分析各向异性板的各向同性化样条积分方程法

本文分别按Reissner理论和Kirchhoff理论导出各向导性板的各向同性化控制方程,并论证了它们间在正交各向异性简支矩形板中的相通性.在用样条积分方程法求解中采用的只是些简单的各向同性板基本解,在稀疏剖分下也能有良好的计算精度.对双参数弹性地基上的板也只需在板上虚载的取值上附加某些项而不致增加多大的工作量.

Isotropicalized Spline Integral Equation Method for the Analysis of Anisotropic Plates

In the view of Reissner's and Kirchhoff's theories, respectively, we formulate the isotropicalized governing equations for the anisotropic plates, and give the proof of the equivalence relation between these two plate-models for the simply-supported rectangular orthotropic plates. The well-known fundamental solutions of the isotropic plates are utilized for the spline integral equation analysis of anisotropic plates. Even with sparse meshes the satisfactory results can be obtained. The analysis of plates on two-parameter elastic foundation is so simple as the common case that only a few terms should be added to the formulas of fictitious loads.