弹性地基上薄板弯曲问题的边界元法及物理参数识别

BOUNDARY ELEMENT METHOD FOR BENDING PLATES ON ELASTIC FOUNDATIONS AND THE IDENTIFICATION OF PHYSICAL PARAMETERS

利用 Hankel 变换导出了弹性地基上薄板弯曲问题的基本解,此基本解对三种常用地基模型具有统一的表达形式,针对近年提出的广义边值问题,建立了统一的边界积分方程和边界元求解格式。在此基础上将边界元法和优化方法相结合,根据现场用激光准直弯沉仪测板上若干点的位移,反算其它力学参量。编制了适用范围较广的计算软件,给出若干典型算例和工程算例。

The fundamental solution for the bending of thin plates on elastic foundations is derived by Hankel transformation.This solution in an unified form includes all three different kinds of foundation models,which are treated separately in existing literature.For the generalized boundary value problem a complete set of boundary integral equations and relevant numerical scheme are established.By combining the boundary element method with the optimization technique a procedure is also presented for identifying mechanical parameters,in which the displacements of plate at several points are measured by JGPD instru- ment.The effectiveness of the proposed method in illustrated by two typical examples with practical appli- cations.