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Boundary element-free method for elastodynamics

Science China(Physics,Mechanics & Astronomy) 2005年第6期48卷 641-657页

作者： CHENG Yumin1 & PENG Miaojuan2 1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China 2. Department of Civil Engineering, Shanghai University, Shanghai 200072, China Shanghai Institute of Applied Mathematics and Mechanics Shanghai University Shanghai China Department of Civil Engineering Shanghai University Shanghai China

The moving least-square approximation is discussed first. Sometimes the method can form an ill-conditioned equation system, and thus the solution cannot be obtained correctly. A Hilbert space is presented on which an orthogonal function system mixed a weight function is defined. Next the improved moving least-square approximation is discussed in detail. The improved method has higher computational efficiency and precision than the old method, and cannot form an ill-conditioned equation system. A boundary element-free method (BEFM) for elastodynamics problems is presented by combining the boundary integral equation method for elastodynamics and the improved moving least-square approximation. The boundary element-free method is a meshless method of boundary integral equation and is a direct numerical method compared with others, in which the basic unknowns are the real solutions of the nodal variables and the boundary conditions can be applied easily. The boundary element-free method has a higher computational efficiency and precision. In addition, the numerical procedure of the boundary element-free method for elastodynamics problems is presented in this paper. Finally, some numerical examples are given.

关键词： moving least-square approximation, improved moving least-square approximation, elastodynamics, boundary integral equation, meshless method, boundary element-free method, Fourier eigen transform.

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Unconventional Hamilton-type variational principles for electromagnetic elastodynamics

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Science China(Physics,Mechanics & Astronomy) 2006年第1期49卷 119-128页

作者： LUO En ZHU Huijian YUAN Lei Department of Applied Mechanics and Engineering Sun Yat-sen University Guangzhou 510275 China Department of Applied Mechanics and Engineering Sun Yat-sen University Guangzhou 510275 China Department of Applied Mechanics and Engineering Sun Yat-sen University Guangzhou 510275 China

According to the basic idea of classical yin-yang complementarity and modern dual-complementarity, in a simple and unified new way proposed by Luo, the unconventional Hamilton-type variational principles for electromagnetic elastodynamics can be established systematically. This new variational principles can fully characterize the initial-boundary-value problem of this dynamics. In this paper, the expression of the generalized principle of virtual work for electromagnetic dynamics is given. Based on this equation, it is possible not only to obtain the principle of virtual work in electromagnetic dynamics, but also to derive systematically the complementary functionals for eleven-field, nine-field and six-field unconventional Hamilton-type variational principles for electromagnetic elastodynamics, and the potential energy functionals for four-field and three-field ones by the generalized Legendre transformation given in this paper. Furthermore, with this approach, the intrinsic relationship among various principles can be explained clearly.

关键词： electromagnetic elastodynamics, unconventional Hamilton-type variational principle, principle of virtual work, dual-complementarity, initial-boundary-value problem.

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