bluuebunny/crossref_metadata_2025_split huggingface dataset:
Numerical solution of linear two‐point boundary problems via the fundamental‐matrix method
Authors: Asfar O. R. , Hussein A. M. 
Published: August 2005

AbstractA numerical method is presented for the‐solution of linear systems of differential equations with initial‐value or two‐point boundary conditions. For y′(x) = A(x)y(x) + f(x) the domain of interest [a,b] is divided into an appropriate number L of subintervals. The coefficient matrix A(x) is replaced by its value Ak at a point xk within the Kth subinterval, thus replacing the original system by the L discretized systems yk(x) = Akyk(x) + fk(x), k = 1,2,…, L. The fundamental matrix solution Φk(x, xk) over each subinterval is found by computing the eigenvalues and eigenvectors of each Ak. By matching the solutions yk(x) at the L – 1 equispaced grid points defining the limits of the subintervals and the boundary conditions, the two‐point problem is reduced to solving a system of linear algebraic equations for the matching constants characterizing the different yk(x). The values of y1(a) and yL(b) are used to calculate the missing boundary conditions. For initial‐value problems this method is equivalent to a one‐step method for generating approximate solutions. By means of a coordinate transformation, as in the multiple shooting method,1 the method becomes particularly suitable for stiff systems of linear ordinary differential equations. Five examples are discussed to illustrate the viability of the method.
Infinite boundary elements
Authors: Beer G. , Watson J. O. 
Published: August 2005

AbstractSpecial types of boundary elements are discussed which can be used for the modelling of surfaces which extend to infinity. The theoretical background and details of implementation are discussed. On test examples it is shown that the elements perform extremely well even for cases in which they are located close to the area of interest. A practical application of the use of the elements for the modelling of mining excavations is given.
Boundary integration and interpolation procedures for plate bending
Authors: Abdel‐Akher Ahmed , Hartley Gilbert A. 
Published: August 2005

AbstractIn the direct boundary element method (DBEM) for thin plate bending analysis, the integration of the kernel‐shape‐function products can lead to complications due to a combination of factors. The first is the existence of a singularity at the source point, leading to the singular kernel, which increases in strength as the integral equation is differentiated once for rotation, again for moment and yet again for shear. The second factor arises from the use of piecewise interpolation polynomials.In the first part of the DBEM analysis where the unspecified boundary values are computed, the numerical procedures are fairly straightforward. It is found in this paper that special care must be taken in calculating internal actions at domain points. The problems which can be encountered are demonstrated, and a modified boundary interpolation procedure is described. Examples are given which show the superiority of the recommended approach.
Stress intensity factors by enriched mixed finite elements
Authors: Heyliger P. R. , Kriz R. D. 
Published: August 2005

AbstractAn enriched finite element model for linear elastic fracture mechanics is developed for a mixed variational statement. The independent approximations for the displacement and stress components are enriched by adding the near‐field analytic expressions for a cracked body to the polynomial approximations of a conventional element. This allows for an accurate representation of the stress and displacement fields near the crack tip and also results in the direct calculation of the appropriate stress intensity factors. The accuracy of this formulation is demonstrated through several numerical examples.
Non‐linear steady state vibration of frames by finite element method
Authors: Leung A. Y. T. , Fung T. C. 
Published: August 2005

AbstractA finite element method based on the virtual work principle to determine the steady state response of frams in free or forced periodic vibration is introduced. The axial and flexural deformations are coupled by mean of the induced axial force along the element. The spatial discretization of the deformations is achieved by the usual finite element method and the time discretization by Fourier coefficients of the nodal displacements. No unconventional element matrices are needed. After applying the harmonic balance method, a set of non‐linear algebraic equations of the Fourier coefficients is obtained. These equations are solved by the Newtonian iteration method in terms of the Fourier coefficient increments. Nodal damping can easily be included by a diagonal damping matrix. The direct numerical determination of the Fourier coefficient increments is difficult owing to the presence of peaks, loops and discontinuities of slope along the amplitude‐frequency response curves. Parametric construction of the response curves using the phase difference between the response and excitation is recommended to provide more points during the rapid change of the phase (i.e. at resonance). For undamped natural vibration, the method of selective coefficients adopted.Numerical examples on the Duffing equation, a hinged–hinged beam, a clamped–hinged beam, a ring and a frame are given. For reasonably accurate results, it is shown that the number of finite elements must be sufficient to predict at least the linear mode at the frequency of interest and the number of harmones considered must satisfy the conditions of completeness and balanceability, which are discussed in detail.
Adaptive time‐step control in creep analysis
Authors: Mahnken Rolf , Stein Erwin 
Published: August 2005

AbstractConcerning the integration in time of constitutive relations for Norton‐type creep problems two families of algorithms are examined, namely the generalized trapezoidal rule and the generalized midpoint rule. Based on a mathematical concept, the accuracy properties are derived for both stresses and strains. Since the choice of the step‐size is crucial for the accuracy of the numerical results, an adaptive step‐size procedure is carried out by means of error estimators. Specifically, attention is paid to features arising in the context of a finite element displacement method. Finally, two numerical examples are given to illustrate the effect of the step‐size control on the accuracy.
A frontal technique for vector computers
Authors: Brusa Luisa , Riccio Francesca 
Published: August 2005

AbstractAt the kernel of most scientific computations lies the solution of linear equations which, in finite element codes, is often performed by the frontal method. This method, like many algorithms for sparse matrices, is usually implemented with extensive use of indirect addressing which scarcely benefits from vectorization. As a consequence, present application codes only partially exploit the innovative features of supercomputer architectures. This paper describes a new version of the frontal technique which is designed for CRAY‐like computers and is well suited to vector processing. Numerical tests have shown that the proposed algorithm is effective in improving the efficiency of finite element solutions on a vector machine.
A mixed finite element formulation for Reissner–Mindlin plates based on the use of bubble functions
Authors: Pinsky Peter M. , Jasti Raja V. 
Published: August 2005

AbstractA new finite element formulation for Reissner–Mindlin plates, based on the Hellinger–Reissner variational principle, is proposed in which the displacement field is additively decomposed into two parts: a part associated with standard interpolation of nodal degrees of freedom and a part associated with a set of independent bubble functions expressed in terms of generalized parameters. The formulation employs independent approximations for every stress component so that the stress field does not a priori satisfy the homogeneous equilibrium equations. It is shown that the bubble functions provide additional variational constraints on the stress field, resulting in optimal accuracy for the mixed formulation, and also eliminating shear locking in the thin limit. A 4‐node and a 9‐node element are described in detail. Both elements pass the patch test for mixed elements described by Zienkiewicz et al.1 and are stable in the sense of the Babuška–Brezzi condition. Numerical results indicate that the elements are accurate in displacements and stresses, including transverse shear, and insensitive to mesh distortion.
A coarse/fine preconditioner for very ill‐conditioned finite element problems
Authors: Farhat Charbel , Sobh Nahil 
Published: August 2005

AbstractWe consider the problem of applying the conjugate gradient method to solve‐ill‐conditioned large algebraic systems of equations resulting from the finite element discretization of some three‐dimensional boundary value problems. We present an effective preconditioner for such systems based on a multigrid technique. We assess its performance with examples borrowed from large flexible aerospace structures.
Mixed‐interpolated elements for Reissner–Mindlin plates
Authors: Brezzi Franco , Bathe Klaus‐Jürgen , Fortin Michel 
Published: August 2005

AbstractWe present in this paper a procedure to establish Reissner–Mindlin plate bending elements. The procedure is based on the idea to combine known results on the approximation of Stokes problems with known results on the approximation of elliptic problems. The proposed elements satisfy the mathematical conditions of stability and convergence, and some of them promise to provide efficient elements for practical solutions.
Coupled use of reduced integration and non‐conforming modes in quadratic Mindlin plate element
Authors: Choi Chang‐Koon , Kim Sun‐Hoon 
Published: August 2005

AbstractThe applications of the reduced integration technique, and the addition of non‐conforming modes and their coupling to Mindlin plate elements to improve their basic behaviour are reviewed and the establishment of a series of new plate elements by combined use of these schemes is presented in this paper. The element formulation is based upon the quadratic Mindlin plate concept. The results obtained by new elements converge to the exact solutions very rapidly as the mesh is refined and show reliable solutions even for severely distorted meshes. The new elements have the requisite numbers of zero eigenvalues associated with rigid body modes to avoid spurious zero energy modes. These elements are shown to solve the shear locking problem completely so that they are applicable to a wide range of plate problems, giving a high accuracy for both thick and thin plates.
A time–space finite element discretization technique for the calculation of the electromagnetic field in ferromagnetic materials
Authors: Axelsson O. , Maubach J. 
Published: August 2005

AbstractThe stability of time‐stepping methods for parabolic differential equations is mostly a critical issue. Furthermore, solving such equations with a classical time‐stepping approach can be very expensive because many small time‐steps have to be taken if steep gradients occur in the solution, even if these occur only in a narrow part of the space domain. In this paper we present a discretization technique in which finite element approximations are used in time and space simultaneously for a relatively large time period called a ‘time‐slab’. This technique may be repeatedly applied to obtain further parts of the solution in subsequent time‐intervals. It will be shown that, with the proposed method, the solution can be computed cheaply even if it has steep gradients and that stability is automatically guaranteed. For the solution of the non‐linear algebraic equations on each time‐slab fast iterative methods can be used.
Analysis of the Zienkiewicz–Zhu a‐posteriori error estimator in the finite element method
Authors: Ainsworth M. , Zhu J. Z. , Craig A. W. , Zienkiewicz O. C. 
Published: August 2005

AbstractAn a‐posteriori error estimator for finite element analysis proposed by Zienkiewicz and Zhu is analysed and shown to be effective and convergent. In addition we analyse wider classes of estimators of which the Zienkiewicz–Zhu estimator is a special case. It is shown that some of these estimators will be asymptotically exact. Numerical evidence is presented supporting the analysis.
Error estimates and convergence rates for various incompressible elements
Authors: Zienkiewicz O. C. , Liu Y. C. , Huang G. C. 
Published: August 2005

AbstractThis note reports numerical experiments on the efficiency of simple error estimates derived earlier1 applied to incompressible mixed or related penalty type formulations. The rate of convergence and performance of various mixed elements is compared. Numerical results from a driven cavity and an incompressible elastic problem demonstrate that the T6B1/3D and T6/3C elements give a faster rate of convergence than the T6/1D element. However, in the case of a plane extrusion analysis (stronger singularity), the rate of convergence for the T6B1/3D element drops and is inferior to that of the T6/1D, while the T6/3C element still proves superior to the other two elements.
Numerical study of incompressible fluids in unbounded domains
Authors: Razafimahery F. 
Published: August 2005

AbstractThe aim is to build up and test a numerical method to calculate the velocity of stationary two‐dimensional flows. Both inviscid and viscous fluids are considered. They act in the unbounded domain surrounding a given profile and a stream function is introduced. A variational procedure, adapted to unbounded domains, reduces the problem to solving a finite sequence of hormonic equations, posed in bounded domains. Some profiles are tested using a finite element method.
A plate bending element based on a generalized laminate plate theory
Authors: Reddy J. N. , Barbero E. J. , Teply J. L. 
Published: August 2005

AbstractA plate bending element based on the generalized laminate plate theory (GLPT) developed by the senior author is described and its accuracy is investigated by comparison with the exact solutions of the generalized plate theory and the 3D‐elasticity theory. The element accounts for transverse shear deformation and layer‐wise description of the inplane displacements of the laminate. The element has improved description of the inplane as well as the transverse deformation response. A method for the computation of interlaminar (transverse) stresses is also presented.
Assumed strain formulation for triangular C0 plate elements based on a weak form of the Kirchhoff constraints
Authors: Stolarski H. K. , Chiang M. Y. M. 
Published: August 2005

AbstractApplication of a weak form of the Kirchhoff constraints in the formulation of triangular assumed shear strain C0 plate element is described. It is shown that, compared to a similar formulation of the quadrilateral elements, formulation of the triangles requires some additional considerations which lead to additional terms in the energy expression. With those terms performance of the assumed shear strain triangular elements is comparable to that of the quadrilateral elements.
On updating the structure of sparse matrix factors
Authors: Law Kincho H. 
Published: August 2005

AbstractStructural analysis often involves the solution of a sparse system of linear equations using matrix factorization. For structural reanalysis problems, the system of equations is progressively changing and matrix factorization is required at each iteration step. In this paper, we study the problem of updating the structure of sparse matrix factors using an ordered‐tree model. The ordered‐tree model provides the information needed to symbolically compute the non‐zero structure of the matrix factor of a sparse matrix. Furthermore, for matrix factor modification problems, this tree model can be used to determine the numerically modified entries in the matrix factor. Examples for modification of a structure and h‐adaptive refinement of a finite element model are given to illustrate the potential application of the procedures developed in this study.
A time domain boundary element method for poroelasticity
Authors: Dargush G. F. , Banerjee P. K. 
Published: August 2005

AbstractThe development of a general boundary element method (BEM) for two‐ and three‐dimensional quasistatic poroelasticity is discussed in detail. The new formulation, for the complete Biot consolidation theory, operates directly in the time domain and requires only boundary discretization. As a result, the dimensionality of the problem is reduced by one and the method becomes quite attractive for geotechnical analyses, particularly those which involve extensive or infinite domains.The presentation includes the definition of the two key ingredients for the BEM, namely, the fundamental solutions and a reciprocal theorem. Then, once the boundary integral equations are derived, the focus shifts to an overview of the general purpose numerical implementation. This implementation includes higher‐order conforming elements, self‐adaptive integration and multi‐region capability. Finally, several detailed examples are presented to illustrate the accuracy and suitability of this boundary element approach for consolidation analysis.
On the problem of modelling for parameter identification in distributed structures
Authors: Norris Mark A. , Meirovitch Leonard 
Published: August 2005

AbstractStructures are often characterized by parameters, such as mass and stiffness, that are spatially distributed. Parameter identification of distributed structures is subject to many of the difficulties involved in the modelling problem, and the choice of the model can greatly affect the results of the parameter identification process. Analogously to control spillover in the control of distributed‐parameter systems, identification spillover is shown to exist as well and its effect is to degrade the parameter estimates. Moreover, as in modelling by the Rayleigh–Ritz method, it is shown that, for a Rayleigh–Ritz type identification algorithm, an inclusion principle exists in the identification of distributed‐parameter systems as well, so that the identified natural frequencies approach the actual natural frequencies monotonically from above.
Towards parallel I/O in finite element simulations
Authors: Farhat Charbel , Pramono Eddy , Felippa Carlos 
Published: August 2005

AbstractI/O issues in finite element analysis on parallel processors are addressed. Viable solutions for both local and shared memory multiprocessors are presented. The approach is simple but limited by currently available hardware and software systems. Implementation is carried out on a CRAY‐2 system. Performance results are reported.
A mixed‐variable continuously deforming finite element method for parabolic evolution problems. Part I: The variational formulation for a single evolution equation
Authors: Kececioglu Ifiyenia , Rubinsky Boris 
Published: August 2005

AbstractThe objective of the research presented here was to develop a generic adaptive computational method for porous media evolution problems that involve coupled heat flow, fluid flow and species transport processes with sharply defined phase‐change interfaces.In this paper we examine the general least squares variational approach and develop the conceptual framework for a rate least squares variational formulation of a continuously deforming mixed variable finite element method for solving highly non‐linear time‐dependent partial differential equations. In Part II of this paper1 we extend the formulation given here for a single evolution equation to a system of coupled evolution equations. In Part III2 we discuss in detail the numerical procedures that were implemented in a computer program and present several numerical examples that demonstrate the performance of this computational method.
Delaunay triangulation of non‐convex planar domains
Authors: Lo S. H. 
Published: August 2005

AbstractThis paper investigates the possibility of integrating the two currently most popular mesh generation techniques, namely the method of advancing front and the Delaunay triangulation algorithm. The merits of the resulting scheme are its simplicity, efficiency and versatility. With the introduction of ‘non‐Delaunay’ line segments, the concept of using Delaunay triangulation as a means of mesh generation is clarified.An efficient algorithm is proposed for the construction of Delaunay triangulations over non‐convex planar domains. Interior nodes are first generated within the planar domain. These interior nodes and the boundary nodes are then linked up together to produce a valid triangulation. In the mesh generation process, the Delaunay property of each triangle is ensured by selecting a node having the smallest associated circumcircle. In contrast to convex domains, intersection between the proposed triangle and the domain boundary has to be checked; this can be simply done by considering only the ‘non‐Delaunay’ segments on the generation front.Through the study of numerous examples of various characteristics, it is found that high‐quality triangular element meshes are obtained by the proposed algorithm, and the mesh generation time bears a linear relationship with the number of elements/nodes of the triangulation.
Axisymmetric contact of an elastic layer underlain by rigid base
Authors: Li Hui , Dempsey J. P. 
Published: August 2005

AbstractAxisymmetric contact problems of an elastic layer are studied in this paper. The lower surface of the layer is either bonded to or in smooth contact with a rigid base. The upper surface is in tensionless smooth contact with a rigid flat cylinder, a rigid sphere, an elastic sphere or a circular plate, respectively. A general method is developed so that all these related problems are treated in a straightforward and like manner. In comparison to the other methods used in previous papers, the simplicity and high numerical accuracy are the major advantages of this method. The convergence is proved by comparing the numerical values to some available analytical solutions. Extensive numerical results for contact radii, displacements and contact pressures are provided.
Total Lagrangian formulation for the large displacement analysis of rectangular plates
Authors: Chang Bilin , Shabana A. A. 
Published: August 2005

AbstractIn this paper, a method for the non‐linear dynamic analysis of rectangular plates that undergo large rigid body motions and small elastic deformations is presented. The large rigid body displacement of the plate is defined by the translation and rotation of a selected plate reference. The small elastic deformation of the midplane is defined in the plate co‐ordinate system using the assumptions of the classical theories of plates. Non‐linear terms that represent the dynamic coupling between the rigid body displacement and the elastic deformation are presented in a closed form in terms of a set of time‐invariant scalars and matrices that depend on the assumed displacement field of the plate. In this paper, the case of simple two‐parameter screw displacement, where the rigid body translation and rotation of the plate reference are, respectively, along and about an axis fixed in space, is first considered. The non‐linear dynamic equations that govern the most general and arbitrary motion of the plate are also presented and both lumped and consistent mass formulations are discussed. The non‐linear dynamic formulation presented in this paper can be used to develop a total Lagrangian finite element formulation for plates in multibody systems consisting of interconnected structural elements.