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.

Weyl-mechanical systems on tangent manifolds of constant w-sectional curvature

Abstract: This paper aims to present Weyl–Euler–Lagrange and Weyl–Hamilton equations on which is a model of tangent manifolds of Constant W-Sectional Curvature. In this study some differential geometrical and physical results on the related Weyl-mechanical systems are given.

An incremental algorithm to trace the non-linear equilibrium paths of pin-jointed structures using the singular value decomposition of the equilibrium matrix

Abstract: This paper is mainly concerned with a new method that analyses the non-linear behaviour of pin-joint structures. Geometrically, non-linear force method (NFM), which is derived from the force method, is now applied instead of geometrically non-linear finite-element method (NFEM). Singular value decomposition operation of the equilibrium matrix is introduced into the calculation of the responses of structures. The relationships between the equilibrium matrix in NFM and the tangent stiffness matrix in NFEM are discussed. The Newton—Raphson method is used in NFM's iteration procedure and the arc-length incremental strategy is also introduced in post-buckling analysis. Two classical structures and an infinitesimal mechanism are used as illustrative examples.

Large deflection analysis of laminated composite platesusing layerwise displacement model

Abstract: In this paper the geometrically nonlinear continuum plate finite element model, hitherto not reported in the literature, is developed using the total Lagrange formulation. With the layerwise displacement field of Reddy, nonlinear Green-Lagrange small strain large displacements relations (in the von Karman sense) and linear elastic orthotropic material properties for each lamina, the 3D elasticity equations are reduced to 2D problem and the nonlinear equilibrium integral form is obtained. By performing the linearization on nonlinear integral form and then the discretization on linearized integral form, tangent stiffness matrix is obtained with less manipulation and in more consistent form, compared to the one obtained using laminated element approach. Symmetric tangent stiffness matrixes, together with internal force vector are then utilized in Newton Raphson\'s method for the numerical solution of nonlinear incremental finite element equilibrium equations. Despite of its complex layer dependent numerical nature, the present model has no shear locking problems, compared to ESL (Equivalent Single Layer) models, or aspect ratio problems, as the 3D finite element may have when analyzing thin plate behavior. The originally coded MATLAB computer program for the finite element solution is used to verify the accuracy of the numerical model, by calculating nonlinear response of plates with different mechanical properties, which are isotropic, orthotropic and anisotropic (cross ply and angle ply), different plate thickness, different boundary conditions and different load direction(unloading/loading). The obtained results are compared with available results from the literature and the linear solutions from the author\'s previous papers.

Finite element corotational formulation for geometric nonlinear analysis of thin shells with large rotation and small strain

Abstract: Based on the consistent symmetrizable equilibrated (CSE) corotational formulation, a linear triangular flat thin shell element with 3 nodes and 18° of freedom, constructed by combination of the optimal membrane element and discrete Kirchhoff triangle (DKT) bending plate element, was extended to the geometric nonlinear analysis of thin shells with large rotation and small strain. Through derivation of the consistent tangent stiffness matrix and internal force vector, the corotational nonlinear finite element equations were established. The nonlinear equations were solved by using the Newton-Raphson iteration algorithm combined with an automatic load controlled technology. Three typical case studies, i.e., the slit annular thin plate, top opened hemispherical shell and cylindrical shell, validated the accuracy of the formulation established in this paper.