Topic
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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01 Jan 2002
TL;DR: In this paper, an extension of the now standard Generalized Backward Euler (GBE) algorithm to a general class of elastoplastic constitutive equations for geomaterials, characterized by mechanical and non-mechanical hardening mechanisms is discussed.
Abstract: The paper discusses an extension of the now standard Generalized Backward Euler (GBE) algorithm to a general class of elastoplastic constitutive equations for geomaterials, characterized by mechanical and non-mechanical hardening mechanisms The resulting integration scheme is well suited for the application to relatively complex, three-invariant yield surface and plastic potential functions A closed form expression for the consistent tangent stiffness matrix is derived for the general case, extending the work of [TAM 02a] for isotropic- hardening models The application of the numerical procedure is discussed with reference to a constitutive model for chemical weathering of bonded geomaterials recently proposed by [TAM 02b] Results from a series of numerical experiments are given to illustrate the accuracy and convergence properties of the algorithm
6 citations
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01 Mar 1991
TL;DR: In this article, the International System of Units (ISUML) is used to measure the stiffness and flexibility of an element and the equivalent actions to be placed at the nodes of a structure using shape functions.
Abstract: Preliminary Considerations Nodal Variables - Stiffness and Flexibility Matrices of a Structure Element Variables - Total Stiffness Matrix of an Element Direct Stiffness Method Supplementary Procedures to the Stiffness Method Basic Element Variables The Equations of Equilibrium and the Equations of Compatibility of a Structure Computation of the Displacements of Statically determinate Framed Structures The Flexibility Method The Displacement or Stiffness Method Appendix A. The International System of Units Appendix B. End Actions in Fixed-At-Both-Ends Elements Appendix C. Vector Quantities Appendix D. Computation of the Total Stiffness Matrix of an Element and the Equivalent Actions to be Placed at the Nodes of a Structure Using Shape Functions.
6 citations
TL;DR: In this article, the general mathematic relationship between structural secant and tangent stiffness matrices is developed in detail based on Taylor series expression of the total potential energy, which can be used not only in finite element method but also Rayleigh-Ritz method, Galerkin method, etc.
6 citations
TL;DR: In this article, it was shown that the tangent stiffness used for determining loss of stability has a specific, simple form, and that these two terms are not mutually conditional, whereas the term "linear prebuckling paths" refers to the shape of the load-displacement diagrams before stability loss.
Abstract: Stability problems are termed linear if the tangent stiffness used for determining loss of stability has a specific, simple form. The term “linear prebuckling paths” refers to the shape of the load–displacement diagrams before loss of stability. In this note, it will be shown that these two terms are not mutually conditional.
6 citations
TL;DR: This technical note presents closed-form finite-element stiffness formulations for the four-node quadrilateral element with a fully populated material stiffness, which is required for the nonlinear analysis of reinforced concrete membrane structures.
Abstract: This technical note presents closed-form finite-element stiffness formulations for the four-node quadrilateral element with a fully populated material stiffness, which is required for the nonlinear analysis of reinforced concrete membrane structures. With the material stiffness matrix accounting for anisotropy of the materials and prestrain effects, the developed closed-form element stiffness can be incorporated into a nonlinear finite-element algorithm. Through use of the developed explicit expressions, the examples provided show that the computational effort required to form the stiffness matrix is greatly reduced, compared to either the conventional numerical integration scheme or the elastic-material-stiffness-oriented Griffths’ FORTRAN subroutine.
6 citations