A buckling solution capable of accounting for prebuckling stress field heterogeneities is proposed. Oftentimes the same structural elements that restrict the out-of-plane displacement of the edges of a plate may also constrain their in-plane movements and cause heterogeneous prebuckling stress fields. The effect of these constraints and the consequent prebuckling stress field heterogeneity is vastly overlooked in the context of approximate analytical buckling solutions. The novelty of this work lies in basing the eigenvalue buckling analysis on a calculated prebuckling in-plane stress field. The in-plane stress field is determined by conducting a displacement-based linear elasticity analysis. In both elasticity and eigenvalue buckling analyses, the deformations of the anisotropic laminate were approximated using a first-order shear deformation theory. The equilibrium and instability equations were derived using the principle of stationary total potential energy and by employing the Ritz method. The derived formulation along with arbitrarily selected sets of boundary conditions was incorporated into a Matlab program and used for demonstrating the effect of in-plane constraints on prebuckling and buckling behavior of plates. Through a parametric study, the effect of the geometric configuration of plates on their buckling strength for selected symmetrical laminates was investigated.

提出了一种能够考虑预屈曲应力场异质性的屈曲解决方案。通常，限制板边缘平面外位移的相同结构元素也可能限制其平面内运动并导致异质预屈曲应力场。在近似解析屈曲解决方案的背景下，这些约束的影响和随之而来的预屈曲应力场异质性被大大忽略了。这项工作的新颖之处在于基于计算的预屈曲平面应力场进行特征值屈曲分析。面内应力场是通过进行基于位移的线性弹性确定的分析。在弹性和特征值屈曲分析中，各向异性层压板的变形使用一阶剪切变形理论进行近似。平衡方程和不稳定方程是利用固定总势能原理和Ritz方法推导出来的。导出的公式以及任意选择的边界条件集被合并到一个Matlab 程序中，并用于演示平面内约束对板的预屈曲和屈曲行为的影响。通过参数研究，研究了板的几何配置对选定对称层压板的屈曲强度的影响。