The elastic post-buckling behavior of thin plates covers a relatively vast region in which geometry nonlinearity (large deflection) and material linearity (Hooke's low) are realized. In this region, a thin rectangular plate has constant stiffnesses in both orthogonal directions. Few simplified analysis guidelines have been analytically represented for in-plane stiffnesses of an elastic post-buckled thin plate subjected to biaxial loads. In this study, Marguerre's equations (the generalized form of von Karman equations), which describe the elastic post-buckling behavior of imperfect thin plates, are solved. Galerkin's method is used to solve these equations in a semi-analytical procedure. Simply supported imperfect thin rectangular plates are considered, and the stresses and displacements functions are obtained in two orthogonal directions to determine corresponding in-plane stiffnesses of the plate. Also, the maximum applicable load is obtained so that the material's linear behavior is maintained. The semi-analytical procedure has accuracy enough to predict the in-plane stiffness of post-buckled plates and can be easily used for practical purposes.

薄板的弹性后屈曲行为覆盖了一个相对较大的区域，在该区域中实现了几何非线性（大挠度）和材料线性（胡克低）。在该区域中，矩形矩形薄板在两个正交方向上具有恒定的刚度。对于承受双轴载荷的弹性后屈曲薄板的平面内刚度，很少有简化的分析准则可以用解析表示。在这项研究中，解决了描述不完善薄板的弹性屈曲后行为的Marguerre方程（von Karman方程的广义形式）。Galerkin方法用于在半解析过程中求解这些方程。考虑简单支撑的不完美的薄矩形板，在两个正交方向上获得应力和位移函数，以确定相应的板内平面刚度。而且，获得了最大可施加的载荷，从而保持了材料的线性性能。半分析程序具有足够的准确性，可以预测后屈曲板的平面内刚度，并且可以很容易地用于实际目的。