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| Virtual Boundary Element-Least Square Method for Solving Bending Problems of Thin Plate |
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| DOI：10.7511/jslx19921003 |
| KeyWord:virtual boundary element, boundary element, least square method, green function. |
| Sun Huanchun Zheng Baojang |
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| Abstract: |
| In this paper a virtual boundary element-least square method for solving bending problems of thin plate with arbitrary shape under the action of arbitrary transverse loads is presented. At first, the Green function of thin plate goverment equation and the unknown to be determining transverse loads and the normal bending moments distributed on the virtual boundary placed apart some distance from the real boundary are used to formulate a system of integral equation satisfing the real boundary conditions by superposition method. Secondly, a system of linear algebraic equation is obtained by numerically solving the above system of integral equation using the least square method and the piece-wise discrete distributing transverse loads and the normal bending moments acted along the virtual boundary. The results of some examples show that the singular integral and it' s complex treatment and calculation consuming much time are all avoided in this method. The accuracy of the solution near the boundary (including the boundary) is improved obviously. |