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.

Nonlinear Analysis of Planar Frames with Semi-rigid Connections and Rigid End Parts

Abstract: In this study, nonlinear analysis of planar frames with semi-rigid connections and rigid end parts is performed. Stiffness influence coefficients in the shear wall axis of the beam connected to the shear wall are obtained with the assumption that the rigid strain would be at the part between the elastic beam end and the shear wall axis. The Richard model, which represents a strain hardening and a strain softening behaviour, is used for the connection model. The tangent stiffness matrix of the second order analysis is obtained from the solution of the linear differential equation governing the moment-curvature relation of a one-dimensional member in which the effects of axial force and semi-rigid connections are accounted for. The loads that influence the frame are applied step by step. The prepared can be used for both nonlinear analysis and stability checks.

Unified plate finite elements for the large strain analysis of hyperelastic material structures

Abstract: This paper proposes a high-order two-dimensional (2D) finite element model for the analysis of isotropic, nearly incompressible hyperelastic material structures based on a decoupled neo-Hookean strain energy function. The model is based on the Carrera Unified Formulation (CUF) , which allows to automatically implement different kinematics by using an opportune recursive notation. The principle of virtual work and a finite element approximation are exploited to obtain the nonlinear governing equations. Considering the three-dimensional full Green–Lagrange strain components and given the material Jacobian tensor, the explicit forms of tangent stiffness matrices of unified plate elements are presented in terms of the fundamental nuclei, which are independent of the theory approximation order. Several problems of soft material plates under uniform pressure are investigated, including a silicone rubber clamped plate and a simply supported plate made of biological material. The proposed model is compared with literature results including those coming from experiments and numerical solutions. The numerical investigation demonstrated the validity and accuracy of the proposed methodology for the analysis of hyperelastic plates.

Solution of non-linear problems with full stiffness matrices

Abstract: In this contribution the non-incremental system of FEM equations containing the full non-linear tangent stiffness matrix is derived from the principle of virtual work. This formulation is applied to the derivation of basic FEM formulae for 1D-bar element. Two iterative solution methods of non-linear equations are presented and their effectiveness is verified on several numerical experiments.

A higher order formulation for geometrically nonlinear space beam element

Abstract: Publisher Summary This chapter describes a consistent incremental tangent stiffness matrix for geometrically nonlinear analysis of space beam element. In this refined finite element formulation, two deformation matrices due to axial force and moment, which represent the higher order effects of the deformations in element, are derived. These matrices are the functions of element deformations and are incorporated with the coupling among axial, lateral, and torsional deformations. These proposed matrices are used together with linear and geometric stiffness for beam elements to analyze deflection behavior of space frames comprising members with negligible sectorial warping. Numerical examples show that the proposed element is accurate and efficient in predicting the nonlinear behavior, such as axial-torsional and lateral-torsional buckling of space frame even when less elements are used to model a member. These proposed matrices are used together with the linear and geometric stiffness for beam elements to analyze the deflection behavior of space frames.

Large displacement geometrically nonlinear finite element analysis of 3D Timoshenko fiber beam element

Abstract: Based on continuum mechanics and the principle of virtual displacements, incremental total Lagrangian formulation (T.L.) and incremental updated Lagrangian formulation (U.L.) were presented. Both T.L. and U.L. considered the large displacement stiffness matrix, which was modified to be symmetrical matrix. According to the incremental updated Lagrangian formulation, small strain, large displacement, finite rotation of three dimensional Timoshenko fiber beam element tangent stiffness matrix was developed. Considering large displacement and finite rotation, a new type of tangent stiffness matrix of the beam element was developed. According to the basic assumption of plane section, the displacement field of an arbitrary fiber was presented in terms of nodal displacement of centroid of cross-area. In addition, shear deformation effect was taken account. Furthermore, a nonlinear finite element method program has been developed and several examples were tested to demonstrate the accuracy and generality of the three dimensional beam element.