The Experts below are selected from a list of 2667 Experts worldwide ranked by ideXlab platform
Erwin Stein - One of the best experts on this subject based on the ideXlab platform.
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Numerical implementation of multiplicative elasto-plasticity into assumed strain elements with application to shells at large strains
Computer Methods in Applied Mechanics and Engineering, 1999Co-Authors: Peter Betsch, Erwin SteinAbstract:Alternative formulations of isotropic large strain elasto-plasticity are presented which are especially well suited for the implementation into assumed strain elements. Based on the multiplicative decomposition of the deformation gradient into elastic and plastic parts three Distinct Eigenvalue problems related to the reference, intermediate and current configuration are investigated. These Eigenvalue problems are connected by similarity transformations which preserve the Eigenvalues. They play an important role in the subsequent development of alternative constitutive formulations and the corresponding finite element implementation. The developed constitutive procedures rely on the right Cauchy–Green tensor, or equivalently on the Green–Lagrangian strain tensor, rather than the deformation gradient. Consequently, they can be applied directly to assumed strain elements. Specifically, we are concerned with efficient low order shell elements for which the assumed strain method has proven to be extremely powerful to overcome spurious locking effects.
Peter Betsch - One of the best experts on this subject based on the ideXlab platform.
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Numerical implementation of multiplicative elasto-plasticity into assumed strain elements with application to shells at large strains
Computer Methods in Applied Mechanics and Engineering, 1999Co-Authors: Peter Betsch, Erwin SteinAbstract:Alternative formulations of isotropic large strain elasto-plasticity are presented which are especially well suited for the implementation into assumed strain elements. Based on the multiplicative decomposition of the deformation gradient into elastic and plastic parts three Distinct Eigenvalue problems related to the reference, intermediate and current configuration are investigated. These Eigenvalue problems are connected by similarity transformations which preserve the Eigenvalues. They play an important role in the subsequent development of alternative constitutive formulations and the corresponding finite element implementation. The developed constitutive procedures rely on the right Cauchy–Green tensor, or equivalently on the Green–Lagrangian strain tensor, rather than the deformation gradient. Consequently, they can be applied directly to assumed strain elements. Specifically, we are concerned with efficient low order shell elements for which the assumed strain method has proven to be extremely powerful to overcome spurious locking effects.
X.l. Liu - One of the best experts on this subject based on the ideXlab platform.
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Accurate modal perturbation in non-self-adjoint Eigenvalue problem
Communications in Numerical Methods in Engineering, 2001Co-Authors: X.l. LiuAbstract:This paper presents an algorithm for the accurate modal perturbation analysis in the non-self-adjoint Eigenvalue problem. Complete perturbation items are obtained from the given straightforward process, satisfying two conditions in a modal analysis: the Eigenvalue equations and normality condition. The zeroth-order perturbation, solved from equations in a form of Rayleigh quotient, is employed in the later perturbations, which helps to improve the accuracy of analysis. Two examples are given to show the modal perturbation with Distinct Eigenvalues and with close Eigenvalues. It is confirmed that the algorithm is applicable to any mode with a Distinct Eigenvalue, repeated Eigenvalues, or close Eigenvalues, and can give an improved accuracy. Copyright © 2001 John Wiley & Sons, Ltd.
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Derivation of formulas for perturbation analysis with modes of close Eigenvalues
Structural Engineering and Mechanics, 2000Co-Authors: X.l. LiuAbstract:The formulas for the perturbation analysis with modes of close Eigenvalues are derived in this paper. Emphasis is made on the consistency of the straightforward perturbation process, given the complete terms of perturbations in the zeroth-order, which is a form of Rayleigh quotient, and in the higher-orders. By dividing the perturbation of eigenvector into two parts, the first-order perturbation with respect to the modes of close Eigenvalues is moved into the zeroth-order perturbation. The normality condition is employed to compute the higher-order perturbations of eigenvector. The algorithm can be condensed to a single mode with a Distinct Eigenvalue, and this can accelerate the convergence of the perturbation analysis. The example confirms that the perturbation approximation obtained from the suggested procedure is in a good accuracy on the Eigenvalues, eigenvectors, and normality.
Tae Hee Lee - One of the best experts on this subject based on the ideXlab platform.
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An adjoint variable method for structural design sensitivity analysis of a Distinct Eigenvalue problem
KSME International Journal, 1999Co-Authors: Tae Hee LeeAbstract:New adjoint variable method for design sensitivity analysis of Distinct eigenvlaues and eigenvectors is presented. In the viewpoint of efficiency for the design sensitivity analysis of eigenvectors especially, the developed adjoint variable method is required to compute adjoint variables from simultaneous linear equations, the so-called adjoint equations, instead of linear combination of eigenvectors. Once we obtain the adjoint variables, design sensitivity analysis of response function that is given in terms of Eigenvalues, eigenvectors and design variables can be computed directly. In this way, design sensitivity analysis of eigenvectors can be obtained by using Eigenvalues and their corresponding eigenvectors of the mode being differentiated only. To verify the proposed method, numerical examples are demonstrated. This can have considerable impact on computer implementation of the developed method in the design sensitivity analysis of eigenproblem needed for practical applications.
Richard Bronson - One of the best experts on this subject based on the ideXlab platform.
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Eigenvalues and Eigenvectors
Matrix Methods, 1991Co-Authors: Richard BronsonAbstract:This chapter discusses Eigenvalues and eigenvectors. A nonzero vector x is an eigenvector or characteristic vector of a square matrix A if there exists a scalar λ, such that, Ax = λ x . Then, λ is an Eigenvalue or characteristic value of A . The eigenvectors and Eigenvalues are only defined for square matrices. In general, it is very difficult to find the Eigenvalues of a matrix. The characteristic equation must be obtained, and for matrices of high order, this is a lengthy task. Then, the characteristic equation must be solved for its roots. If the equation is of high order, then this can be impossibility in practice. To each Distinct Eigenvalue of a matrix A , there will correspond at least one eigenvector that can be found by solving the appropriate set of homogeneous equations. If λ is an Eigenvalue of A , then λ is an Eigenvalue of A T . The product of the Eigenvalues of a matrix equals the determinant of the matrix. The dominant Eigenvalue of a matrix is the one having largest absolute value. The dominant Eigenvalue of a matrix is real and is strictly greater in absolute value than all other Eigenvalues.