P波入射时含圆柱形空腔板弹性波散射与动应力集中

Dynamic stress concentrations in a plate with cylindrical cavity by incident P wave

采用波函数展开法给出了板的横截面处孔洞在平面P波入射下动应力集中问题的解。本文使用大圆弧假定法来满足板中的自由表面的边界条件。数值结果表明,上表面和孔洞间的距离与下表面和孔洞间的距离都对结果有影响。如果孔洞半径相对板的厚度很小,解近似等于孔洞全空间解。所给出的解是半解析解。因此能被用来验证诸如BEM,FEM,FDM等数值法。

A solution for dynamic stress concentration of the plate having a circular cavity subjected to incident plane P waves is given by wave function expansion method. The plate boundary in the vicinity of the cylindrical cavity is approximated by an almost flat circular boundary. The numerical results show that the distance between the upper surface and the center of cavity has effect on dynamic stress concentration. The distance between the lower surface and the center of cavity also has effect. If the radius of the cavity is relatively small compared with the thickness of the plate, the solutions approach to the full space＇s solutions for the cavity. It is concluded that the presented solutions are partially analytical solutions. So they can be used for construction and verification of approximate numerical techniques, such as the boundary element method（ BEM）, finite element method（FEM） and finite difference method（FDM）