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.
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TL;DR: In this article, a continuum-based shape and configuration design sensitivity analysis (DSA) method for a finite deformation elastoplastic shell structure has been developed, where shell elastasticity is treated using the projection method that performs the return mapping on the subspace defined by the zero-normal stress condition.
Abstract: SUMMARY A continuum-based shape and configuration design sensitivity analysis (DSA) method for a finite deformation elastoplastic shell structure has been developed. Shell elastoplasticity is treated using the projection method that performs the return mapping on the subspace defined by the zero-normal stress condition. An incrementally objective integration scheme is used in the context of finite deformation shell analysis, wherein the stress objectivity is preserved for finite rotation increments. The material derivative concept is used to develop a continuum-based shape and configuration DSA method. Significant computational efficiency is obtained by solving the design sensitivity equation without iteration at each converged load step using the same consistent tangent stiffness matrix. Numerical implementation of the proposed shape and configuration DSA is carried out using the meshfree method. The accuracy and efficiency of the proposed method is illustrated using numerical examples. Copyright 2006 John Wiley & Sons, Ltd.
3 citations
01 Jan 2009
TL;DR: An efficient One-Step inverse approach based on nodal tangent plane (NTP) is proposed to predict the optimum blank shapes and sizes and reasonable estimation of forming severity (i.e., thickness, strain distributions) from desired final workpieces as discussed by the authors.
Abstract: An efficient One-Step inverse approach (IA) based on nodal tangent plane (NTP) is proposed to predict the optimum blank shapes and sizes and reasonable estimation of forming severity (i.e., thickness, strain distributions) from desired final workpieces. According to the deformation theory of plasticity, Hill’s planar isotropic yield criteria and the principle of virtual work (PVW), the non-linear elasto-plastic finite element equilibrium equations are obtained, in which the simplified boundary force conditions are also implemented to simulate the effects of punch, die, blank-holder and draw-bead. For solving the non-linear problem, Newton-Raphson method is used. However, in traditional One-Step IA, the local element stiffness matrix is assembled in the global coordinate system where bad convergence is always a severe problem, especially when vertical or quasi-vertical walls happen. Fortunately, the NTP method provides a smart solution to enhance the convergence, where the ill-conditioned matrix is avoided by assembling the local element stiffness matrix to the tangent plane and to the normal of node. The developed algorithm is integrated into independently developed KMAS (KingMesh Analysis System) for sheet metal forming. To validate its efficiency and feasibility, it is applied to square cup deep drawing of Numisheet’93 and front fender forming of Numisheet’2002 by comparing with DynaForm based on incremental algorithm and traditional One-Step IA.Copyright © 2009 by ASME
3 citations
TL;DR: In this paper, a non-linear shear deformable shell element is presented for the solution of stability problems of stiffened plates and shells, which is exactly defined on the midsurface.
Abstract: The formulation of a non-linear shear deformable shell element is presented for the solution of stability problems of stiffened plates and shells. The formulation of the geometrical stiffness presented here is exactly defined on the midsurface and is efficient for analyzing stability problems of thick plates and shells by incorporating bending moment and transverse shear resultant force. As a result of the explicit integration of the tangent stiffness matrix, this formulation is computationally very efficient in incremental nonlinear analysis. The element is free of both membrane and shear locking behaviour by using the assumed strain method such that the element performs very well in the thin shells. By using six degrees of freedom per node, the present element can model stiffened plate and shell structures. The formulation includes large displacement effects and elasto-plastic material behaviour. The material is assumed to be isotropic and elasto-plastic obeying Von Mises`s yield condition and its associated flow rules. The results showed good agreement with references and computational efficiency.
3 citations
TL;DR: In this article, the authors present methods to generate a directed strain perturbation for the Green-Lagrange, Euler-Almansi and logarithmic strain measures as a function of the deformation gradient and compare them with other commonly used methods.
3 citations
TL;DR: A new method for reliable detection and accurate computation of singular points on load paths is presented and applied to a space truss subjected to symmetric and asymmetric snow loads.
Abstract: A space truss is in an unstable configuration if it can displace incrementally without an incremental change in its loading and its supports. The load path which follows after an unstable configuration can be unique (snap-through), or there can be several possible load paths (bifurcation). This paper presents a method to detect nearly unstable configurations of a truss, a method to determine the loading, displacements and reactions of the unstable configuration and a method to traverse the load path which follows after the unstable configuration. The detection of structural configurations with singular tangent stiffness matrix is essential because they can be unstable. The secondary paths, especially in unstable buckling, can play the most important role in the loss of stability and collapse of the structure. A new method for reliable detection and accurate computation of singular points on load paths is presented and applied to a space truss subjected to symmetric and asymmetric snow loads.
3 citations