Topic
Tangent stiffness matrix
About: Tangent stiffness matrix is a research topic. Over the lifetime, 1031 publications have been published within this topic receiving 21140 citations.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this paper, a rank-constrained linear matrix inequality (LMI) based approach was proposed to solve the tense-grity structure topology problem, where the rank constraint on the rank of the force density matrix was considered.
14 citations
TL;DR: In this article, a finite element procedure is derived from a recently published finite deformation membrane theory, in which Lagrangian type equilibrium equations, expressed in terms of Biot stresses, are employed along with constitutive equations relating the principal components of the Biot stress tensor and of the principal stretches.
14 citations
14 citations
TL;DR: In this article, the performance of several single-parameter techniques for accelerating the convergence of the initial stiffness scheme has been surveyed for the expansion of a thick cylinder, the collapse of a rigid strip footing, and the failure of a vertical cut.
Abstract: Iterative methods for the solution of non-linear finite element equations are generally based on variants of the Newton–Raphson method. When they are stable, full Newton–Raphson schemes usually converge rapidly but may be expensive for some types of problems (for example, when the tangent stiffness matrix is unsymmetric). Initial stiffness schemes, on the other hand, are extremely robust but may require large numbers of iterations for cases where the plastic zone is extensive. In most geomechanics applications it is generally preferable to use a tangent stiffness scheme, but there are situations in which initial stiffness schemes are very useful. These situations include problems where a nonassociated flow rule is used or where the zone of plastic yielding is highly localized.
This paper surveys the performance of several single-parameter techniques for accelerating the convergence of the initial stiffness scheme. Some simple but effective modifications to these procedures are also proposed. In particular, a modified version of Thomas' acceleration scheme is developed which has a good rate of convergence. Previously published results on the performance of various acceleration algorithms for initial stiffness iteration are rare and have been restricted to relatively simple yield criteria and simple problems. In this study, detailed numerical results are presented for the expansion of a thick cylinder, the collapse of a rigid strip footing, and the failure of a vertical cut. These analyses use the Mohr–Coulomb and Tresca yield criteria which are popular in soil mechanics. Copyright © 2000 John Wiley & Sons, Ltd.
14 citations
01 Dec 2013
TL;DR: In this article, the von Karmann strain measure is used to provide the special format of the tangent stiffness matrix, leading to a general linear eigenvalue problem for critical load multiplier estimates.
Abstract: In this work we propose a novel procedure for direct computation of buckling loads for extreme mechanical or thermomechanical conditions. The procedure efficiency is built upon the von Karmann strain measure providing the special format of the tangent stiffness matrix, leading to a general linear eigenvalue problem for critical load multiplier estimates. The proposal is illustrated on a number of validation examples, along with more complex examples of interest for practical applications. The comparison is also made against a more complex computational procedure based upon the finite strain elasticity, as well as against a more refined model using the frame elements. All these results confirm a very satisfying performance of the proposed methodology.
14 citations