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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 article, the dynamic stiffness matrix of a rectangular plate is derived by solving the bi-harmonic equation and finally casting the solution in terms of the force-displacement relationship of the freely vibrating plate.
60 citations
TL;DR: This article describes a formulation of the finite element method and its implementation on a data parallel computing system and the Connection Machine® system, CM-2, has been used as the model archi ...
Abstract: This article describes a formulation of the finite element method and its implementation on a data parallel computing system. The Connection Machine® system, CM-2, has been used as the model archi ...
60 citations
TL;DR: In this article, a method to compute consistent response sensitivities of force-based finite element models of structural frame systems to both material constitutive and discrete loading parameters is presented, which is based on the general so-called direct differentiation method (DDM).
Abstract: This paper presents a method to compute consistent response sensitivities of force-based finite element models of structural frame systems to both material constitutive and discrete loading parameters. It has been shown that force-based frame elements are superior to classical displacement-based elements in the sense that they enable, at no significant additional costs, a drastic reduction in the number of elements required for a given level of accuracy in the computed response of the finite element model. This advantage of force-based elements is of even more interest in structural reliability analysis, which requires accurate and efficient computation of structural response and structural response sensitivities. This paper focuses on material non-linearities in the context of both static and dynamic response analysis. The formulation presented herein assumes the use of a general-purpose non-linear finite element analysis program based on the direct stiffness method. It is based on the general so-called direct differentiation method (DDM) for computing response sensitivities. The complete analytical formulation is presented at the element level and details are provided about its implementation in a general-purpose finite element analysis program. The new formulation and its implementation are validated through some application examples, in which analytical response sensitivities are compared with their counterparts obtained using forward finite difference (FFD) analysis. The force-based finite element methodology augmented with the developed procedure for analytical response sensitivity computation offers a powerful general tool for structural response sensitivity analysis.
60 citations
TL;DR: In this article, the Carrera unified formulation (CUF) is employed to derive the equations of motion through the use of a first-order layer-wise assumption for a plate with a single layer first.
60 citations
TL;DR: The hybrid compliance-stiffness matrix method is presented for stable analysis of elastic wave propagation in multilayered anisotropic media and is self-sufficient without hybrid asymptotic method and may achieve low error level over a wide range of sublayer thickness or the number of recursive operations.
Abstract: This paper presents the hybrid compliance-stiffness matrix method for stable analysis of elastic wave propagation in multilayered anisotropic media. The method utilizes the hybrid matrix of each layer in a recursive algorithm to deduce the stack hybrid matrix for a multilayered structure. Like the stiffness matrix method, the hybrid matrix method is able to eliminate the numerical instability of transfer matrix method. By operating with total stresses and displacements, it also preserves the convenience for incorporating imperfect or perfect interfaces. However, unlike the stiffness matrix, the hybrid matrix remains to be well-conditioned and accurate even for zero or small thicknesses. The stability of hybrid matrix method has been demonstrated by the numerical results of reflection and transmission coefficients. These results have been determined efficiently based on the surface hybrid matrix method involving only a subset of hybrid submatrices. In conjunction with the recursive asymptotic method, the hybrid matrix method is self-sufficient without hybrid asymptotic method and may achieve low error level over a wide range of sublayer thickness or the number of recursive operations.
60 citations