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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: The relationship between stress rates and tangent stiffness values with orthogonal group SO (3) for finite-element formulation was shown in Part1, and stiffness elements of finite beam element using SO(3) were shown in part2.
Abstract: The relationship between stress rates and tangent stiffness values with special orthogonal group SO (3) for finite-element formulation was shown in Part1, and stiffness elements of finite beam element using SO (3) were shown in Part2. Those stress rates are the Truesdell stress rate, the Jaumann stress rate, the Neo-Green stress rate and the Ishihara stress rate, a nonsymmetric stress rate that will be defined by this author in this report. In this study, the constitutive equation of the Ishihara stress rate will be considered. It will be shown that although the stress rate and the strain rate are nonsymmetric, the material stiffness matrix is symmetric. Next, it is shown that although the geometric stiffness of a rigid rotation is nonsymmetric, even if only the symmetric part of the stiffness is used, the second-order convergent rate determined by the Newton-Raphson method is conserved. Finally, it will be shown that the tangent stiffness formulated with SO (3) is different from that of the conventional formulation with linear rotation.
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TL;DR: The finite element formulation for deriving the soil stiffness matrix by idealizing the foundation as an elastic half space is presented in this paper, where the procedure for condensation of the soil stiff matrix taking symmetry into consideration is discussed.
Abstract: The finite element formulation for deriving the soil stiffness matrix by idealizing the foundation as an elastic half space is presented. The procedure for condensation of the soil stiffness matrix taking symmetry into consideration is discussed. Computation time is considerable reduced when a condensed soil stiffness matrix is used for the finite element analysis of rafts resting on an elastic half space.
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TL;DR: In this paper, the authors present a technique of tangent stiffness matrix generation using discrete body total potential energy stationary conditions considering geometrically nonlinear 2D frame element taking account of interelement interaction forces only.
Abstract: The expressions of the finite element method tangent stiffness matrix of geometrically nonlinear constructions are not fully presented in publications. The matrixes of small displacements stiffness are usually presented only. To solve various problems of construction analysis or design and to specify the mode of the real deflection of construction, it is necessary to have a fully described tangent matrix analytical expression. This paper presents a technique of tangent stiffness matrix generation using discrete body total potential energy stationary conditions considering geometrically nonlinear 2D frame element taking account of interelement interaction forces only. The obtained vector-function derivative of internal forces considering nodal displacements is the tangent stiffness matrix. The analytical expressions having nodal displacements of matrixes forming the content of the 2D frame construction element tangent stiffness matrix are presented in the article. The suggested methodology has been checked making symbolical calculations in the medium of MatLAB calculation complex. The analytical expression of the stiffness matrix has been obtained. Article in Lithuanian
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TL;DR: In this article, a fully coupled poroelastoplasticity reservoir model based on Drucker-Prager yield criterion is implemented the tangent stiffness method, and the computational efficiency is compared with the constant stiffness method.
1 citations