论文部分内容阅读
基于平面弹性与板弯曲之间的相似性原理及混合能变分原理 ,进一步将Hamilton体系引入到正交各向异性板弯曲问题之中 .于是 ,与平面弹性问题相类似 ,许多有效的数学物理方法如分离变量法和本征函数展开法等可应用于正交各向异性板弯曲问题 .从而可直接给出矩形板问题的分析解 ,扩大了解析求解的范围 .此方法与传统的半逆法有着本质上的区别 ,作为其应用 ,对两侧边固支的正交各向异性板进行了具体的分析与求解 ,结果表明此方法是十分有效和精确的 .
Based on the principle of similarity between plane elasticity and plate bending and the theory of mixed variational principle, Hamilton system is further introduced into the problem of bending of orthotropic plates. So, similar to the problem of plane elasticity, many effective mathematical physics Methods such as the method of separating variables and the eigenfunctions of eigenfunctions can be applied to the bending problem of orthotropic plates, so the analytic solution of the rectangular plate can be directly obtained and the scope of analytical solution is expanded. Method is essentially different. As its application, the analysis and solution of the orthotropic plates with two sides fixed are carried out. The results show that this method is very effective and accurate.