The postbuckling of a Kirchhoff isotropic simply supported plate is considered in detail. The in-plane displacements on the edges of the plate are not constrained. The solution is obtained using the principle of the total potential energy stationarity. The expression for energy is written in the three versions: in terms of the Biot strains, the Cauchy-Green strains, and the strains corresponding to Füppl-von Kármán plate theory. Some approximate solution is constructed by the classical Ritz method. The basis functions are taken in the form of Legendre polynomials and their linear combinations. The obtained diagram of equilibrium states is rather similar to the classical diagrams of compressed shells. We show the failure of Föppl-von Kármán theory under large deflections. Using the Biot strains and the Cauchy-Green strains leads to the discrepancy between the results of at most 5 %. We demonstrate the high accuracy and convergence of the approximate solution.

中文翻译：

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具有平面内自由平移边缘的均匀压缩简支板的后屈曲

详细考虑了基尔霍夫各向同性简单支撑板的后屈曲。板边缘上的平面内位移不受限制。该解决方案是使用总势能平稳性原理获得的。能量的表达以三种形式写成：就毕奥特菌株，柯西-格林菌株以及与Füppl-vonKármán板理论相对应的菌株而言。通过经典的Ritz方法构造了一些近似解。基本函数采用勒让德多项式及其线性组合的形式。所获得的平衡态图与压缩壳的经典图非常相似。我们展示了大挠度下Föppl-vonKármán理论的失败。使用Biot菌株和Cauchy-Green菌株导致结果之间的差异最多为5％。我们证明了近似解的高精度和收敛性。