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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.


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TL;DR: In this article, the implicit stress integration and consistent tangent matrix calculations for an elasto-plastic model with rotational hardening are implemented within the framework of the finite element method.
Abstract: Within the framework of the finite element method, this paper presents new algorithms implementing implicit stress integration and consistent tangent matrix calculations for an elasto-plastic model with rotational hardening. The sub-stepping technique is used for both the numerical integration of the constitutive relations and determination of the consistent tangent matrix in order to overcome the convergence difficulty arising from the complexity of the elasto-plastic model with rotational hardening. The integration of the constitutive relations and the computation of the consistent tangent matrix are incorporated into a unique procedure. Numerical tests are carried out and discussed to demonstrate the global accuracy and stability of the presented algorithms.

20 citations

01 Jan 2016
TL;DR: In this article, a co-rotational finite element (FE) formulation for fast and highly efficient computation of large three-dimensional elastic deformations is presented, which aims at a simple way of separating the element rigid body rotation and the elastic deformational part by means of the polar decomposition of deformation gradient.
Abstract: Co-rotational finite element (FE) formulations can be seen as a very efficient approach to resolving geometrically nonlinear problems in the field of structural mechanics. A number of co-rotational FE formulations have been well documented for shell and beam structures in the available literature. The purpose of this paper is to present a co-rotational FEM formulation for fast and highly efficient computation of large three-dimensional elastic deformations. On the one hand, the approach aims at a simple way of separating the element rigid-body rotation and the elastic deformational part by means of the polar decomposition of deformation gradient. On the other hand, a consistent linearization is introduced to derive the internal force vector and the tangent stiffness matrix based on the total Lagrangian formulation. It results in a non- linear projector matrix. In this way, it ensures the force equilibrium of each element and enables a relatively straightforward upgrade of the finite elements for linear analysis to the finite elements for geometrically non-linear analysis. In this work, a simple 4-node tetrahedral element is used. To demonstrate the efficiency and accuracy of the proposed formulation, nonlinear results from ABAQUS are used as a reference.

20 citations

Journal ArticleDOI
TL;DR: In this paper, a non-linear finite element analysis for the elasto-plastic behavior of thick/thin shells and plates with large rotations and damage effects is presented, where damage modelled through the evolution of porosity is incorporated directly into the yield function, giving a generalized and convenient loading surface expressed in terms of stress resultants and stress couples.
Abstract: This paper presents a non-linear finite element analysis for the elasto-plastic behaviour of thick/thin shells and plates with large rotations and damage effects. The refined shell theory given by Voyiadjis and Woelke (Int. J. Solids Struct. 2004; 41:3747–3769) provides a set of shell constitutive equations. Numerical implementation of the shell theory leading to the development of the C0 quadrilateral shell element (Woelke and Voyiadjis, Shell element based on the refined theory for thick spherical shells. 2006, submitted) is used here as an effective tool for a linear elastic analysis of shells. The large rotation elasto-plastic model for shells presented by Voyiadjis and Woelke (General non-linear finite element analysis of thick plates and shells. 2006, submitted) is enhanced here to account for the damage effects due to microvoids, formulated within the framework of a micromechanical damage model. The evolution equation of the scalar porosity parameter as given by Duszek-Perzyna and Perzyna (Material Instabilities: Theory and Applications, ASME Congress, Chicago, AMD-Vol. 183/MD-50, 9–11 November 1994; 59–85) is reduced here to describe the most relevant damage effects for isotropic plates and shells, i.e. the growth of voids as a function of the plastic flow. The anisotropic damage effects, the influence of the microcracks and elastic damage are not considered in this paper. The damage modelled through the evolution of porosity is incorporated directly into the yield function, giving a generalized and convenient loading surface expressed in terms of stress resultants and stress couples. A plastic node method (Comput. Methods Appl. Mech. Eng. 1982; 34:1089–1104) is used to derive the large rotation, elasto-plastic-damage tangent stiffness matrix. Some of the important features of this paper are that the elastic stiffness matrix is derived explicitly, with all the integrals calculated analytically (Woelke and Voyiadjis, Shell element based on the refined theory for thick spherical shells. 2006, submitted). In addition, a non-layered model is adopted in which integration through the thickness is not necessary. Consequently, the elasto-plastic-damage stiffness matrix is also given explicitly and numerical integration is not performed. This makes this model consistent mathematically, accurate for a variety of applications and very inexpensive from the point of view of computer power and time. Copyright © 2006 John Wiley & Sons, Ltd.

20 citations

Journal ArticleDOI
TL;DR: In this article, a nonlinear dynamic finite element technique is developed to analyze the elastoplastic dynamic response of single-layer reticulated shells under strong earthquake excitation, in which the nonlinear three-dimensional beam elements are employed.

20 citations

Journal ArticleDOI
TL;DR: In this paper, the effect of inclination on the static behaviors of inclined variable-arc-length (VAL) beams has been developed via the variational approach, and the critical values of uniform self-weight of the inclined VAL beams are obtained by equating the determinant of the tangent stiffness to zero.

20 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202319
202241
202128
202016
201920
201829