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.
Papers published on a yearly basis
Papers
More filters
TL;DR: A method is presented whereby an explicit expression for the tangent moduli consistent with a closest point return mapping algorithm may be developed for generalized pressure-dependent elastolasticity models, and no matrix inversion is necessary.
90 citations
TL;DR: In this paper, three mode types are proposed for reducing nonlinear dynamical system equations, resulting from finite element discretizations: tangent modes, modal derivatives, and newly added static modes.
89 citations
TL;DR: In this paper, the analytical properties of the constitutive equations in plasticity with a nonassociated flow rule are investigated under the assumption of small deformations and the tangent stiffness tensor is assessed.
88 citations
TL;DR: In this article, a non-linear formulation of the second-order terms in the strain-displacement relationship is proposed to represent axial displacement along the deformed (instead of undeformed) axis.
Abstract: In this paper, the equations of motion of flexible multibody systems are derived using a nonlinear formulation which retains the second-order terms in the strain-displacement relationship. The strain energy function used in this investigation leads to the definition of three stiffness matrices and a vector of nonlinear elastic forces. The first matrix is the constant conventional stiffness matrix, the second one is the first-order geometric stiffness matrix ; and the third is a second-order stiffness matrix. It is demonstrated in this investigation that accurate representation of the axial displacement due to the foreshortening effect requires the use of large number or special axial shape functions if the nonlinear stiffness matrices are used. An alternative solution to this problem, however, is to write the equations of motion in terms of the axial coordinate along the deformed (instead of undeformed) axis. The use of this representation yields a constant stiffness matrix even if higher order terms are retained in the strain energy expression. The numerical results presented in this paper demonstrate that the proposed new approach is nearly as computationally efficient as the linear formulation. Furthermore, the proposed formulation takes into consideration the effect of all the geometric elastic nonlinearities on the bending displacement without the need to include high frequency axial modes of vibration.
87 citations
TL;DR: In this paper, a class of plasticity models which utilize Rankine's (principal stress) yield locus is formulated to simulate cracking in concrete and rock under monotonic loading conditions.
Abstract: SUMMARY A class of plasticity models which utilize Rankine’s (principal stress) yield locus is formulated to simulate cracking in concrete and rock under monotonic loading conditions. The formulation encompasses isotropic and kinematic hardenindsoftening rules, and incremental (flow theory) as well as total (deformation theory) formats are considered. An Euler backward algorithm is used to integrate the stresses and internal variables over a finite loading step and an explicit expression is derived for a consistently linearized tangent stiffness matrix associated with the Euler backward scheme. Particular attention is paid to the corner regime, that is when the two major principal stresses become equal. A detailed comparison has been made of the proposed plasticity-based crack formulations and the traditional fixed and rotating smeared-crack models for a homogeneously stressed sample under a non-proportional loading path. A comparison between the flow-theory-based plasticity crack models and experimental data has been made for a Single Edge Notched plain concrete specimen under mixed-mode loading conditions.
86 citations