开孔薄板过屈曲分析的边界元法

Bounday Element Method of post─buckled Aralysis of Thin Plates with Holes

从开孔薄板大挠度问题的一般数学理论出发．建立了一组新型边界积分方程用以求解开孔薄板的临界载荷、过屈曲分析。并且从分支理论出发，对离散的边界积分方程进行了分析和求解。通过算例．计算了环形板在中面内受均匀推力．横向为简支、夹紧情况下的屈曲载荷以及过屈曲状态。与已知结果吻合良好．证明边界元法对开孔薄板后屈曲状态的分析是有效的。与区域型解法比较．具有处理的矩阵维数少．输入数据量少．计算时间短等优点。

In this peper,a system of new boundary integral equations is established to solve the plane stress problem,critical loads and pet--buckled analysis of perforated thin plates,based on the general mathematic theory of large deflection problem of thin plates with holes.After that,the bifurcatim theory is introduced to analyze and compute the critical boundary integral eguations.At last,as an example, we compute the critial load and post-- buckled behavior of annular plate with simply supported and clamped conditions under uniformly distributed load. The results accord well to the results by other methods,which proves the boundary element method that is efficient to the analysis of buckling of plates and has the advantages of less dimension matrices to proccess,date to input and less time to use in computation compared with other domain type solution.