bluuebunny/crossref_metadata_2025_split huggingface dataset:
A novel finite element for treating inhomogeneous solids
Authors: Meguid S. A. , Zhu Z. H. 
Published: August 2005

AbstractThis study is concerned with the development and implementation of a novel finite element which is capable of treating the problem of interacting circular inhomogeneities in heterogeneous solids. The general form of the element, which is constructed from a cell containing a single circular inhomogeneity in a surrounding matrix, is derived explicitly using the complex potentials of Muskhelishvili and the Laurent series expansion method. The strength of the proposed eight‐noded plane element is demonstrated by its ability to treat arbitrarily and periodically located multiple inhomogeneities under general loading conditions using a limited number of elements. Assessment of the accuracy and efficiency of the devised element is obtained by comparing its performance against existing analytical and traditional finite element attempts. The current element enables the determination of the local and effective elastic properties of composite materials with relative ease.
A hybrid finite element method for heterogeneous materials with randomly dispersed rigid inclusions
Authors: Zhang J. , Katsube N. 
Published: August 2005

AbstractA hybrid finite element approach is proposed for the mechanical response of two‐dimensional heterogeneous materials with linearly elastic matrix and randomly dispersed rigid circular inclusions of arbitrary sizes. In conventional finite element methods, many elements must be used to represent one inclusion. In this work, each inclusion is embedded inside a polygonal element and only one element is required to represent one inclusion.In numerically approximating stress and displacement distributions around the inclusion, classical elasticity solutions for a multiply‐connected region are employed. A modified hybrid functional is used as the basis of the element formulation where the displacement boundary conditions of the element are automatically considered in a variational sense.The accuracy and efficiency of the proposed method are demonstrated by two boundary value problems. In one example, the results based on the proposed method with only 64 hybrid elements (450 degrees of freedom) are shown to be almost identical to those based on the traditional method with 2928 conventional elements (5526 degrees of freedom).
Non‐conforming mesh gluing in the finite elements method
Authors: Quiroz Luis , Beckers Pierre 
Published: August 2005

AbstractA methodology to connect two or more non‐conforming meshes generated from a geometric model is presented. The problem leads to a variational problem subject to constraints. The emphasis of the work is on constraints construction. Two methods, namely, discrete connection and continuous connection, are developed. The relation with hybrid formulations is considered and two application examples are presented.
An application of Trefftz method to the sensitivity analysis of two‐dimensional potential problem
Authors: Kita Eisuke , Kamiya Norio , Ikeda Youichi 
Published: August 2005

AbstractThis paper presents a new formulation for the sensitivity analysis with the help of the Trefftz boundary‐type solution procedure. Direct differentiation of the expressions of the field variables leads to the expressions of the sensitivities. Since the field variables are approximated by linear combination of regular T‐complete functions, the analytical expressions of the sensitivities are also regular. Sensitivity analysis schemes with respect to variations of dimensions of the object and boundary conditions are explained in detail. Two‐dimensional potential problems in the bounded region are considered as a numerical example in order to confirm its validity.
Finite element evaluation of free‐edge singular stress fields in anisotropic materials
Authors: Pageau Stephane S. , Biggers Sherrill B. 
Published: August 2005

AbstractA finite element formulation based on the work of Yamada and Okumura14 is presented to determine the order of singularity and angular variation of the stress and displacement fields surrounding a singular point on a free edge of anisotropic materials. Emphasis is placed on the computational aspects of this method when applied to configurations including fully bonded multi‐material junctions intersecting a free edge as well as materials containing cracks intersecting a free edge. The study shows that the singularity of the three‐dimensional stress field may be accurately determined with a relatively small number of elements only when a proper level of numerical integration is used. The method is applied to isotropic and orthotropic materials with a crack intersecting a free edge and an anisotropic three‐material junction intersecting a free edge. The efficiency and accuracy of the method indicates it could be used to develop a numerical solution for the singular field that could in turn be used to create free‐edge enriched finite elements.
The green element method
Authors: Taigbenu Akpofure E. 
Published: August 2005

AbstractThis paper discusses an element‐by‐element approach of implementing the Boundary Element Method (BEM) which offers substantial savings in computing resource, enables handling of a wider range of problems including non‐linear ones, and at the same time preserves the second‐order accuracy associated with the method. Essentially, by this approach, herein called the Green Element Method (GEM), the singular integral theory of BEM is retained except that its implementation is carried out in a fashion similar to that of the Finite Element Method (FEM). Whereas the solution procedure of BEM couples the information of all nodes in the computational domain so that the global coefficient matrix is dense and full and as such difficult to invert, that of GEM, on the other hand, involves only nodes that share common elements so that the global coefficient matrix is sparse and banded and as such easy to invert. Thus, GEM has the advantage of being more computationally efficient than BEM. In addition, GEM makes the singular integral theory more flexible and versatile in the sense that GEM readily accommodates spatial variability of medium and flow parameters (e.g., flow in heterogeneous media), while other known numerical features of BEM—its second‐order accuracy and ability to readily handle problems with singularities are retained by GEM.A number of schemes is incorporated into the basic Green element formulation and these schemes are examined with the goal of identifying optimum schemes of the formulation. These schemes include the use of linear and quadratic interpolation functions on triangular and rectangular elements. We found that linear elements offer acceptable accuracy and computational effort. Comparison of the modified fully implicit scheme against the generalized two‐level scheme shows that the modified fully implicit scheme with weight of about 1·25 offers a marginally better approximation of the temporal derivative. The Newton–Raphson scheme is easily incoporated into GEM and provides excellent results for the time‐dependent non‐linear Boussinesq problem. Comparison of GEM with conventional BEM is done on various numerical examples, and it is observed that, for comparable accuracy, GEM uses less computing time. In fact, from the numerical simulations carried out, GEM uses between 15 and 45 per cent of the simulation time of BEM.
Axisymmetric three‐ and four‐node finite elements for large strain elastoplasticity
Authors: Heiduschke K. 
Published: August 2005

AbstractWithin the framework of the finite element method an application of the logarithmic strain space formulation of large strain elastoplasticity is illustrated for the examples of axisymmetric three‐node triangular and four‐node quadrilateral finite elements. The formulation of the large strain elastoplasticity is based on a strain space formulation in conjunction with logarithmic (or Hencky) strain tensors with respect to the reference configuration. It is therefore—from a material point of view—a full Lagrangian formulation. The use of logarithmic strains enables an additive split of finite dilatation and distortion, which are given by the logarithmic strain trace and deviator. As a consequence of the strain space formulation no stress tensors are involved in order to describe the plasticity. The stress which is work‐conjugate to the logarithmic strain follows from the stress‐strain relations and may be transformed to Cauchy stress. The desired finite element matrices are derived via the principle of virtual work applied to the Cauchy stress distribution of the current configuration. It should be noted that our considerations are not restricted to axisymmetry and that they remain valid for isoparametric, position‐ (displacement‐) based finite elements in general.
Numerical resolution of the boundary integral equations for elastic scattering by a plane crack
Authors: Alves Carlos , Duong Tuong Ha 
Published: August 2005

AbstractThe problem of wave scattering by a plane crack is solved, either in the case of acoustic waves or in the case of elastic waves incidence using the boundary integral equation method. A collocation method is often used to solve that equation, but here we will use a variational method, first writing the problem of Fourier variables, and then writing the associated integrals in the sesquilinear form with weak singularity kernels. This representation is used in the numerical approach, made with a finite element method in the surface of the crack. Numerical tests were made with circular and elliptical cracks, but this method can be extended to other shapes, with the same convergence profiles. Extensive results are given concerning the crack opening displacement, the scattering cross‐section, the back‐scattered amplitude and far‐field patterns.
Remarks on the Gauss quadrature rule for a particular class of finite‐part integrals
Authors: Ioakimidis Nikolaos I. 
Published: August 2005

AbstractThe method of finite‐part (Hadamard‐type or hypersingular) integrals is already a standard approach in applied numerical methods in engineering and, mainly, in acoustics, fluid dynamics, elasticity and fracture mechanics. Here we study the convergence of the non‐classical (possessing a negative node, outside the integration interval, as well as a negative weight corresponding to this node) Gauss‐Legendre quadrature rule for finite‐part integrals on the interval [0,1] with the weight function 1/y and we prove its validity for integrands possessing a continuous first derivative. The case of integrands possessing a higher‐order derivative is also considered and the rate of convergence is established. These results are based on the derivation of a bound for the negative node in the above quadrature rule and, further, on the theory of convergence of the classical Gauss quadrature rule. Numerical results, verifying the results of this paper, are also displayed. The present results can be generalized to the Gauss‐Laguerre similarly non‐classical quadrature rule for finite‐part integrals (on the interval [0], ∞)) as well as to the two special, but important in engineering applications, non‐classical Gaussian quadrature rules for Cauchy‐type principal‐value integrals and Mangler‐type finite‐part integrals have been proposed by Tsamasphyros and Dimou.
A new 12 DOF quadrilateral element for analysis of thick and thin plates
Authors: Jirousek J. , Wróblewski A. , Szybiński B. 
Published: August 2005

AbstractThis paper presents a simple quadrilateral 12 DOF plate bending element based on a modified version of the hybrid‐Trefftz approach. This element makes use of two independent fields of generalized displacements:

a non‐conforming field (11 Trefftz terms for transverse displacement w and the corresponding rotations Θx, Θy) satisfying the governing differential equations of Reissner‐Mindlin theory;
an auxiliary conforming field with displacements w̃ linked to rotations \documentclass{article}\pagestyle{empty}\begin{document}$ \tilde \Theta _x,\tilde \Theta _y$\end{document}, by the requirement of constant boundary distribution of the corresponding tangential component S̃t, of the transverse shear. This allows quadratic w̃ and linear \documentclass{article}\pagestyle{empty}\begin{document}$ \tilde \Theta _x,\tilde \Theta _y $\end{document}, at the element boundary to be obtained with only 3 DOF at the corner nodes.
The resulting element, denoted by Q̃21–11, is robust and free of shear locking in the thin limit. The numerical assessment involves comparison with several recently presented 12 DOF thick plate quadrilaterals as well as with the standard 16 DOF hybrid‐Trefftz quadrilateral, Q21‐15S, with 15 Trefftz terms and independently interpolated w̃ and \documentclass{article}\pagestyle{empty}\begin{document}$ \tilde \Theta _x,\tilde \Theta _y $\end{document}.
An algorithm to generate quadrilateral or triangular element surface meshes in arbitrary domains with applications to crack propagation
Authors: Potyondy David O. , Wawrzynek Paul A. , Ingraffea Anthony R. 
Published: August 2005

AbstractA new hybrid algorithm for automatically generating either an all‐quadrilateral or an all‐triangular element mesh within an arbitrarily shaped domain is described. The input consists of one or more closed loops of straight‐line segments that bound the domain. Internal mesh density is inferred from the boundary density using a recursive spatial decomposition (quadtree) procedure. All‐triangular element meshes are generated using a boundary contraction procedure. All‐quadrilateral element meshes are generated by modifying the boundary contraction procedure to produce a mixed element mesh at half the density of the final mesh and then applying a polygon‐splitting procedure. The final meshes exhibit good transitioning properties and are compatible with the given boundary segments which are not altered. The algorithm can support discrete crack growth simulation wherein each step of crack growth results in an arbitrarily shaped region of elements deleted about each crack tip. The algorithm is described and examples of the generated meshes are provided for a representative selection of cracked and uncracked structures.
A uniform deformation gradient hexahedron element with artificial hourglass control
Authors: Bonet J. , Bhargava P. 
Published: August 2005

AbstractAn 8‐noded linear hexahedron element for large strain hyperelastic analysis is presented in this paper. The element is based on a constant deformation gradient interpolation and is formulated using a mixed variational principle of the Hu–Washizu type. Volumetric and isochoric components of the deformation are treated independently to ensure the correct evaluation of the element volume. A simple procedure to control the propagation of spurious hourglass deformation modes is also discussed. This is based on the addition of artificial hourglass forces which vanish under constant deformation gradient conditions, thereby ensuring that the element passes a non‐linear version of the patch test. Applications in the field of neo‐Hookean materials and superplastic forming processes are also considered.
On augmented Lagrangian algorithms for thermomechanical contact problems with friction
Authors: Zavarise G. , Wriggers P. , Schrefler B. A. 
Published: August 2005

AbstractThe detailed discretization of contact zones with contact stiffness based on real physical characteristics of contact surfaces can produce stiffness terms which induce ill‐conditioning of the global stiffness matrix. Moreover the consistent treatment of frictional behaviour generates non‐symmetric tangent stiffness matrices due to the non‐associativity of the slip phase. Other non‐symmetries are due to the coupling terms and to the dependencies on various parameters that can be involved. To overcome these difficulties almost consistent techniques based on two‐step algorithms have been proposed in the past. Here an augmentation technique is proposed which takes into account micro‐mechanical effects, and permits the symmetrization of the tangent stiffness during frictional slip phase.
Shape optimal design of elastic planar frames with non‐linear response
Authors: Kegl M. , Butinar B. J. , Oblak M. M. 
Published: August 2005

AbstractThis paper describes an approach to shape optimal design of elastic planar frames with non‐linear response. The foundation of the proposed approach forms an appropriate strategy of shape representation of the structure, based on the design element technique. A frame structure is treated as to be assembled from several frame design elements, which in turn may consist of several appropriately joined beam finite elements. The shape of each frame design element is defined by convenient functions involving Bezier blending polynomials. The original formulation of the beam finite element, proposed by Saje, is modified in order to fit nicely into the context of the frame design element technique. The formulation of the shape optimal design problem in a form of a problem of non‐linear mathematical programming and its solution by employing gradient‐based methods of mathematical programming are discussed briefly. The theory is illustrated with two numerical examples.
The effect of grid irregularity on truncation error for discretizations of Laplaces's equation
Authors: Montgomery Matthew , Fleeter Sanford 
Published: August 2005

AbstractThe discretization of differential equations to obtain numerical solutions introduces truncation error (TE). The form of the TE depends on the differential equation, the discretization scheme, and the discretization grid in a fairly complicated fashion. The character and magnitude of the TE determines in part the discrepancy between the approximate and exact solutions to the PDE. In this study, a symbolic manipulator was used to investigate the geometrical dependence of the TE in discrete approximations to Laplace's equation. The effect of various grid irregularities on the leading TE terms was investigated for two discretization schemes. A nine point centered stencil was varied in aspect ratio, skewness, and non‐uniformity (irregular spacing). The first scheme was the common centered finite difference (FD) method, applied by transforming to a uniform, orthogonal computational space. The second scheme was the implicit interpolation method (II), developed for discretization on irregular grids. Both discretization methods had leading TE that was second order (inversely proportional to the number of grid points squared) and had a sharp rise in TE for skewness angles beyond sixty degrees. The FD method skewness errors were greater than those for the II method, but high aspect ratio errors were less. For non‐linear transformations the FD method TE contained second derivatives, the same order as the governing differential equation, while the II method's lowest order TE derivatives were third order. Thus while both methods have the same order of accuracy, the nature of the numerical error in the discrete solution would be different.
A numerical green's function approach for boundary elements applied to fracture mechanics
Authors: Telles J. C. F. , Castor G. S. , Guimarães S. 
Published: August 2005

AbstractThe most accurate boundary element formulation to deal with fracture mechanics problems is obtained with the implementation of the associated Green's function acting as the fundamental solution. Consequently, the range of applications of this formulation is dependent on the availability of the appropriate Green's function for actual crack geometry. Analytical Green's functions have been presented for a few single crack configurations in 2‐D applications and require complex variable theory. This work extends the applicability of the formulation through the introduction of efficient numerical means of computing the Green's function components for single or multiple crack problems, of general geometry, including the implementation to 3‐D problems as a future development. Also, the approach uses real variables only and well‐established boundary integral equations.
Coarse/fine mesh preconditioners for the iterative solution of finite element problems
Authors: Dracopoulos M. C. , Crisfield M. A. 
Published: August 2005

AbstractA class of preconditioners built around a coarse/fine mesh framework is presented. The proposed method involves the reconstruction of the stiffness equations using a coarse/fine mesh idealization with relative degrees‐of‐freedom derived from the element shape functions. This approach leads naturally to effective preconditioners for iterative solvers which only require a factorization involving coarse mesh variables. A further extension is the application of the proposed method to super‐elements in conjunction with substructuring (domain decomposition) techniques. The derivation of the coarse/fine mesh discretization via the use of transformation matrices, allows a straightforward implementation of the proposed techniques (as well as multigrid type procedures) within an existing finite element system.
An incremental formulation for the linear analysis of thin viscoelastic structures using generalized variables
Authors: Ghazlan G. , Caperaa S. , Petit C. 
Published: August 2005

AbstractThis paper is concerned with the development of an incremental formulation in the time domain for the displacement and stress analysis of quasistatic, linear, thin viscoelastic structures undergoing mechanical deformation. By representing the viscoelastic behaviour of a material by a discrete creep spectrum and by an incremental constitutive equations, the difficulty of retaining the stress history in computer solutions is avoided. A complete general formulation of linear viscoelastic stress analysis is developed in terms of increments of midsurface strains and curvatures and corresponding stress resultants.
Hexahedral mesh generation by medial surface subdivision: Part I. Solids with convex edges
Authors: Price M. A. , Armstrong C. G. , Sabin M. A. 
Published: August 2005

AbstractA method is presented for subdividing a large class of solid objects into topologically simple subregions suitable for automatic finite element meshing with hexahedral elements. The technique uses a geometric property of a solid, its medial surface, to define the necessary subregions. The subregions are defined explicitly to be one of only 13 possible types. The subdividing cuts are between parts of the object in geometric proximity and produce good quality meshes of hexahedral elements. The method as introduced here is applicable to solids with convex edges and vertices, but the extension to complete generality is feasible.
An augmented Lagrangian quasi‐Newton solver for constrained nonlinear finite element applications
Authors: Laursen T. A. , Maker B. N. 
Published: August 2005

AbstractA solution scheme is presented for constrained non‐linear equations of evolution that result, for example, from the finite element discretization of mechanical contact problems. The algorithm discussed utilizes a quasi‐Newton non‐linear equation solving strategy, with constraints enforced by an augmented Lagrangian iteration procedure. Through presentation of a simple model problem and its generalization, it is shown that the iterations associated with both the quasi‐Newton algorithm and the augmentation procedure can be interwoven to produce a highly efficient and robust solution strategy.
Modelling and simulation of high‐speed machining
Authors: Marusich T. D. , Ortiz M. 
Published: August 2005

AbstractA Lagrangian finite element model of orthogonal high‐speed machining is developed. Continuous remeshing and adaptive meshing are the principal tools which we employ for sidestepping the difficulties associated with deformation‐induced element distortion, and for resolving fine‐scale features in the solution. The model accounts for dynamic effects, heat conduction, mesh‐on‐mesh contact with friction, and full thermo‐mechanical coupling. In addition, a fracture model has been implemented which allows for arbitrary crack initiation and propagation in the regime of shear localized chips. The model correctly exhibits the observed transition from continuous to segmented chips with increasing tool speed.