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.

Shape Optimization under Shakedown Constraints

Abstract: Based on Melan’s static shakedown theorem for linear unlimited kinematic hardening material behaviour, we formulate an integrated approach for all necessary variations within direct analysis, shakedown analysis and variational design sensitivity analysis based on convected coordinates. Using a special formulation of the optimization problem of shakedown analysis, we easily derive the necessary variations of residuals, objectives and constraints. Subsequent discretizations w.r.t. displacements and geometry using e.g. an isoparametric finite element method yield the well known tangent stiffness matrix and tangent sensitivity matrix, as well as the corresponding matrices for the variation of the Lagrange-functional. Thus, all expressions on the element level are dependent only on the nodal values of the displacements and the coordinates but not on a single design variable or the corresponding design velocity field. Remarks on the computer implementation and a numerical example show the efficiency of the proposed formulation.

Nonlinear Stability Analysis of Long-Span Continuous Rigid Frame Bridge with Thin-Wall High Piers

Abstract: By utilizing the current finite element program ANSYS, two types of finite element models (FEM), the beam model (BM) and shell model (SM), are established for the nonlinear stability analysis of a practical rigid frame bridge-Longtanhe Great Bridge. In these analyses, geometrical and material nonlinearities are simultaneously taken into account. For geometrical nonlinearity, updated Lagrangian formulations are adopted to derive the tangent stiffness matrix. In order to simulate the nonlinear behavior of the plastic hinge of the piers, the multi-lines spring element COMBIN39 is used in the SM while the bilinear rotational spring element COMBIN40 is employed in the BM. Numerical calculations show that satisfying results can be obtained in the stability analysis of the bridge when the double coupling nonlinearity effects are considered. In addition, the conclusion is significant for practical engineering.

Tangent plane approximation and some of its generalizations

Abstract: A review of the tangent plane approximation proposed by L.M. Brekhovskikh is presented. The advantage of the tangent plane approximation over methods based on the analysis of integral equations for surface sources is emphasized. A general formula is given for the scattering amplitude of scalar plane waves under an arbitrary boundary condition. The direct generalization of the tangent plane approximation is shown to yield approximations that include a correct description of the Bragg scattering and allow one to avoid the use of a two-scale model.

Three-dimensional nonlinear mixed 6-DOF beam element for thin-walled members

Abstract: This paper presents a three-dimensional mixed beam element formulation for fully nonlinear distributed plasticity analysis of members composed of sections with no significant torsional warping such as steel angles and tees. This formulation is presented using a corotational total Lagrangian approach and implemented in the OpenSees corotational framework. In this context, a basic coordinate system is lined up with the element chord and translates and rotates as the element deforms. The element tangent stiffness matrix and resisting forces in the basic system are derived through linearization of the two-field Hellinger-Reissner variational principle. The displacement shape functions are cubic Hermitian functions for the transverse displacements and a linear shape function for the axial and torsional deformation. The generalized stress resultant shape functions are linear for moments and constant for axial force and torque with the P - δ effect considered, which are developed from equilibrium equations. The fiber section method with uniaxial constitutive laws is adopted to account for material nonlinearity. Since the degrees-of-freedom in the basic system are defined with respect to different reference points, all element responses are transformed to acting about the shear center before conducting the corotational transformation. The mixed element is validated through a number of experimental and numerical examples.