithmic aspects of a solution method (implicit/explicit computations), and the architectural specifics of a multiprocessor (SIMD/MIMD, startup/transmission time), on the design of a mesh partitioning algorithm are discussed. The impact of the partitioning strategy on load balancing, operation count, operator conditioning, rate of convergence and processor mapping is also addressed. Finally, the proposed mesh decomposition algorithms are demonstrated with realistic examples of finite element, finite volume, and finite difference meshes associated with the parallel solution of solid and fluid mechanics problems on the iPSC/2 and iPSC/860 multiprocessors.
Trefftz method for Kirchhoff plate bending problems
Authors: Jin W. G. , Cheung Y. K. , Zienkiewicz O. C. 
Published: August 2005

AbstractKirchhoff plate bending problems were studied by both the Trefftz direct and indirect approximations in which non‐singular, complete Trefftz functions are used as the weighting and/or trial functions. The Trefftz direct method involved only the quantities of engineering interest. Numerical results are given to show the efficiency and the excellent accuracy of the present method.
A new 3‐D finite element model to evaluate added mass for analysis of fluid‐structure interaction problems
Authors: Rajasankar J. , Iyer Nagesh R. , Rao T. V. S. R. Appa 
Published: August 2005

AbstractThe paper presents the results of investigations conducted to evaluate the added mass to represent fluid‐structure interaction effects in vibration/dynamic analysis of floating bodies such as ship hulls. While the structural plating is idealized by 9‐noded plate/shell finite elements, the fluid domain is modelled by 20‐noded/21‐noded 3‐D finite elements in the investigations conducted. A new 8‐noded element has been developed to model the interface between the structure and the fluid. An efficient computational methodology has been used for computation of added mass. The finite element models are validated by comparing the results with those given by analytical solution for a submerged sphere. The efficacy of the finite element model is demonstrated through convergence of the results obtained for a floating barge problem. A better convergence rate and distribution of added mass in three orthogonal directions have been obtained.
General behaviour of collapsed 8‐node 2‐D and 20‐node 3‐D isoparametric elements
Authors: Dhondt Guido 
Published: August 2005

AbstractThis paper presents a simple and thorough technique to examine the general behaviour of two‐dimensional (2‐D) 8‐node and 3‐D 20‐node isoparametric elements, collapsed at one side. With this method the conditions for the well‐known quarter‐point and half‐point elements, frequently used in fracture mechanics applications to model the crack tip behaviour, are arrived at in a natural way. It also allows for an in‐depth analysis of the Jacobian determinant, and can easily be applied to other types of elements.
Three‐dimensional solid‐to‐beam transition elements for structural dynamics analysis
Authors: Gmür Thomas C. , Kauten Randy H. 
Published: August 2005

AbstractComplex structural components such as those encountered in many industrial applications may generally be considered as being composed of shell‐ or beam‐like portions linked to three‐dimensional solid continua. When discretized into finite elements, these structures present geometrical and mathematical difficulties at the connections between the different element types since the nodal degrees of freedom allocated to the solid, shell and beam elements are incompatible with each other. The development of specific and reliable transition finite elements is, thus, of outstanding practical importance. This paper presents efficient C0 compatible transition elements with a variable number of nodes for modelling solid to beam junctions. Based upon the standard isoparametric solid and beam formulations, the current approach includes the properties of both solids and beams, verifies the basic continuity, smoothness and completeness criteria inherent in the finite element convergence requirements, and avoids the shear locking phenomenon typical of C0 elements by using a strain‐projection method. Several numerical examples which compare this formulation to analytical and experimental solutions are provided in order to show the applicability and efficiency of this approach.
Regularization of hypersingular and nearly singular integrals in the potential theory and elasticity
Authors: Sladek V. , Sladek J. , Tanaka M. 
Published: August 2005

AbstractBoth the hypersingular and nearly singular integrals, which appear in the hypersingular boundary integralequations and integral representations of the secondary fields, respectively, are regularized by the application of the superposition principle. Two kinds of the non‐singular formulations, namely, those with the strongly singular and weakly singular kernels, are presented in this paper. The formulations are given in terms of the relevant boundary quantities and the collocation at element junctions is possible. Two‐ and three‐dimensional problems are analysed simultaneously in a unique way for either internal or external problems of the potential theory and elasticity.
Generation of unstructured tetrahedral meshes by advancing front technique
Authors: Jin H. , Tanner R. I. 
Published: August 2005

AbstractAn algorithm for generating unstructured tetrahedral meshes by the advancing front technique is presented. Emphasis is placed on the construction of tetrahedral elements. Several measures are employed to prevent difficult situations. A control line/surface scheme is used to specify element size. Numerical examples are provided to show the performance of the algorithm.
Thin shells with finite rotations formulated in biot stresses: Theory and finite element formulation
Authors: Wriggers P. , Gruttmann F. 
Published: August 2005

AbstractA bending theory for thin shells undergoing finite rotations is presented, and its associated finite element model is described. The kinematic assumption is based on a shear elastic Reissner‐Mindlin theory. The starting point for the derivation of the strain measures are the resultant equilibrium equations and the associated principle of virtual work. Within this formulation the polar decomposition of the shell material deformation gradient leads to symmetric strain measures. The associated work‐conjugate stress resultants and stress couples are integrals of the Biot stress tensor. This tensor is invariant with respect to rigid body motions and, therefore, appropriate for the formulation of constitutive equations. Finite rotations are introduced via Eulerian angles. The finite element discretization of arbitrary shells is based on the isoparametric concept formulated with respect to a plane reference configuration. The numerical model is applied to different non‐linear plate and shell problems and compared with existing formulations. Due to a consistent linearization, the step size of a load increment is only limited by the local convergence behaviour of Newton's method.
Symmetric Galerkin boundary formulations employing curved elements
Authors: Kane J. H. , Balakrishna C. 
Published: August 2005

AbstractAccounts of the symmetric Galerkin approach to boundary element analysis (BEA) have recently been published. This paper attempts to add to the understanding of this method by addressing a series of fundamental issues associated with its potential computational efficiency. A new symmetric Galerkin theoretical formulation for both the (harmonic) heat conduction and the (biharmonic) elasticity problem that employs regularized singular and hypersingular boundary integral equations (BIEs) is presented. The novel use of regularized BIEs in the Galerkin context is shown to allow straightforward incorporation of curved, isoparametric elements. A symmetric reusable intrinsic sample point (RISP) numerical integration algorithm is shown to produce a Galerkin (i.e. double) integration strategy that is competitive with its counterpart (i.e. singular) integration procedure in the collocation BEA approach when the time saved in the symmetric equation solution phase is also taken into account. This new formulation is shown to be capable of employing hypersingular BIEs while obviating the requirement of C1 continuity, a fact that allows the employment of the popular continuous element technology. The behaviour of the symmetric Galerkin BEA method with regard to both direct and iterative equation solution operations is also addressed. A series of example problems are presented to quantify the performance of this symmetric approach, relative to the more conventional unsymmetric BEA, in terms of both accuracy and efficiency. It is concluded that appropriate implementations of the symmetric Galerkin approach to BEA indeed have the potential to be competitive with, if not superior to, collocation‐based BEA, for large‐scale problems.
Performance of the h–p version of the finite element method with various elements
Authors: Babuška I. , Elman H. C. 
Published: August 2005

AbstractThe paper addresses the performance of square elements of type Q(p) and Q′(p). (Q(p) and Q′(p) are elements of degree p, analogous to the well‐known 9‐ and 8‐noded elements for p = 2.) The performance is analysed theoretically for the class of analytic functions. Numerical experiments confirm the conclusions drawn from the theory. The computational complexity of a solution algorithm is studied using timings of the computation on an Alliant FX/8 computer. The data show that high‐order elements are very effective for the considered class of solutions.
A new boundary element approach for contact problems with friction
Authors: Olukoko O. A. , Becker A. A. , Fenner R. T. 
Published: August 2005

AbstractA new boundary element solution algorithm for two‐dimensional and axisymmetric contact problems with friction, based on an independent discretization of the contacting surfaces and under static and proportional loading conditions, is presented. The solution procedure uses the element shape functions to distribute the geometry, tractions and displacements on each contact element. The contact constraints are then applied between each contacting node and the opposite contact segment. The overall boundary element matrix equations for the contacting bodies are coupled using the contact conditions at the interface without introducing any additional variables into the solution matrix. The algorithm is applied to several two‐dimensional and axisymmetric frictional contact examples and the results obtained are in very good agreement with finite element and analytical solutions.