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.

Development of the distinct lattice spring model for large deformation analyses

Abstract: SUMMARY This study develops the distinct lattice spring model (DLSM) for geometrically nonlinear large deformation problems The formulation of a spring bond deformation under a large deformation is derived under the Lagrange framework using polar decomposition The results reveal that the DLSM's stiffness matrix under small deformations is the tangent stiffness matrix of the DLSM under large deformations The formulation of the spring bond internal force under a given configuration is also presented and can be used to calculate the unbalanced force Using these formulations, three nonlinear solving methods (the Euler method, modified Euler method, and Newton method) are developed for the DLSM with which to tackle large deformation problems To investigate the performance of the developed model, three numerical examples involving large deformations are presented, the results of which are also in good agreement with the analytical and finite element method solutions Copyright © 2013 John Wiley & Sons, Ltd

Dynamic Analysis of Finitely Stretched and Rotated 3-D Space-Curved Beams

Abstract: A novel theory and its computational implementation are presented for the analysis of strongly nonlinear dynamic response of highly-flexible space-beams that undergo large overall motions as well as elastic motions with arbitrarily large rotations and stretches. The case of conservative force loading, which may also lead to configuration-dependent moments on the beam, is treated. A symmetric tangent stiffness matrix is derived at all times even if the distributed external moments exist. An example of transient dynamic response of the beam is presented to illustrate the validity of the theoretical methodology developed herein.

On the algorithmic and implementational aspects of a Discontinuous Galerkin method at finite strains

Abstract: In this work, algorithmic modifications are proposed and analyzed for a recently developed stabilized finite strain Discontinuous Galerkin (DG) method. The distinguishing feature of the original method, referred to as VMDG, is a consistently derived expression for the numerical flux and stability tensor that account for evolving material and geometric nonlinearity in the vicinity of the interface. Herein, the proposed modifications involve simplifications to the residual force vector and tangent stiffness matrix of the VMDG method that lead to formulations similar to other existing DG methods but retain the enhanced definition for the stability parameters. The primary objective is to reduce the costs associated with implementing the method as well as executing simulations while retaining accuracy and flexibility, thereby making the formulation amenable to boarder material classes such as inelasticity. Each simplification has associated implications on the mathematical and algorithmic properties of the method, such as L 2 convergence rate, solution accuracy, continuity enforcement, and stability of the nonlinear equation solver. These implications are carefully quantified and assessed through a comprehensive numerical performance study. The range of two and three dimensional problems under consideration involves both isotropic and anisotropic materials. Both triangular and quadrilateral element types are employed along with h and p refinement. The ability of the proposed methods to produce stable and accurate results for such a broad class of problems is highlighted.

Complementarity framework for non‐linear dynamic analysis of skeletal structures with softening plastic hinges

Abstract: In this paper, we describe an algorithm for the incremental state update of elasto-plastic systems with softening. The algorithm uses a complementary pivoting technique and is based on casting the incremental state update as a complementarity problem. In developing the algorithm, we take advantage of the special features of solid and structural mechanics problems to achieve good computational performance, and hence the ability to compute numerical solutions to practical size problems. For example, the notion of a tangent stiffness matrix arises. Numerical examples using models of skeletal structures are presented to demonstrate the practicability of the algorithm. The numerical examples also raise some interesting questions about multiplicity of the solutions. Copyright © 2010 John Wiley & Sons, Ltd.