Boundary element-free method for elastodynamics |
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| Authors: | Cheng Yumin and Peng Miaojuan |
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| Institution: | (1) Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, 200072 Shanghai, China;(2) Department of Civil Engineering, Shanghai University, 200072 Shanghai, China |
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| Abstract: | 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. |
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| Keywords: | 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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