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For an efficient force method of frame analysis, the formation of localized self-equilibrating systems is an important issue. Such systems can be constructed on minimal cycle basis of the graph model of the structure. In this paper, algorithms are presented for the formation of minimal cycle bases of graph products corresponding to sparse cycle adjacency matrices, leading to the formation of highly sparse flexibility matrices. The algorithms presented employ concepts from three graph products namely Cartesian, strong Cartesian and lexicographic products. Though the formulation for the first two products exist, however, efficient implementations are made in this paper. The formulation for the generation of minimal cycle basis is extended to the lexicographic product. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper deals with a coupled finite element/scaled boundary finite element method (FE/SBFEM) and its application to wave propagation problems in fluids in the time domain. This method is already well established and has proven to be an efficient technique for treating radiation problems. In its application to time domain problems, convolution integrals arise. For each time step ti, i matrix–vector multiplications have to be performed, where the involved influence matrix—due to the non-locality in space—is fully populated. This numerical evaluation becomes a significant, time-consuming task for long time calculations, thus decreasing the attractiveness of the method. In this paper, the application of hierarchical matrices (ℋ-matrices) is to overcome this drawback. ℋ-Matrices represent an octree-based clustered low-rank approximation of the original, fully populated matrix and allow a considerable increase in efficiency for matrix–vector products encountered, e.g. in convolution integrals. The application of ℋ-matrices to this method results in an increase in efficiency without noticeable loss in accuracy. Since convolution integrals arise in various large-scale engineering computations the application of ℋ-matrix techniques might turn out to be a highly promising way to pursue. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents a general rank-1 matrix formula which allows for proper rearrangement of individual terms in multiproduct forms involving vectors and matrices. A far-reaching application of the new matrix formula to eigenvalue sensitivity evaluation is presented in the paper. Such an application reduces the sensitivity expressions to elegant, very fast and recursive forms with substantial savings in computer resources. The formula is applicable to rank-1 matrices of special structures which may constitute derivatives of the system state matrix, which is widely used in control system applications, with respect to various parameters of interest. In such cases, the use of the rank-1 formula yields exact non-approximate solutions which are identical to those obtained by other conventional formulas. The applicability of the rank-1 formula is believed to cover a wide variety of practical engineering systems pertaining to control and stability. © 1998 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents a two-dimensional frequency domain model for analyzing resonant structures. In this model, the transverse waves in the waveguide cross-section at any point are simulated by superposition of two waves in two perpendicular directions. The relationships between the physical wave parameters and the model parameters are derived. Results for cutoff wave numbers of homogeneous arbitrarily shaped cylindrical waveguides are given to test the validity of the model. These results are compared with available analytical solutions and results given by other published methods. The model proves to give good treatment for boundary conditions and accurate results with smaller matrix size in comparison with other numerical methods. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Material parameter identification based on in situ measurements plays a very important role in engineering. Since noises are inevitable in measurements and the parameter identification is inherently ill posed, it is necessary to consider some methods to stabilize the identification procedure. One choice is properly designing the sensor placement, which has attracted much attention over the past 30 years. Most existing sensor placement design methods are based on certain sensitivity analysis, which commonly requires evaluating Jacobian matrix for given parameters. However, the ‘true’ values of parameters are unknown at that moment, because sensor placement design is carried out before the parameter identification. Consequently, roughly estimated ‘true’ parameters have to be used and less optimal sensor placement could be obtained. To solve this problem, this paper presents an integrated method in which the parameter identification and sensor placement design are carried out alternatively. The validity of the proposed method is illustrated by two simple academic examples. Then it is implemented to detect damages in a real highway bridge. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper an efficient method is developed for the formation of null bases of finite element models (FEMs) composed of tetrahedron elements, corresponding to highly sparse and banded flexibility matrices. This is achieved by associating special graphs with the FEM and selecting appropriate subgraphs and forming the self-stress systems on these subgraphs. The efficiency of the present method is illustrated through two examples. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, substructuring techniques for the analysis of frame structures by the force method are reviewed. An algorithm is presented for the formation of cycle basis of the graph model of a frame structure. A simple and efficient graph method is proposed for preserving the sparsity of the matrices involved for including the boundary conditions when algebraic and graph force methods are employed. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, an improved procedure for imposing displacement boundary conditions in the direct stiffness method of the finite element analysis is presented. The proposed procedure neither changes the original order of the master stiffness matrix, nor does it require the rearrangement of the coefficient matrix. Consequently, it is easy to be implemented. Especially, the condition numbers of coefficient matrices of the improved procedure are remarkably reduced; hence the sensitivity of the solution to perturbations is considerably lowered. Numerical examples are used to demonstrate the validity of the proposed procedure. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents the implementation of Reissner's (J. Appl. Math. Phys. 1972; 23:795–804) strain–displacement relations for a planar beam using a variable order secant matrix (VOSM) technique. The secant matrices are formed using a Taylor expansion of the strain energy and hence the order of the secant and tangent matrices to be included in the nonlinear analysis can be varied depending upon the degree of nonlinearity involved in the problem. Nevertheless, a maximum of 24 matrices is sufficient to obtain predicted internal stress resultants to within 0.2% of the converged solution in all the problems tested. Using a three-noded isoparametric beam element, the accuracy of the VOSM method is demonstrated for the elastic postbuckling of arches. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The quadrilateral area co-ordinate (QAC) method is a new tool for developing quadrilateral finite element models. Compared with those traditional elements using isoparametric co-ordinates, models formulated by QAC method are less sensitive to mesh distortion. Furthermore, another advantage for QAC system is that the analytical expressions for element stiffness matrix can be obtained theoretically by basic formulae of QAC integrals, which are beneficial to finite element computation procedure. However, because of the relative complexity of the derivation process, no such explicit form of the stiffness matrix has been presented before. In this paper, the analytical element stiffness matrix of a recent 4-node quadrilateral membrane element, AGQ6-I, is given out for the first time. This element AGQ6-I, which was constructed by QAC method and generalized conforming conditions, successfully overcomes various locking problems and exhibits much better performances than many isoparametric models. And its formulations have also been introduced in shell analysis by other researchers. Numerical examples show that obvious higher computation efficiency can be achieved by presented explicit formulations. So the analytical form of the element stiffness matrix of element AGQ6-I possesses significance for its further applications. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, an eigenvalue problem that involves uncertain-but-non-random parameters is discussed. A new method is developed to evaluate the reliable upper and lower bounds on frequencies of structures for these problems. In this method the matrix in the deviation amplitude interval is considered to be a perturbation around the nominal value of the interval matrix, and the upper and lower bounds to the maximum and minimum eigenvalues of this perturbation matrix are computed, respectively. Then based on the matrix perturbation theory, the eigenvalue bounds of the original interval eigenvalue problem can be obtained. Finally, two numerical examples are provided and the results show that the proposed method is reliable and efficient. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents a method for finding the eigenvalues of some equations, or the zeros of analytic functions. There are two steps in the method. In the first step, integration along the edges of rectangle for an analytic function is performed. From the result of integration, one can know whether the zero exists in the rectangle or not. If the zero of an analytic function exists in the rectangle, we can perform the second step. In the second step, the zero is obtained by iteration. Therefore, the method is called a region searching method. Particular advantage of the suggested method is that the process for finding zero can be visualized. For example, one can clearly indicate the rectangles, which contain the zeros of an analytic function. Three numerical examples are presented. The obtained results are satisfactory even for a complicated case, for example, for finding eigenvalues of a composed wedge of dissimilar materials. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to study those matrices which can be written as the sum of two Kronecker products. Special decompositions are proposed. Applications are extended to the eigensolution of problems from structural mechanics. It is also shown how the analysis of structures can be performed without finding the inverse of the structural matrices. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We develop a numerical method to solve $$L_{\varepsilon} u_{\varepsilon} =- {{\partial} \over {\partial x_{i}}} a_{ij} (x / \varepsilon ) {{\partial} \over {\partial x_{j}}} u_{\varepsilon} = f \quad {\rm in} \, \, \Omega, \quad u_{ \varepsilon} =0 \quad {\rm on} \, \, \partial \Omega $$ where the matrix a(y)=(aij(y)) is symmetric positive definite, whose entries are periodic functions of y with periodic cell Y. More specifically we assume $ a_{ij} \in C^{1, \beta} (\Re^{2}), \quad \beta > 0 $. It is also assumed that there exists positive constants γa and βa such that $ \gamma_{a} ||\xi ||^{2} \le a_{ij} (y) \xi_{i} \xi_{j} \le \beta_{a} ||\xi||^{2} $ for all $ \xi \in \Re^{2} $ and $ y \in {\bar Y} $. The major goal in this paper is to develop a numerical approximation scheme on a mesh size h > ℇ (or h≫ℇ) with quasi-optimal approximation on L2 and broken H1 norms. The new method is based on asymptotic analysis and a careful treatment of the boundary corrector term. This kind of equation has applications in areas such as the study of flow through porous media and composite materials. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

It is well known that numerical methods designed to solve the compressible Euler equations, when written in terms of conservation variables behave poorly in the incompressible limit, that is, when density variations are negligible. However, a change to pressure based variables seem to, partly, eliminate the problem by making the Jacobian matrices fully invertible whatever the flow regime may be. Despite this apparent benefit, the stabilization matrix plus discontinuity capturing operator (for the compressible regime) still need attention, since they tend to be ill behaved for either conservation or pressure variables. In this paper, we introduce a simple way of balancing two stabilizing matrices, one of them suitable for low Mach flows and the other one for supersonic flows, so that a wide range of flow regimes are covered with only one formulation. Comparison between conservation and pressure variables is made and numerical examples are shown to validate the method. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper deals with static reanalysis of a structure with added degrees of freedom where the nodes of the original structure form a subset of the nodes of the modified structure. A preconditioned conjugate-gradient approach is developed. The preconditioner is constructed, and the implementation of the approach involves only decomposition of the stiffness matrix corresponding to the newly added degrees of freedom. In particular, the approach can adaptively monitor the accuracy of approximate solutions. The approach is applicable to the reanalysis of the structural layout modifications for the case of addition of some nodes, deletion and addition of elements and further changes in the geometry as well as to the local mesh refinements. Numerical examples show that the condition number of the selected preconditioned matrix is largely reduced. Therefore, the fast convergence and accurate results can be achieved by the approach. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, the properties of previously developed Form II symmetry (Commun. Numer. Meth. Engng 2003; 19:125–136; 2004; 20:133–146) is further investigated. Additivity properties of graphs with this form are formulated, and the effect of adding or deleting members on the eigenvalues of the Laplacian matrices of the corresponding graphs, is studied. Depending on the category of the added or deleted members, the condensed submatrices on which changes occur are identified, and the necessary modifications are suggested. A mass-spring dynamic system is presented to illustrate a typical application of the latter approach. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper new forms are introduced for efficient eigensolution of special tri-diagonal and five-diagonal matrices. Applications of these forms are illustrated using problems from mechanics of structures. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, a unified method is developed for calculating the eigenvalues of the weighted adjacency and Laplacian matrices of three different graph products. These products have many applications in computational mechanics, such as ordering, graph partitioning, and subdomaining of finite element models. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, the eigenanalysis for the multiply-connected domain problem is studied by using the dual boundary element method. The occurrence and treatment of the spurious eigenvalues for multiply-connected domain problem are reviewed when the complex-valued BEM in used. Three approaches, Burton and Miller method, CHIEF concept and SVD updating techniques, are adopted to suppress the occurrence of spurious eigensolutions. Instead of using the singular and hypersingular formulations, the singularity-free methods, the null-field equation approach and the fictitious BEM, are also utilized to deal with the eigenproblem. Both the eigenvalues and eigenmodes are compared with the analytical solutions and those of FEM for the illustrative examples. Good agreement is made. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents a fast approach for rapidly solving problems with multiple load cases using the boundary element method (BEM). The basic idea of this approach is to assemble the BEM matrices separately and to compress them using fast wavelet transforms. Using a technique called ‘virtual assembly’, the matrices are then combined inside an iterative solver according to the boundary conditions of the problem, with no need for recompression each time a new load case is solved. This technique does not change the condition number of the matrices—up to a small variation introduced by compression—so that previous theoretical convergence estimates are still valid. Substantial savings in computer time are obtained with the present technique. Copyright © 2003 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Numerical manifold method (NMM) by Shi tries to unify the solution of problems in both continuous and discontinuous domains. Presently, NMM is commonly adopted on finite triangular and quadrilateral covers and the shape functions used in classical finite element analysis are also commonly adopted in manifold analysis. In this paper, the Wilson non-conforming element is used in quadrilateral covers. The corresponding matrices of equilibrium equations are derived and a cantilever slab is considered. The results from the use of non-conforming element in NMM are in good agreement with theoretical solution as compared with the classical Q4 isoparametric element. Copyright © 2002 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

An adaptive iteration algorithm is presented in this paper for structural modal reanalysis of topological modifications. The rules of adaptation are given. The method is based on matrix perturbation and can be implemented easily on the computer. A little computation effort is involved, which is very important for topological modification with the increase of the joints and the number of degrees of freedom. In order to illustrate the method, three examples are given. The results show that the proposed method is effective for structural modal reanalysis of topological modifications. Copyright © 2002 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The paper presents an extension of a stress resultant based axisymmetric shell element by Reissner to the elasto-plastic computations. In the elastic range, the element exhibits exact kinematics for large displacements and rotations thus enabling the use of large increments in the global equilibrium path continuation. In order to preserve this desired property also in the elasto-plastic range, the general closest point projection algorithm is utilized for the elasto-plastic stress increment computation. In the case of the used element, consistent linearization of the stress updating algorithm results in a very simple form so that the element offers an efficient and computationally cheap approach to the large deflection elasto-plastic axisymmetric shell problems. Copyright © 2001 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper an efficient method is developed for decomposition of finite element meshes. The present method is based on concepts from algebraic graph theory and consists of an efficient algorithm to calculate the Fiedler vector of the Laplacian matrix of a graph. The problem of finding the second eigenvalue of the Laplacian matrix is converted into that of evaluating the maximal eigenvalue of the complementary Laplacian matrix. The corresponding eigenvector is constructed by a simple iterative method and applied to graph partitioning. An appropriate transformation maps the graph partitioning into that of domain decomposition of the corresponding finite element mesh. Copyright © 2000 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The natural vibration frequency of a bending beam with the adhesive mass is investigated in this paper. From the numerical solution of the governing equation under the relevant boundary conditions, we can define a function which is called the target function. It is proved that the problem for evaluating the natural vibration frequencies is equivalent to finding the zeros of the target function. The zeros of target function can be easily evaluated by the well-known half-division technique. It is also proved that the target function method provides one more effective way in this field. The presented numerical examples generally show that the adhesive mass has a significant influence on lowering the vibration frequency of bending beam. Copyright © 2000 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Based on the usual perturbation and Padé approximation, a new static displacement reanalysis method for structures is developed in this paper. By this method, the accuracy of the static displacements for moderate- to-large modifications of the parameters of structures is improved. As an application of the method, a numerical example is given, and the third-order perturbation method, Kirsch's combined method and the proposed method are compared in the computational accuracy. The results show that the presented method is effective. Copyright © 2000 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, Lanczos and Arnoldi reduction methods as the special cases of the generalized Hessenberg method are briefly reviewed. Attention is paid to the effect of symmetry of matrices on the behaviour of the reduction schemes, such as serious numerical breakdown. Based on the summation decomposition of matrices, two structures of the upper Hessenberg form of a general unsymmetric matrix and their relationship are revealed, in terms of which, Arnoldi reduction schemes for unsymmetric matrices can be reformulated in two respective forms. The relationship between the reformulated reduction scheme and the current Lanczos schemes for skew and symmetric matrices are also discussed. Copyright © 1999 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper the Carey non-conforming finite element is considered for solving eigenvalue problems of the second-order elliptic operator. Based on an interpolation postprocessing, high-accuracy estimates of both eigenfunctions and eigenvalues are obtained: $$\Vert \Pi ^{2}_{2h}u_{h}-u\Vert _{1}\leq Ch^{2}\Vert u\Vert _{3}$$ $$0\leq \hat{\lambda }_{h}-\lambda \leq Ch^{4}\Vert u\Vert ^{2}_{3}$$ Here, Π22h is an interpolation operator, (λ, u) and (λh, uh) are eigenpairs for the exact problem and its Carey element approximations, respectively, and $$ \hat{\lambda }_{h}$$ is defined by the Rayleigh ratio of Π22huh. Copyright © 1999 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents a substructuring-frontal combined algorithm for the analysis of fully coupled heat, moisture and displacement problems in unsaturated soil. The method adopted for solving the assembled matrix equations has a significant bearing on the computer storage requirement and execution time. Numerical examples are given to validate the proposed model. © 1998 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The discretization of the differential equation governing the axial vibration of a rod with varying cross-section leads to a specially structured matrix pencil. This paper deals with the reconstruction of this pencil from its spectrum. An iterative algorithm for this problem and an analytic characterization of complementary solutions are given. The method is demonstrated on some examples. © 1998 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In connection with previously published work, this paper presents further results about the bounding properties of eigenvalues provided by a linear eigenmatrix formulation A-λB. The linear eigenmatrix is formed by expressing the elements of a non-linear dynamic stiffness matrix, K(λ), as linear functions of the eigenparameter λ. This is achieved by choosing two fixed values of the eigenparameter and calculating K(λ) at these two values. The eigenvalues of A-λB provide error bounds on the exact eigenvalues of the non-linear eigenmatrix if the two fixed values chosen are below the lowest pole of K(λ). Choosing two identical fixed values, the error bounds on the exact eigenvalues provided by traditional linearization techniques are found as special cases. © 1998 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Numerical integration is widely used for the computation of stiffness matrices in the finite element method (FEM). However, for simple cases such as the upright prismatic element such procedures are obviated by using an analytical method, thus reducing the computation burden. In this paper, the analytical stiffness matrices for both the first- and second-order upright triangular prismatic elements are derived. © 1997 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The purpose of the paper is twofold: firstly to show that a very large range of finite element linear and non-linear computations have been conducted without the use of quadrature; secondly to present some of the prerequisites that have been used in order to accomplish this task. Although some of the rules stated here have been well known in the scientific literature and may have been applied for separate subtasks, to our knowledge they have not been put in practice for the conduction of numerous large-scale practical engineering computations and the estimation of nearly all important elemental matrices. © 1997 by John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The paper deals with the symbolic integration of a 4-noded isoparametric finite element for plane elasticity. An efficient approach to generate explicit formulas for computing the elementary stiffness matrix is discussed. The procedure is based on the use of the Derive symbolic manipulation code as well as in a posteriori manipulation of the expressions obtained. The accuracy of the results is tested in extremely distorted and geometrically ill-conditioned elements. Three practical engineering models are presented and the accuracy of the results is discussed. A computer time comparison between both numerical and symbolic integration approaches is also included, showing that relevant CPU savings are obtained when applying symbolic integration. [ABSTRACT FROM AUTHOR]

The structure of weighting coefficient matrices of harmonic differential quadrature (HDQ) is found to be either centrosymmetric or skew centrosymmetric, depending on the order of the corresponding derivatives. The properties of both matrices are briefly discussed in the paper. It is noted that the computational effort of the harmonic quadrature for some problems can be further reduced by up to 75 per cent by using the properties of the above-mentioned matrices. [ABSTRACT FROM AUTHOR]

The paper lays out an exact method, using the receptance strategy, to calculate the frequency response of a modified structure. A direct inversion of the modified impedance matrix is proposed, which reduces the computation time for successive calculations of an evolving design of the structure. [ABSTRACT FROM AUTHOR]

In elasticity theory involving anisotropic materials, the rotational transformation of stress, strain and constitutive relations is of major importance. Also, when these problems are represented in matrix form there are several different contracted notations used to express the stress and strain tensors as column matrices. In general, the contracted notations used lead to unnecessary complications and may lead to errors. In the paper, contracted forms which yield orthonormal rotational transformations are advocated. These transformations are illustrated for stress, strain, modulus and compliance and are also applicable for strength transformation. The gains to be made are procedural and mathematically simple, leading to easier understanding. [ABSTRACT FROM AUTHOR]

The free vibration and the forced dynamic responses of a uniform cantilever Timoshenko beam carrying any number of concentrated masses, translational and rotational springs and subjected to various external loadings are studied by means of the analytical-and-numerical-combined method (ANCM), where the locations and the magnitudes of the masses, springs and loadings are arbitrary. First of all, the (exact) closed-form solutions for the natural frequencies and the normal mode shapes of the 'unconstrained' Timoshenko beam (without carrying any concentrated elements) are determined; then the eigenvalue equation for free vibration analysis and the equation of motion for forced vibration analysis of the 'constrained' Timoshenko beam (carrying the prescribed concentrated elements) are derived analytically by applying the expansion theorem and the mode superposition methodology; finally the approximate natural frequencies and mode shapes of the 'constrained' Timoshenko beam and its dynamic responses due to external excitations are calculated numerically. It is found that the ANCM presented in the paper has the advantages of both the pure analytical method (to be able to save computing time) and the pure numerical method (to be able to solve various practical problems). [ABSTRACT FROM AUTHOR]

In this paper, I discuss the convergence and divergence rates for a class of generalized matrix multisplitting relaxation methods in a detailed manner. In particular, when the coefficient matrix is an L-matrix, I obtain several sufficient and necessary conditions ensuring the convergence of these methods. [ABSTRACT FROM AUTHOR]

Many finite elements based on Reissner-Mindlin plate bending theory with discrete constraints have been developed in the past few years. This approach avoids the C continuity required by the classical Kirchhoff plate theory. However, in those elements the shape functions for deflections (or their derivatives) are not integrated. Particularly in DKT (discrete Kirchhoff triangle) and in DST (discrete shear triangle) elements, the lateral deflections are defined only on the boundaries. In the paper we briefly discuss the definition of the transverse displacement for these elements, and present a simple approach to define a pseudoconsistent load vector and mass matrix. [ABSTRACT FROM AUTHOR]

Hybrid shell elements have long been regarded with reserve by the commercial finite element developers despite the high degree of reliability and accuracy associated with such formulations. The fundamental reason is the inherent higher computational cost of the hybrid approach as compared to the displacement- based formulations. However, a noteworthy factor in favor of hybrid elements is that numerical integration to generate element matrices can entirely be avoided by the use of symbolic integration. In this paper, the use of the symbolic computational approach is presented for an assumed-stress hybrid shell element with drilling degrees of freedom, and the significant time saving achieved is demonstrated through an example. [ABSTRACT FROM AUTHOR]

The investigation of the non-linear response of shell-like structures requires insight into stability behavior. In the paper we compare two strategies to compute singular points based on different eigenvalue problems. We show a simple algorithm to calculate critical load factors A used in engineering buckling analysis from the eigenvalues of the standard eigenvalue problem (KT - ωl)φ = 0. Some numerical examples illustrate the derived results and algorithms. [ABSTRACT FROM AUTHOR]

In the paper, a simple modification of the internal dissipation term in coupled thermoplastic finite element equations is presented. A modified form of the heat capacity and the thermomechanical coupling matrices are derived. These modifications are based on a decomposition of the internal dissipation term into two parts, which depend on the total strain rate and the rate of temperature change, respectively. [ABSTRACT FROM AUTHOR]

Based on the concept of the Laplacian matrix of a graph, this paper presents the SGPD (spectral graph pseudoperipheral and pseudodiameter) algorithm for finding a pseudoperipheral vertex or the end-points of a pseudodiameter in a graph. This algorithm is compared with the ones by Grimes eta!. (1990), George and Liu (1979), and Gibbs et a!. (1976). Numerical results from a collection of benchmark test problems show the effectiveness of the proposed algorithm. Moreover, it is shown that this algorithm can be efficiently used in conjunction with heuristic algorithms for ordering sparse matrix equations. Such heuristic algorithms, of course, must be the ones which use the pseudoperipheral vertex or pseudodiameter concepts [ABSTRACT FROM AUTHOR]

Enhanced 8-node three-dimensional solid and 4-node shell elements are proposed in the paper. Improvement of the response of the 3-D solid is achieved through additional strains corresponding to generalized displacements incompatible between elements. In the case of the 4-node shell, the membrane behaviour is improved through addition of incompatible membrane strains. Some linear and geometrically non-linear examples demonstrate significant improvements of the elements. Results are compared with solutions obtained with the standard, displacement-based elements and with results available in the literature. [ABSTRACT FROM AUTHOR]

In the paper the use of a truncated envelope technique is discussed as a preconditioning for the conjugate gradient method for solving large linear systems of equations with symmetric positive-definite matrices. An algorithm to generate a truncated envelope is introduced. Computational experience with systems of linear equations from the Harwell-Boeing collection is presented to highlight the efficiency of this approach. [ABSTRACT FROM AUTHOR]

Structural models of large space structures have a substantial number of degrees of freedom (DOF) and possess semi-positive-definite stiffness matrices. The paper presents an efficient co-ordinate reduction procedure for structural dynamic analysis of large space structures. The method is based on the superposition of load-dependent Ritz vectors, which are computed in block form using a shifted stiffness matrix. Comparative transient dynamic analyses are performed on a 2803 DOF model of the space station Freedom using the load-dependent method (LDM) and the mode-displacement method (MDM) based on the superposition of eigenvectors. It is shown that the LDM is able to provide convergence of displacements with a small number of vectors. The acceleration response is found to be more sensitive to vector truncation than the displacement response. Error norms based on the representation of the dynamic load by the vector basis are developed to provide an indication of the effect of vector truncation on the structural response. [ABSTRACT FROM AUTHOR]

The multiple reciprocity method is based on using higher-order fundamental solutions to eliminate domain integrals encountered in transient boundary integral formulations. The paper considers the numerical stability of this approach through an eigenvalue decomposition of the system matrix. We demonstrate that the multiple reciprocity method for transient heat conduction is stable only for appropriately chosen time steps. [ABSTRACT FROM AUTHOR]

A method for analyzing eigenvalues of the Helmholtz equation using a standard existing subroutine for eigenvalue determination is developed in this paper. It is based on the boundary integral equation formulation known as the multiple reciprocity method (MRM). The above-mentioned formulation, having polynomial matrices in terms of the eigenvalue as the coefficient matrices, is transformed into the standard-type eigenvalue problem. The resulting formulation makes it possible to determine the required eigenvalues only by boundary discretisation without any initial rough estimation. [ABSTRACT FROM AUTHOR]