bluuebunny/crossref_metadata_2025_split huggingface dataset:
Numerical integration of non‐linear elastic multi‐body systems
Authors: Bauchau O. A. , Damilano G. , Theron N. J. 
Published: August 2005

AbstractThis paper is concerned with the modelling of nonlinear elastic multi‐body systems discretized using the finite element method. The formulation uses Cartesian co‐ordinates to represent the position of each elastic body with respect to a single inertial frame. The kinematic constraints among the various bodies of the system are enforced via the Lagrange multiplier technique. The resulting equations of motion are stiff, non‐linear, differential‐algebraic equations. The integration of these equations presents a real challenge as most available techniques are either numerically unstable, or present undesirable high frequency oscillations of a purely numerical origin. An approach is proposed in which the equations of motion are discretized so that they imply conservation of the total energy for the elastic components of the system, whereas the forces of constraint are discretized so that the work they perform vanishes exactly. The combination of these two features of the discretization guarantees the stability of the numerical integration process for non‐linear elastic multi‐body systems. Examples of the procedure are presented.
Non‐linear finite element formulation of kinematic limit analysis
Authors: Jiang Gong‐Liang 
Published: August 2005

AbstractThe objective of the research presented in this paper was to develop a general computational method for kinematic limit analysis problems that involve the determination of an optimal kinematically admissible velocity field of the studied structure under external loads. With the failure velocity field available, we can obtain a numerical estimate of the limit load exerted to the structure. The general kinematic limit analysis is characterized by the minimization of the plastic potential power dissipation functional of the mechanical system. This minimization problem was approached previously by linear and non‐linear programming schemes. In this paper, a new non‐linear solution scheme is described which is based on previous research on the regularized method. The regularized functional is a convex and non‐linear functional whose minimum represents a viscoplastic potential power dissipation, the velocity which minimizes this functional was proved to be kinematically admissible and can be obtained by the augmented Lagrangian method. This paper demonstrates that the non‐linear programming scheme is applicable to direct limit analysis. The basic idea of using this optimization method is to tranform the functional with a non‐linear term of the first‐order derivatives of the velocity to a functional in which this term is uncoupled with the strain rates, and in consequence the augmented Lagrangian (transformed functional) can be solved more easily. Some special problems related to incompressibility and discontinuity are discussed. A simple and accurate scheme is proposed to deal with the incompressibility problem and the problem of the linear Mohr–Coulomb yield surface in the principal stress space. Examples of plane stress and plane strain problems are given for von Mises and Mohr–Coulomb materials. Numerical results are provided in graphical form which serves to illustrate the kinematic admissibility. The limit loads obtained agreed well with the analytical results, which demonstrates the efficiency and accuracy of the non‐linear computational method presented.
Shape design sensitivity analysis via material derivative‐adjoint variable technique for 3‐D and 2‐D curved boundary elements
Authors: Burczyński T. , Kane J. H. , Balakrishna C. 
Published: August 2005

AbstractA general approach to shape design sensitivity analysis of three‐ and two‐dimensional elastic solid objects is developed using the material derivative‐adjoint variable technique and boundary element method. The formulation of the problem is general and first‐order sensitivities in the form of boundary integrals for the effect of boundary shape variations are derived for an arbitrary performance functional. Second‐order quadrilateral surface elements (for 3‐D problems) and quadratic boundary elements (for 2‐D problems) are employed in the solution of primary and adjoint systems and discretization of the boundary integral expressions for sensitivities. The accuracy of sensitivity information is studied for selected global performance functionals and also for boundary state fields at discrete points. Numerical results are presented to demonstrate the accuracy and efficiency of this approach.
Some observations on element performance in isochoric and dilatant plastic flow
Authors: De Borst René , Groen Arend E. 
Published: August 2005

AbstractThe performance of finite elements is scrutinized in isochoric and dilatant/contractant plastic flow. Standard displacement based elements, uniformly and selectively integrated elements, and elements with augmented strain rate fields are considered in plane‐strain, axisymmetric and three‐dimensional configurations with particular reference to the kinematic constraint imposed by dilatant/contractant plastic flow. It turns out that findings for isochoric deformations do not necessarily carry over to cases with plastic dilatancy or contraction. For the elements with augmented strain rate fields the danger of spurious mechanisms in ideal plasticity is brought out. A particular strategy which augments only the normal strain rates at the expense of a lesser improvement for the bending behaviour does not suffer from the possibility of spurious modes, while preserving the ability to accommodate dilatant/contractant plastic flow. Illustrative examples on plane‐strain, axisymmetry and three‐dimensional structures are included which support the above findings.
Equilibrium constrained assumed natural co‐ordinate strain plate elements
Authors: Jensen Daniel D. , Park K. C. 
Published: August 2005

AbstractEquilibrium constraints are used to improve the stress accuracy of existing assumed natural‐co‐ordinate strain (ANS) plate elements. This is accomplished by introducing hierarchical degrees of freedom, which are subsequently eliminated by invoking kinematic consistency and element‐interior homogeneous equilibrium conditions. The resulting element enrichments are completely contained in the strain‐displacement matrix. In addition, the modified displacement shape functions become available for consistent mass and nodal load calculations, a feat not shared by some hybrid‐type elements. The performance of the present element (ANS‐EC) is compared with other plate bending elements. This performance comparison includes convergence studies for both displacements and stresses.
A continuum approach for second‐order shape design sensitivity of elastic solids with loaded boundaries
Authors: Chen Chin‐Jung , Choi Kyung K. 
Published: August 2005

AbstractA second‐order shape design sensitivity analysis (DSA) method applicable to the shape change on the loaded boundaries is derived for three‐dimensional linear elastic solids using a continuum method with the material derivative. The continuum method is also used to derive mixed second‐order variations of stress and displacement performance measures with respect to shape design variables and distribution of non‐conservative traction loads, and also with respect to shape design variables and material properties. A shape design acceleration field is defined for the second‐order shape design sensitivity. Both direct differentiation and hybrid methods are presented in this paper. A numerical method, which can be implemented using established finite element analysis (FEA) codes, is developed. The feasibility and accuracy of the proposed second‐order shape DSA method has been demonstrated by solving a structural example‐doubly curved arch dam.
On advancing front mesh generation in three dimensions
Authors: Möller Peter , Hansbo Peter 
Published: August 2005

AbstractThis paper deals with some aspects of unstructured mesh generation in three dimensions by the advancing front technique. In particular, the parameters used in the algorithm are characterized, and strategies that may be used to improve robustness are suggested. We also describe a method whereby structured tetrahedral meshes with exceptionally stretched elements adjacent to boundary surfaces may be produced. The suggested method can be combined with the advancing front concept in a natural way.
Boundary element method for thermoelastoplastic problems
Authors: Sladek J. , Sladek V. 
Published: August 2005

AbstractIn this paper, we present the boundary integral formulation for inelastic stationary thermoelasticity including thermally induced non‐homogeneity. Generally, the unique BEM formulation for crack problems is achieved by using the traction boundary integral equations which are now considered in a non‐singular form. Both the two‐ and three‐dimensional boundary value problems are analysed simultaneously. Numerical examples for 2‐D problems are presented, in order to illustrate the suitability of this boundary element approach in the inelastic thermoelasticity.
Computational aspects of vector‐like parametrization of three‐dimensional finite rotations
Authors: Ibrahimbegović Adnan , Frey François , Kožar Ivica 
Published: August 2005

AbstractTheoretical and computational aspects of vector‐like parametrization of three‐dimensional finite rotations, which uses only three rotation parameters, are examined in detail in this work. The relationship of the proposed parametrization with the intrinsic representation of finite rotations (via an orthogonal matrix) is clearly identified. Careful considerations of the consistent linearization procedure pertinent to the proposed parametrization of finite rotations are presented for the chosen model problem of Reissner's non‐linear beam theory. Pertaining details of numerical implementation are discussed for the simplest choice of the finite element interpolations for a 2‐node three‐dimensional beam element. A number of numerical simulations in three‐dimensional finite rotation analysis are presented in order to illustrate the proposed approach.
Unified approach to numerical methods, part II: Finite elements, boundary methods, and their coupling
Authors: Herrera Ismael 
Published: August 2005

AbstractThis is the second in a series of three papers devoted to the presentation of a direct procedure of analysis of numerical methods for partial differential equations. The procedure consists of applying the method of weighted residuals and then interpreting the resulting equations by means of Green's formulas for discontinuous functions. Here, the general Green's formulas for operators defined in discontinuous fields developed in the first article, are applied to formulate the method of weighted residuals for arbitrary linear operators. Finite elements, boundary methods, and general procedures for coupling finite elements and boundary methods are discussed.
Mixed finite element methods for computing groundwater velocities
Authors: Allen M. B. , Ewing R. E. , Koebbe J. V. 
Published: August 2005

AbstractCentral to the understanding of problems in water quality and quantity for effective management of water resources is the development of accurate numerical models to stimulate groundwater flows and contaminant transfer. We discuss several important difficulties arising in modeling of subsurface flow and present promising numerical procedures for alleviating these problems. Furthermore, we describe mixed‐finite element techniques for accurately approximating fluid velocities, and review computational results on a variety of hydrologic problems.
A compact finite element method for elastic bodies
Authors: Rose Milton E. 
Published: August 2005

AbstractA nonconforming finite element method is described for treating linear equilibrium problems, and a convergence proof showing second order accuracy is given. The close relationship to a related compact finite difference scheme due to Phillips and Rose [1] is examined. A Condensation technique is shown to preserve the compactness property and suggests an approach to a certain type of homogenization.
A finite element collocation method for variably saturated flows in porous media
Authors: Allen Myron B. , Murphy Carolyn 
Published: August 2005

AbstractOne common formulation of Richard's equation for variably saturated flows in porous media treats pressure head as the principal unknown and moisture content as a constitutive variable. Numerical approximations to this “head‐based” formulation often exhibit mass‐balance errors arising from inaccuracies in the temporal discretization. This article presents a finite‐element collocation scheme using a mass‐conserving formulation. The article also proposes a computable index of global mass balance.
A nondispersive and nondissipative numerical method for first‐order linear hyperbolic partial differential equations
Authors: Watanabe Yoichi 
Published: August 2005

AbstractWe propose a new numerical method for a solution of first‐order linear hyperbolic equations. The leap‐frog scheme is converted to a nondispersive scheme by introducing an adjustable constant in a fictitious absorption term. Then the erroneous decrease in th solution is eliminated by solving two equations equivalent to the original equation. The new scheme perfectly preserves the form of a discontinuous solution.
Superconvergent recovery of gradients on subdomains from piecewise linear finite‐element approximations
Authors: Wheeler M. F. , Whiteman J. R. 
Published: August 2005

AbstractEngineers have been aware for some time of the phenomenon of superconvergence, whereby there exist (stress) points at which the accuracy of a finite‐element solution is superior to that of the approximation generally. This phenomenon has been treated in recent years by mathematicians who have proved, for certain two‐dimensional secondorder elliptic problems, superconvergent error estimates for retrieved finite‐element derivatives. These results have demanded high global regularity of the solutions of the bondary value problems. In this present article cut‐off functions are used to prove similar superconvergence results over interior subdomains. This allows superconvergence estimates to be derived for problems with solutions of low global regularity, particularly those involving singularities.
Open boundary conditions for hyperbolic equations
Authors: Lick Wilbert , Ziegler Kirk , Lick James 
Published: August 2005

AbstractA previously developed general procedure for deriving accurate difference equations to describe conditions at open boundaries for hyperbolic equations is extended and further illustrated by means of several examples of practical importance. Problems include those with both incoming and outgoing waves at the boundary, the use of locally cylindrical and spherical wave approximations at each point of the boundary, and nonlinear wave propagation. Reflected waves in all cases are minimal and less than 10−2 of the incident wave.
An investigation of chaos in reaction‐diffusion equations
Authors: Wachholz James J. , Bruch John C. 
Published: August 2005

AbstractThe purpose of this article is to investigate graphically and numerically the topic of chaos in reaction‐diffusion equations. This article is based on the article by Mitchell and Bruch [1]. One‐ and two‐dimensional forms of the reaction‐diffusion equation are discretized using the explicit Euler finite difference scheme. Plots are presented to show the effect of bifurcation parameters on the difference equations. Varying these parameters produce single point, periodic, chaotic, intermittent, and divergent solutions.
Numerical implementation of the Sinc‐Galerkin method for second‐order hyperbolic equations
Authors: McArthur Kelly M. , Bowers Kenneth L. , Lund John 
Published: August 2005

AbstractA fully Galerkin method in both space and time is developed for the second‐order, linear hyperbolic problem. Sinc basis functions are used and error bounds are given which show the exponential convergence rate of the method. The matrices necessary for the formulation of the discrete system are easily assembled. They require no numerical integrations (merely point evaluations) to be filled. The discrete problem is formulated in two different ways and solution techniques for each are described. Consideration of the two formulations is motivated by the computational architecture available. Each has advantages for the appropriate hardware. Numerical results reported show that if 2N + 1 basis functions are used then the exponential convergence rate \documentclass{article}\pagestyle{empty}\begin{document}$ 0\left[{\exp \left({- \kappa \sqrt N} \right)} \right] $\end{document}, κ > 0, is attained for both analytic and singular problems.
High‐order methods for elliptic equations with variable coefficients
Authors: Ananthakrishnaiah U. , Manohar R. , Stephenson J. W. 
Published: August 2005

AbstractIn this article, we give a simple method for developing finite difference schemes on a uniform square gird. We consider a general, two‐dimensional, second‐order, partial differential equation with variable coefficients. In the case of a nine‐point scheme, we obtain the known results of Young and Dauwalder in a fairly elegant fashion. We show how this can be extended to obtain fourth‐order schemes on thirteen points. We derive two such schemes which are attractive because they can be adapted quite easily bnto obtain formulas for gird points near the boundary. In addition to this, these formulas only require nine evaluations for the typical forcing function. Numerical examples are given to demonstrate the performance of one of the fourth‐order schemes.
Fourth‐order finite difference methods for three‐dimensional general linear elliptic problems with variable coefficients
Authors: Ananthakrishnaiah U. , Manohar R. , Stephenson J. W. 
Published: August 2005

AbstractIn this article, we give a simple method for deriving finite difference schemes on a uniform cubic grid. We consider a general, three‐dimensional, second‐order, linear, elliptic partial differential equation with variable coefficients. We derive two simple fourth‐order schemes. When the coefficients of the second‐order mixed derivatives are equal to zero, the fourth‐order scheme requires only 19 grid points. When the coefficients of the mixed derivatives are not equal to zero and the coefficients of Uxx, Uyy, and Uzz are equal, we require the 27 points of the cubic grid. Numerical examples are given to demonstrate the performance of the two schemes derived. There does not exist a fourth‐order scheme involving 27 grid points for the general case.
Hermitian operator methods for reaction‐diffusion equations
Authors: Ramos J. I. 
Published: August 2005

AbstractA variety of time‐linearization, quasilinearization, operator‐splitting, and implicit techniques which use compact or Hermitian operators has been developed for and applied to one‐dimensional reaction‐diffusion equations. Compact operators are compared with second‐order accurate spatial approximations in order to assess the accuracy and efficiency of Hermitian techniques. It is shown that time‐linearization, quasilinearization, and implicit techniques which use compact operators are less accurate than second‐order accurate spatial discretizations if first‐order approximations are employed to evaluate the time derivatives. This is attributed to first‐order accurati temporal truncation errors. Compact operator techniques which use second‐order temporal approximations are found to be more accurate and efficient than second‐order accurate, in both space and time, algorithms. Quasilinearization methods are found to be more accurate than time‐linearization schemes. However, quasilinearization techniques are less efficient because they require the inversion of block tridiagonal matrices at each iteration. Some improvements in accuracy can be obtained by using partial quasilinearization and linearizing each equation with respect to the variable whose equation is being solved. Operator‐splitting methods which use compact differences to evaluate the diffusion operator were found to be less accurate than operator‐splitting procedures employ second‐order accurate spatial approximations. Comparisons among the methods presented in this paper are shown in terms of the L2‐norm errors and computed wave speeds for a variety of time steps and grid spacings: The numerical efficiency is assessed in terms of the CPU time required to achieve the same accuracy.
Difference methods for quasilinear parabolic systems from plasma physics
Authors: Von Finckenstein Karl Graf Finck 
Published: August 2005

AbstractA class of nonlinear implicit one‐step difference methods for quasilinear strongly coupled parabolic systems in cylinderical symmetry is considerd. The main part of the article deals with proving convergence of both the semi‐discrete and the fully discrete approximations. For this purpose, bounds for the inverse difference operators have to be derived previously. This is possible subject to a condition which can be considered as a generalization of the concept “parabolic” to systems. Furthermore, a linearized scheme already used by Düchs some years ago turns out to be nothing but one iteration step of the Newton mehod for solving the complete system of nonlinear difference equations. A surprising improvement on the linearized scheme is achievd, if two or more Newton iterations are performed.
Superconvergent recovery of gradients on subdomains from piecewise linear finite‐element approximations
Authors: Wheeler M. F. , Whiteman J. R. 
Published: August 2005

AbstractEngineers have been aware for some time of the phenomenon of superconvergence, whereby there exist (stress) points at which the accuracy of a finite‐element solution is superior to that of the approximation generally. This phenomenon has been treated in recent years by mathematicians who have proved, for certain two‐dimensional second‐order elliptic problems, superconvergent error estimates for retrieved finite‐element derivatives. These results have demanded high global regularity of the solutions of the boundary value problems. In this present article cut‐off functions are used to prove similar superconvergence results over interior subdomains. This allows superconvergence estimates to be derived for problems with solutions of low global regularity, particularly those involving singularities.
Numerical comparison of preconditionings for large sparse finite element problems
Authors: Gambolati G. , Pini G. , Zilli G. 
Published: August 2005

AbstractA numerical study of the efficiency of the modified conjugate gradients (MCG) is performed using different preconditioning schemes. The MCG behavior is evaluated in connection with the solution of large linear sets of symmetric positive definite (p.d.) equations, arising from the finite element (f.e.) integration of partial differential equations of parabolic and elliptic type and the analysis of the leftmost eingenspectrum of the corresponding matrices. A simple incomplete Cholesky factorization ICCG(O) having the same sparsity pattern as the original problem is compared with a more complex technique ICAJ (Ψ) where the triangular factor is allowed to progressively fill in depending on a rejection parameter Ψ. The performance of the preconditioning algorithms is explored on finite element equations whose sizeNranges between 150 and 2300. The results show that an optimal Ψoptmay be found which minimizes the overall CPU time for the solution of both the linear system and the eigenproblem. The comparison indicates that ICAJ (Ψopt) is not significantly more efficient than ICCG(O), which therefore appears to be a simple, robust, and reliable method for the preconditioning of large sparse finite element models.