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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: In this paper, the distance minimization data-driven computing method is extended to deal with boundary value problems of continuum mechanics within the finite strain theory, where the solution process is carried out by using directly the experimental data instead of the conventional constitutive laws.
119 citations
TL;DR: In this paper, the authors deal with elasto-plastic large deformation analysis of space-frames, where each member of the frame, modelled as an initially straight space-beam, is represented by a single finite element, each member can undergo arbitrarily large rigid rotations, but only moderately large relative rotations.
Abstract: SUMMARY This paper deals with elasto-plastic large deformation analysis of space-frames. It is based on a complementary energy approach. A methodology is presented wherein: (i) each member of the frame, modelled as an initially straight space-beam, is sought to be represented by a single finite element, (ii) each member can undergo arbitrarily large rigid rotations, but only moderately large relative rotations; (iii) a plastic-hinge method, with arbitrary locations of the hinges along the beam, is used to account for plasticity, (iv) the non-linear bending-stretching coupling is accounted for in each member, (v) the applied loading may be non-conservative and (vi) an explicit expression for the tangent stiffness matrix of each element is given under conditions (i) to (v). Several examples, with both quasi-static and dynamic loading, are given to illustrate the accuracy and efficiency of the approaches presented.
108 citations
TL;DR: In this article, the authors present a finite element formulation for static analysis of linear elastic spatial frame structures and apply exact non-linear kinematic relationships of the space finite-strain beam theory, assuming the Bernoulli hypothesis and neglecting the warping deformations of the cross-section.
108 citations
TL;DR: In this paper, an incremental total Lagrangian formulation for curved beam elements that includes the effect of large rotation increments is developed, and a complete and symmetric tangent stiffness matrix is obtained.
Abstract: SUMMARY An incremental Total Lagrangian Formulation for curved beam elements that includes the effect of large rotation increments is developed. A complete and symmetric tangent stiffness matrix is obtained and the numerical results show, in general, an improvement over the standard formulation where the assumption of infinitesimal rotation increments is made in the derivation of the tangent stiffness matrix.
105 citations
TL;DR: In this paper, an accelerated Newton algorithm based on Krylov subspaces is applied to solving nonlinear equations of structural equilib- rium, where the algorithm uses a low-rank least-squares analysis to advance the search for equilibrium at the degrees of freedom DOFs where the largest changes in structural state occur; then it corrects for smaller changes at the remaining DOFs using a modified Newton computation.
Abstract: An accelerated Newton algorithm based on Krylov subspaces is applied to solving nonlinear equations of structural equilib- rium. The algorithm uses a low-rank least-squares analysis to advance the search for equilibrium at the degrees of freedom DOFs where the largest changes in structural state occur; then it corrects for smaller changes at the remaining DOFs using a modified Newton computation. The algorithm is suited to simulating the dynamic progressive collapse analysis of frames where yielding and local collapse mechanisms form at a small number of DOFs while the state of the remaining structural components is relatively linear. In addition, the algorithm is able to resolve erroneous search directions that arise from approximation errors in the tangent stiffness matrix. Numerical examples indicate that the Krylov subspace algorithm has a larger radius of convergence and requires fewer matrix factorizations than Newton-Raphson in the dynamic progressive collapse simulation of reinforced concrete and steel frames. DOI: 10.1061/ASCEST.1943-541X.0000143 CE Database subject headings: Algorithms; Failures; Nonlinear analysis; Progressive collapse; Steel frames. Author keywords: Algorithms; Collapse; Nonlinear analysis; Progressive failure.
104 citations