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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, a general theory to develop the dynamic stiffness matrix of a structural element is outlined, and substantial saving in computer time can be achieved if explicit analytical expressions for the elements of the matrix are used instead of numerical methods.
246 citations
TL;DR: In this article, the authors proposed a split node technique for finite element numerical computations, where the value of the displacement at a single node point shared between two elements depends upon which element it is referred to, thus introducing a displacement discontinuity between the two elements.
Abstract: This paper outlines a new method, the “split node technique” for introducing fault displacements into finite element numerical computations. The value of the displacement at a single node point shared between two elements depends upon which element it is referred to, thus introducing a displacement discontinuity between the two elements. We show that the modification induced by this splitting can be contained in the load vector, so that the stiffness matrix is not altered. The number of degrees of freedom is not increased by splitting. This method can be implemented entirely on the local element level, and we show rigorously that no net forces or moments are induced on the finite element grid when isoparametric elements are used. This method is thus of great utility in many geological and engineering applications.
246 citations
TL;DR: In this article, a structural approximation scheme is introduced which is referred to as the generalised reciprocal approximation, and optimality conditions for the problem are formulated based on this generalized reciprocal approximation.
244 citations
29 Jul 2005
TL;DR: A novel quasistatic algorithm is presented that alleviates geometric and material indefiniteness allowing one to use fast conjugate gradient solvers during Newton-Raphson iteration and a novel strategy for treating both collision and self-collision in this context is proposed.
Abstract: Quasistatic and implicit time integration schemes are typically employed to alleviate the stringent time step restrictions imposed by their explicit counterparts. However, both quasistatic and implicit methods are subject to hidden time step restrictions associated with both the prevention of element inversion and the effects of discontinuous contact forces. Furthermore, although fast iterative solvers typically require a symmetric positive definite global stiffness matrix, a number of factors can lead to indefiniteness such as large jumps in boundary conditions, heavy compression, etc. We present a novel quasistatic algorithm that alleviates geometric and material indefiniteness allowing one to use fast conjugate gradient solvers during Newton-Raphson iteration. Additionally, we robustly compute smooth elastic forces in the presence of highly deformed, inverted elements alleviating artificial time step restrictions typically required to prevent such states. Finally, we propose a novel strategy for treating both collision and self-collision in this context.
240 citations
TL;DR: The numerical instability problem in the standard transfer matrix method has been resolved by introducing the layer stiffness matrix and using an efficient recursive algorithm to calculate the global stiffness matrix for an arbitrary anisotropic layered structure.
234 citations