具有大挠度的四边固定矩形板的弹塑性动力响应

DINAMIC RESPONSE FOR AN ELASTIC-PLASTIC RECTANGULAR PLATE OF LARGE DEFLECTION WITH ALL EDGES BUILT IN

本文首先给出了四边固定矩形板在冲击载荷作用下的弹性动力响应,先求解自由振动,得到相应的本征值和本征函数,然后求得强迫振动,所得到的弹性解是解析解。弹性解一经求得,就可利用巳知弹性解求得板的弹塑性动力响应。在这个基础上可以进一步去求得在大挠度情况下的弹塑性动力响应,本文是作者过去工作〔1,2〕的进一步发展,所得的结果具有良好的规律性而且是比较合理的,说明本文不仅在弹性解而且在弹塑性动力响应方面所做的工作都是可行的。

In this paper, the elastic analytical solution for the dynamic response of a rectangular thin plate with all edges built in is giver at first. The elastic solution that we obtained is the analytical solution. Once the elastic solution is obtained, we may emplay the known elastic solution to analyze the elastic-plastic dynamic response for the plate. On the basis of elastic solution, dynamic response for an elastic-plastic plate of large deflection may further be solved. This paper is the further development for the past works of authors. The computational results obtained in this paper are reasonable and with considerable regularity. It is shown that the present method is valid not only in the elastic analysis but also in the elastic-plastic analysis.