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Elastodynamic Problems (elastodynamic + problem)
Selected AbstractsAnalytical and numerical solution of the elastodynamic strip load problemINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 1 2008A. Verruijt Abstract Analytical and numerical solutions of the elastodynamic problem of an instantaneous strip load on a half space are presented and compared. The analytical solution is obtained using the De Hoop,Cagniard method, and the numerical solution is obtained using the dynamic module of the finite element package Plaxis. The purpose of the paper is to validate the numerical solution by comparison with a completely analytical solution, and to verify that the main characteristics of the analytical solution are also obtained in the numerical solution. Particular attention is paid to the magnitude, the velocity, and the shape of the Rayleigh wave disturbances. Copyright © 2007 John Wiley & Sons, Ltd. [source] Forced vibrations in the medium frequency range solved by a partition of unity method with local informationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 9 2005E. De Bel Abstract A new approach for the computation of the forced vibrations up to the medium frequency range is formulated for thin plates. It is based on the partition of unity method (PUM), first proposed by Babu,ka, and used here to solve the elastodynamic problem. The paper focuses on the introduction of local information in the basis of the PUM coming from previous approximations, in order to enhance the accuracy of the solution. The method may be iterative and generates a PUM approximation leading to smaller models compared with the finite element ones required for a same accuracy level. It shows very promising results, in terms of frequency range, accuracy and computational time. Copyright © 2004 John Wiley & Sons, Ltd. [source] An improved meshless collocation method for elastostatic and elastodynamic problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 8 2008P. H. Wen Abstract Meshless methods for solving differential equations have become a promising alternative to the finite element and boundary element methods. In this paper, an improved meshless collocation method is presented for use with either moving least square (MLS) or compactly supported radial basis functions (RBFs). A new technique referred to as an indirect derivative method is developed and compared with the direct derivative technique used for evaluation of second-order derivatives and higher-order derivatives of the MLS and RBF shape functions at the field point. As the derivatives are obtained from a local approximation (MLS or compact support RBFs), the new method is computationally economical and efficient. Neither the connectivity of mesh in the domain/boundary nor integrations with fundamental/particular solutions is required in this approach. The accuracy of the two techniques to determine the second-order derivative of shape function is assessed. The applications of meshless method to two-dimensional elastostatic and elastodynamic problems have been presented and comparisons have been made with benchmark analytical solutions. Copyright © 2007 John Wiley & Sons, Ltd. [source] P-wave and S-wave decomposition in boundary integral equation for plane elastodynamic problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2003Emmanuel Perrey-Debain Abstract The method of plane wave basis functions, a subset of the method of Partition of Unity, has previously been applied successfully to finite element and boundary element models for the Helmholtz equation. In this paper we describe the extension of the method to problems of scattering of elastic waves. This problem is more complicated for two reasons. First, the governing equation is now a vector equation and second multiple wave speeds are present, for any given frequency. The formulation has therefore a number of novel features. A full development of the necessary theory is given. Results are presented for some classical problems in the scattering of elastic waves. They demonstrate the same features as those previously obtained for the Helmholtz equation, namely that for a given level of error far fewer degrees of freedom are required in the system matrix. The use of the plane wave basis promises to yield a considerable increase in efficiency over conventional boundary element formulations in elastodynamics. Copyright © 2003 John Wiley & Sons, Ltd. [source] A rational approach to mass matrix diagonalization in two-dimensional elastodynamicsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 15 2004E. A. Paraskevopoulos Abstract A variationally consistent methodology is presented, which yields diagonal mass matrices in two-dimensional elastodynamic problems. The proposed approach avoids ad hoc procedures and applies to arbitrary quadrilateral and triangular finite elements. As a starting point, a modified variational principle in elastodynamics is used. The time derivatives of displacements, the velocities, and the momentum type variables are assumed as independent variables and are approximated using piecewise linear or constant functions and combinations of piecewise constant polynomials and Dirac distributions. It is proved that the proposed methodology ensures consistency and stability. Copyright © 2004 John Wiley & Sons, Ltd. [source] | ||||||||||