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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]

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]

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, 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]

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]

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]

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]

Explicit finite-element programs, such as DYNA3D, are frequently used to solve large structural problems, such as automobile impacts, that involve tens of thousands of shell elements. Since the explicit finite-element programs do not use a stiffness matrix, the major cost of the calculation is the evaluation of the force vector. A significant part of that cost is the evaluation of the constitutive models. The standard algorithm for integrating J2 plasticity at the stress points is the radial return method. An iterative variation of radial return is commonly used to impose the zero normal stress condition within the shell elements. In this paper we explore several different non-iterative methods that impose the zero normal stress condition in an approximate manner. We show that the cost of the constitutive evaluation can be reduced by 25 per cent without introducing significant errors. [ABSTRACT FROM AUTHOR]

This paper presents an algorithm for obtaining the inverse of a tridiagonal matrix numerically. The algorithm does not require diagonal dominance in the matrix and is also computationally efficient. [ABSTRACT FROM AUTHOR]

In this paper, we have proved in theory that the sign of the current stiffness matrix provides a correct indicator for determining the sign of the loading parameter in the arc-length algorithm before the first bifurcation point is encountered, but may not be the case thereafter. © 1997 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]