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Boundary Finite Element Method (boundary + finite_element_method)
Selected AbstractsLarge Scale Simulation with Scaled Boundary Finite Element MethodPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2009Marco Schauer Nowadays scientific and engineering applications often require wave propagation in infinite or unbounded domains. In order to model such applications we separate our model into near-field and far-field. The near-field is represented by the well-known finite element method (FEM), whereas the far-field is mapped by a scaled boundary finite element (SBFE) approach. This latter approach allows wave propagation in infinite domains and suppresses the reflection of waves at the boundary, thus being a suitable method to model wave propagation to infinity. It is non-local in time and space. From a computational point of view, those characteristics are a drawback because they lead to storage consuming calculations with high computational time-effort. The non-locality in space causes fully populated unit-impulse acceleration influence matrices for each time step, leading to immense storage consumption for problems with a large number of degrees of freedom. Additionally, a different influence matrix has to be assembled for each time step which yields unacceptable storage requirements for long simulation times. For long slender domains, where many nodes are rather far from each other and where the influence of the degrees of freedom of those distant nodes is neglectable, substructuring represents an efficient method to reduce storage requirements and computational effort. The presented simulation with substructuring still yields satisfactory results. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Asymptotic Analysis of Free-Edge and Free-Corner Effects in Laminate StructuresPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2005Christian Mittelstedt Stress fields in the vicinity of free edges and corners of composite laminates exhibit singular characteristics and may lead to premature interlaminar failure modes like delamination fracture. It is of practical interest to investigate the nature of the arising free-edge and free-corner stress singularities - i.e. the singularity orders and modes - closely. The present investigations are performed using the Boundary Finite Element Method (BFEM) which in essence is a fundamental-solution-less boundary element method employing standard finite element formulations. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Diagonalization procedure for scaled boundary finite element method in modeling semi-infinite reservoir with uniform cross-sectionINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2009S. M. Li Abstract To improve the ability of the scaled boundary finite element method (SBFEM) in the dynamic analysis of dam,reservoir interaction problems in the time domain, a diagonalization procedure was proposed, in which the SBFEM was used to model the reservoir with uniform cross-section. First, SBFEM formulations in the full matrix form in the frequency and time domains were outlined to describe the semi-infinite reservoir. No sediments and the reservoir bottom absorption were considered. Second, a generalized eigenproblem consisting of coefficient matrices of the SBFEM was constructed and analyzed to obtain corresponding eigenvalues and eigenvectors. Finally, using these eigenvalues and eigenvectors to normalize the SBFEM formulations yielded diagonal SBFEM formulations. A diagonal dynamic stiffness matrix and a diagonal dynamic mass matrix were derived. An efficient method was presented to evaluate them. In this method, no Riccati equation and Lyapunov equations needed solving and no Schur decomposition was required, which resulted in great computational costs saving. The correctness and efficiency of the diagonalization procedure were verified by numerical examples in the frequency and time domains, but the diagonalization procedure is only applicable for the SBFEM formulation whose scaling center is located at infinity. Copyright © 2009 John Wiley & Sons, Ltd. [source] | ||||||||||