正交各向异性矩形板小变形弹性屈曲与过屈曲分析

Elastic buckling and post-buckling analysis of an orthotropic rectangular plate with small deformation

讨论了受一般边界条件约束的正交各向异性矩形板受面内边界力作用下的屈曲和过屈曲状态，证明了在参数满足一定关系的条件下，不论最小临界载荷是单重的还是多重的，问题的平凡解都必定发生分支，而且分支解是连续的，且分支解的个数与材料参数及边界约束条件有关。文中还给出了计算每个分支解的能量表达式。

The elastic buckling and post--buckling of an orthotropic rectangular plate with general edgeconditions,which is subjected to arbitrary forces and stresses along its boundary in the mid --plane of theplate is considered by the bifurcation theory. h is proved that under some conditions satisfied by materialparameters the trivial solution of the problem is bound to branch at an eigenvalue despite that the eigenvalue is simple or double,and bifurcation solutions are shown to be continual. The number of bifurcation solutions is dependent on material parameters.The energy expression is given to calculate the energy of eachbifurcation solutions.