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.

Automated solution procedures for negotiating abrupt non‐linearities and branch points

Abstract: In the inelastic stability analysis of plated structures, incremental‐iterative finite element methods sometimes encounter prohibitive solution difficulties in the vicinity of sharp limit points, branch points and other regions of abrupt non‐linearity. Presents an analysis system that attempts to trace the non‐linear response associated with these types of problems at minor computational cost. Proposes a semi‐heuristic method for automatic load incrementation, termed the adaptive arc‐length procedure. This procedure is capable of detecting abrupt non‐linearities and reducing the increment size prior to encountering iterative convergence difficulties. The adaptive arc‐length method is also capable of increasing the increment size rapidly in regions of near linear response. This strategy, combined with consistent linearization to obtain the updated tangent stiffness matrix in all iterative steps, and with the use of a “minimum residual displacement” constraint on the iterations, is found to be effective in avoiding solution difficulties in many types of severe non‐linear problems. However, additional procedures are necessary to negotiate branch points within the solution path, as well as to ameliorate convergence difficulties in certain situations. Presents a special algorithm, termed the bifurcation processor, which is effective for solving many of these types of problems. Discusses several example solutions to illustrate the performance of the resulting analysis system.

Bandwidth Minimization of Stiffness Matrices

Abstract: The purpose of this note is to examine the form of the structural stiffness matrix that results from a coupled harmonic type of analysis. It is to be shown that such a matrix can be banded, thereby leading toward the practicality of the coupled harmonic finite-element analysis method for complex asymmetrically loaded solids of revolution.

Viscoelastoplastic Response of Axisymmetric Shells under Impulsive Loadings

Abstract: A derivation of finite element equations of and solution to the viscoelastoplastic response of an isotropic axisymmetric shell are presented herein. The generalized Maxwell model is incorporated into the von Mises isotropic yield function. This permits a derivation of the incremental stress as a function of elastic, viscous, and plastic strains. With this relationship inserted into the incremental equation of motion, a direct numerical integration scheme is then used to solve for incremental responses. The plastic tangent stiffness matrix is updated at each incremental time step. Numerical results are presented for a circular plate to verify correctness of the program and subsequently for a spherical cap subjected to uniformly distributed transverse impulsive load of infinite duration.

Stiffness analysis and optimization of a hybrid machine tool based on the stiffness matrix

Abstract: The stiffness of a hybrid machine tool using a redundantly actuated parallel mechanism was analyzed by considering the deformation of the straight rolling slide-way pair and bearings. Stiffness assembly theory was used to develop the stiffness matrix for the machine tool. The impact of the straight rolling guide-way pair on the whole machine was also analyzed to optimizate design of the weakest part of the machine tool. The analysis results show that the position stiffness is symmetric along the x, y and z directions within a specified workspace, with the best position stiffness along the z direction and the worst along the x direction. The results also show that the straight rolling guide-way pair significantly affects the whole machine stiffness.

Using More Accurate Strain For Three-Dimensional Truss Analysis

Abstract: Instead of the usual neglecting, this study takes advantage of the second-order axial strain terms in the elastic constitutive equation of three-dimensional truss. This leads to higherorder terms on the resulting unbalanced force and on its corresponding tangent stiffness. The finite element procedure and updated Lagrangian descriptions are utilized with the new stiffness matrix. Furthermore, governing equilibrium equations are solved by using cylindrical arc-length approach. The validity of the proposed algorithm is checked by numerical examples. The outcomes indicate that the authors' formulation possesses the ability to trace the equilibrium path completely. Moreover, the obtained answers are identical with the exact results of other researchers.