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Direct stiffness method
About: Direct stiffness method is a research topic. Over the lifetime, 2584 publications have been published within this topic receiving 53131 citations.
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TL;DR: In this paper, the authors derived a 12 by 12 tangent stiffness matrix for a space frame member with constant cross-section, where the member end forces are expressed in the coordinate axes of the deformed geometry of the member in terms of the total end displacements.
Abstract: This presentation is concerned with the derivation of a 12 by 12 tangent stiffness matrix for a space frame member with constant cross-section. At first, the member end forces are expressed in the coordinate axes of the deformed geometry of the member in terms of the total end displacements. Then, in accordance with the Taylor expansion method, the stiffness influence coefficients are obtained as the partial derivatives of the force vector with respect to each one of the twelve member end displacements. It is believed that when this tangent stiffness matrix is used in connection with the Newton-Raphson iteration scheme in analyzing geometrically nonlinear structures, both the speed of convergence and the accuracy of the results are substantially increased. Numerical results are included to demonstrate the efficiency of the tangent stiffness matrix presented.
19 citations
TL;DR: Explicit expressions for stiffness matrix of triangular torus elements associated with linear displacement fields and generalized Hookian material are given in this article for linear displacement field and generalized hookian material.
Abstract: Explicit expressions for stiffness matrix of triangular torus elements associated with linear displacement fields and generalized Hookian material
19 citations
TL;DR: Using the technical computing program Mathematica, the dynamic stiffness matrix for the spatially coupled free vibration analysis of thin-walled curved beam with non-symmetric cross-section on two-types of elastic foundation is newly presented based on the power series method.
19 citations
TL;DR: In this paper, an approximate inverse of the stiffness matrix is derived for more general structural problems by resorting to the Sherman-Morrison-Woodbury formula, which allows a non-conventional assembly of the global stiffness matrix.
19 citations
TL;DR: In this article, a theoretical background and computation algorithms of equilibrium finite element method are presented there, and different external effects are estimated, namely: load, prestressing, inicial strains and support settlements.
Abstract: Summary A problem of elastic structures stress-strain field determination is considered in this article. A theoretical background and computation algorithms of equilibrium finite element method are presented there. The different external effects are estimated, namely: load, prestressing, inicial strains and support settlements. The dual relationships (equilibrium and geometrical equations, stiffness and flexibility equations) of equilibrium element, also the expressions of stiffness and flexibility matrices are given. These relationships describe the stress-strain field of the finite element and allow to transforme the flexibility matrix to the stiffness matrix and on the contrary. There are presented direct and variational formulations of the problem. The algorithms of the forces method and displacements method are made for their solution. Easier is the algorithm of displacements method, because making equations of the forces method needs to solve the system of equilibrium equations. But the formulation ...
18 citations