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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 Fourier series-based virtual fields method (F-VFM) is used to identify the spatially varying stiffness distributions in 3D spatial frequency domain.
Abstract: We present an inverse method to identify the spatially varying stiffness distributions in 3 dimensions. The method is an extension of the classical Virtual Fields Method—a numerical technique that exploits information from full-field deformation measurements to deduce unknown material properties—in the spatial frequency domain, which we name the Fourier-series-based virtual fields method (F-VFM). Three-dimensional stiffness distributions, parameterised by a Fourier series expansion, are recovered after a single matrix inversion. A numerically efficient version of the technique is developed, based on the Fast Fourier Transform. The proposed F-VFM is also adapted to deal with the challenging situation of limited or even non-existent knowledge of boundary conditions. The three-dimensional F-VFM is validated with both numerical and experimental data. The latter came from a phase contrast magnetic resonance imaging experiment containing material with Poisson's ratio close to 0.5; such a case requires a slightly different interpretation of the F-VFM equations, to enable the application of the technique to incompressible materials.
12 citations
TL;DR: In this paper, a finite element method based on exact inverse of stiffness matrix is proposed for beam bending problems with stochastic stiffness, which avoids the error due to truncating the expansion series of random stiffness matrix.
12 citations
TL;DR: In this article, a direct method based on the orthogonality constraints is proposed for updating the mass and stiffness matrices of the structure first using a single set of modal data.
Abstract: Discrepancies always exist between the dynamic properties predicted by a finite element model and those measured directly from the structure. In this study, a direct method based on the orthogonality constraints is proposed for updating the mass and stiffness matrices of the structure first using a single set of modal data. This method hinges on replacement of the modal vector of concern by the modal matrix in computing the correction matrices to solve the problem of insufficient known conditions. Such a method is then extended and applied in a consecutive manner to update the structural model for each of the first few modes that are experimentally made available. In the numerical studies, it was demonstrated that for buildings of the shear type, the natural frequencies predicted by the updated model agree well with the measured ones for those modes that are experimentally made available, while the rest modes remain basically untouched. The approach proposed herein is simple, accurate and robust, which sh...
12 citations
TL;DR: In this article, an approach for extension of the optimal design method to include the structural uncertainty with the random parameters is presented, where the stiffness parameter and external load are treated as random variables.
12 citations
TL;DR: In this article, an unsymmetric geometric stiffness matrix for a membrane finite element (triangular, constant stress/strain) was derived by taking the gradient of the equilibrium equations.
12 citations