In this study, the inelastic buckling equation of a thin plate subjected to all in-plane loads is analytically solved and the inelastic buckling coefficient is explicitly estimated. Using the deformation theory of plasticity, a multiaxial nonlinear stress–strain curve is supposed which is described by the Ramberg–Osgood representation and the von Mises criterion. Due to buckling, the variations are applied on the secant modulus, the Poisson’s ratio and the normal and shear strains. Then, the inelastic buckling equation of a perfect thin rectangular plate subjected to combined biaxial and shear loads is completely developed. Applying the generalized integral transform technique, the equation is straightforwardly converted to an eigenvalue problem in a dimensionless form. Initially, a geometrical solution and an algorithm are presented to find the lowest inelastic buckling coefficient \(\left( {k_{s} } \right)\). The solution is successfully validated by some results in the literature. Then, a semi-analytical solution is proposed to simplify the calculation of \(k_{s}\). The method of linear least squares is applied in two stages on the obtained results and an approximate polynomial equation is found which is usually solved by trial and error. The obtained results show good agreement between the proposed semi-analytical and geometrical methods, so that the differences are < 12%. The semi-analytical solution is easily programmed in usual scientific calculators and can be applied for practical purposes.

在这项研究中，分析了薄板在所有面内载荷下的非弹性屈曲方程，并明确估计了非弹性屈曲系数。使用塑性变形理论，假定了多轴非线性应力-应变曲线，该曲线由Ramberg-Osgood表示法和von Mises准则描述。由于屈曲，变化适用于割线模量，泊松比以及法向和剪切应变。然后，完全发展了理想的矩形薄板在双轴和剪力共同作用下的非弹性屈曲方程。应用广义积分变换技术，可以将方程以无量纲形式直接转换为特征值问题。最初，\（\ left（{k_ {s}} \ right）\）。该解决方案已通过文献中的一些结果成功验证。然后，提出了一种半解析解来简化\（k_ {s} \）的计算。对获得的结果分两个阶段应用线性最小二乘法，并找到一个近似多项式方程，通常通过反复试验求解。所得结果表明，所提出的半解析方法与几何方法之间具有很好的一致性，因此差异<12％。半解析解决方案可在常规科学计算器中轻松编程，并可用于实际目的。