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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: An efficient computational procedure is proposed for identifying singular points in global bifurcation analysis of the static behavior of symmetric discrete structures such as symmetric truss domes using a suitable “local” coordinate transformation.
Abstract: An efficient computational procedure is proposed for identifying singular points in global bifurcation analysis of the static behavior of symmetric discrete structures such as symmetric truss domes. Assuming group equivariance of the system of equations describing the steady state, and making use of group representation theory, the proposed method decomposes the Jacobian matrix (or tangent stiffness matrix) into block-diagonal form, with possibly repeated occurrences of identical blocks, by means of a suitable “local” coordinate transformation. The “local” transformation is computationally favorable in that it requires a small amount of computation and preserves the sparsity of the original Jacobian matrix fairly well. A concrete procedure is described for symmetric truss structures which are equivariant to dihedral groups; an explicit formula is given to the number of diagonal blocks into which the Jacobian matrix splits, and an estimate of the required number of computations shows the efficiency of the proposed method.
49 citations
TL;DR: In this article, a complementary energy approach based on a weak form of the compatibility condition as a whole of a frame member, and of the joint equilibrium conditions for the frame, is best suited for the analysis of flexibly jointed frames.
Abstract: This paper deals with the effect of non-linearly flexible hysteritic joints on the static and dynamic response of space frames. It is shown that a complementary energy approach based on a weak form of the compatibility condition as a whole of a frame member, and of the joint equilibrium conditions for the frame, is best suited for the analysis of flexibly jointed frames. The present methodology represents an extension of the authors' earlier work14 on rigidly connected frames. In the present case also, an explicit expression for the tangent stiffness matrix is given when (i) each frame member, along with the flexible connections at its ends, is represented by a single finite element, (ii) each member can undergo arbitrarily large rigid rotations and only moderate relative rotations and (iii) the non-linear bending–stretching coupling is accounted for in each member. Several examples, with both quasi-static and dynamic loading, are included, to illustrate the accuracy and efficiency of the developed methodology.
49 citations
TL;DR: In this paper, a simple four-noded geometrically nonlinear shell element is presented, which handles arbitrarily large displacements and rotations, based on the assumption of small incremental strain in each load step, a corotational procedure is employed to extract the pure deformational displacements, and update element stresses and internal force vectors through a piecewise linearized strain-displacement relation.
49 citations
TL;DR: In this article, an explicit arc-length method is simulated to trace the post-buckling equilibrium path of structures by using dynamic relaxation method with kinetic damping, which does not require the computation and formulation of any tangent stiffness matrix to search the snap-through or snap-back problems.
49 citations
TL;DR: An efficient second-order finite element-based method is presented in this article considering geometric and material nonlinear behavior of steel frames with nonlinear flexible connections and local plasticity effects, where the assumed stress method is used to derive the governing equations which satisfy joint equilibrium and displacement compatibility conditions.
48 citations