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Direct stiffness method
About: Direct stiffness method is a research topic. Over the lifetime, 2584 publications have been published within this topic receiving 53131 citations.
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TL;DR: In this paper, the design formulation of compliant mechanisms is posed as a topology optimization problem, where the stiffness matrix of a single-input, single-output (SISO) mechanism is represented by the stiffness matrices of its structure with respect to the input-output ports.
Abstract: This article focuses on design formulation of compliant mechanisms posed as a topology optimization problem. With the use of linear elasticity theory, a single-input, single-output compliant mechanism is represented by the stiffness matrix of its structure with respect to the input–output ports. It is shown that the stiffness model captures the intrinsic stiffness properties of the mechanism. Furthermore, in order for the optimization problem to be properly defined, it is necessary that the stiffness matrix of the mechanism's structure must be guaranteed to be always positive definite. An exploratory design formulation is then presented based on this necessary condition. Numerical examples are provided to illustrate the potential benefits of using the intrinsic stiffness properties for compliant mechanism design with topology optimization techniques.
54 citations
TL;DR: Three domain decomposition formulations combined with the Preconditioned Conjugate Gradient (PCG) method for solving large-scale linear problems in mechanics are presented.
54 citations
TL;DR: In this article, the steady-state dynamic response of a multi-layered transversely isotropic half-space generated by a point load moving along a horizontal straight line with constant speed is investigated.
54 citations
TL;DR: It is shown that a few universal geometric quantities have the same dominant effect on the stiffness matrix conditioning for different finite element spaces for both linear algebraic solvers and the unstructured geometric meshing.
Abstract: The performance of finite element computation depends strongly on the quality of the geometric mesh and the efficiency of the numerical solution of the linear systems resulting from the discretization of partial differential equation (PDE) models. It is common knowledge that mesh geometry affects not only the approximation error of the finite element solution but also the spectral properties of the corresponding stiffness matrix. In this paper, for typical second-order elliptic problems, some refined relationships between the spectral condition number of the stiffness matrix and the mesh geometry are established for general finite element spaces defined on simplicial meshes. The derivation of such relations for general high-order elements is based on a new trace formula for the element stiffness matrix. It is shown that a few universal geometric quantities have the same dominant effect on the stiffness matrix conditioning for different finite element spaces. These results provide guidance to the studies of both linear algebraic solvers and the unstructured geometric meshing.
54 citations
TL;DR: In this paper, a Laplace-Hankel transform is applied to the governing equations of Biot's consolidation by using the eigenvalue approach, and the analytical layer-element of a single soil layer can be obtained in the transformed domain by synthesizing the generalized displacements and stresses, which are both expressed by six arbitrary constants.
53 citations