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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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31 Oct 2000
TL;DR: This method provides a systematic way of constructing 6/spl times/6 stiffness matrix in robotic grasping/manipulation and stiffness control and shows that the stiffness matrix is symmetric at the unloaded equilibrium configuration.
Abstract: In this paper, we study the 6/spl times/6 Cartesian stiffness matrices of conservative systems using the method of changing basis in differential geometry of the motion of the rigid body. We show that the stiffness matrix is symmetric at the unloaded equilibrium configuration. When the system is subjected to external loads, the 6/spl times/6 Cartesian stiffness matrix becomes asymmetric. The skew-symmetric part of the stiffness matrix is equal to the negative one-half of the cross-product matrix formed by the externally applied load, referenced to the inertial frame. This method presented in this paper provides a systematic way of constructing 6/spl times/6 stiffness matrix in robotic grasping/manipulation and stiffness control.
18 citations
TL;DR: Based on the governing equations of 3D thermoelasticity, the relationship between generalized displacements and stresses of a single layer is described by an analytical layer-element, which is obtained in the Laplace-Fourier transformed domain by using the eigenvalue approach as discussed by the authors.
Abstract: This paper presents a numerically efficient and stable method to study the thermoelastic problem of layered medium containing a heat source. Based on the governing equations of 3D thermoelasticity, the relationship between generalized displacements and stresses of a single layer is described by an analytical layer-element, which is obtained in the Laplace–Fourier transformed domain by using the eigenvalue approach. Considering the continuity conditions between adjacent layers, the global stiffness matrix of layered medium is gotten by assembling the interrelated layer-elements. Once the solution in the transformed domain is obtained, the actual solution can be recovered by an inverse transformation. Finally, numerical examples are given to study the influence of the layered medium’s properties on the behavior of thermoelastic problems.
18 citations
TL;DR: In this article, the scattering of plane SH-waves by topographic features in a layered transversely isotropic (TI) half-space was investigated by using an indirect boundary element method (IBEM).
Abstract: The scattering of plane SH-waves by topographic features in a layered transversely isotropic (TI) half-space is investigated by using an indirect boundary element method (IBEM). Firstly, the anti-plane dynamic stiffness matrix of the layered TI half-space is established and the free fields are solved by using the direct stiffness method. Then, Green’s functions are derived for uniformly distributed loads acting on an inclined line in a layered TI half-space and the scattered fields are constructed with the deduced Green’s functions. Finally, the free fields are added to the scattered ones to obtain the global dynamic responses. The method is verified by comparing results with the published isotropic ones. Both the steady-state and transient dynamic responses are evaluated and discussed. Numerical results in the frequency domain show that surface motions for the TI media can be significantly different from those for the isotropic case, which are strongly dependent on the anisotropy property, incident angle and incident frequency. Results in the time domain show that the material anisotropy has important effects on the maximum duration and maximum amplitudes of the time histories.
18 citations
TL;DR: In this paper, a stochastic fracture analysis method for random nonhomogenous cracked structures using the scaled boundary finite element method (SBFEM) is presented, where the analyzed cracked domain is divided into polygon-based sub-domains such that the material property of each sub-domain can be modeled differently in the SBFEM.
Abstract: This paper presents a stochastic fracture analysis method for random non-homogenous cracked structures using the scaled boundary finite element method (SBFEM). The analyzed cracked domain is divided into polygon-based sub-domains such that the material property of each sub-domain can be modeled differently in the SBFEM. The spatial variability of the material property is represented as random field which is then incorporated directly into the coefficient matrices of the SBFEM. The stochastic global stiffness matrix and the stochastic equilibrium equation of the SBFEM through which the stochastic structural responses can be successfully calculated are further formulated. The stochastic stress intensity factors (SIFs) considering the spatial variability of the material property are then directly extracted from the stress solution of the cracked polygon. Numerical examples are given to demonstrate the validity of the proposed method and investigate the effect of the spatial distribution of the material property on the SIFs.
18 citations
TL;DR: In this paper, the authors generalize this formulation for the analysis of the dynamic response of elastic systems submitted to arbitrary nodal loads as well as initial displacements, which yields a stiffness matrix for which only boundary integrals are required, for arbitrary domain shapes and any number of degrees of freedom.
18 citations