Composition Feature of the Element Tangent Stiffness Matrix of Geometrically Nonlinear 2D Frame Structures
Romanas Karkauskas,Michail Popov +1 more
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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 Lithuanianread more
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The Analysis of Geometrically Nonlinear Elastic-Plastic Space Frames
Romanas Karkauskas,Michail Popov +1 more
TL;DR: In this article, the authors developed a technique for constructing a finite element tangent matrix for the nonlinear analysis of the space frame structure aimed at determining plastic deformations, based on static and kinematic formulations using the dual theory of mathematical programming.
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