Abstract The buckling characteristic of rectangular orthotropic plates under axial compression with simply supported boundary has been extensively studied. To enhance the structural efficiency, the stacking sequence of laminate should be optimized to maximize the critical buckling load. In this study, the discrete stiffness parameters are employed to yield the theoretical optimal ply orientation corresponding to the maximum critical buckling load at a layer level, and the buckling mode shapes are calculated analytically. Subsequently, the derivation is performed based on optimal ply orientation to derive the optimal stacking sequence of the laminate, in which a sign vector is adopted to minimize the bending-twisting coupling effects. As a result, two laminate optimal design problems are solved: maximizing critical buckling load with fixed thickness, as well as minimizing the thickness with buckling constraint. Two numerical examples are adopted to verify the yielded optimal solutions. Lastly, the theoretical optimal ply orientations exhibiting different load ratios and aspect ratios are presented.

中文翻译：

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简支正交异性板最大屈曲载荷的半解析最优解

摘要 矩形正交各向异性板在简支边界轴压作用下的屈曲特性得到了广泛的研究。为了提高结构效率，应优化层压板的堆叠顺序，以最大化临界屈曲载荷。在这项研究中，离散刚度参数用于产生对应于层级最大临界屈曲载荷的理论最佳层片方向，并分析计算屈曲模式形状。随后，基于最佳层板方向进行推导，以推导出层压板的最佳堆叠顺序，其中采用符号向量来最小化弯曲-扭曲耦合效应。结果，解决了两个层压板优化设计问题：在固定厚度下最大化临界屈曲载荷，以及在屈曲约束下最小化厚度。采用两个数值例子来验证得到的最优解。最后，提出了表现出不同载荷比和纵横比的理论最佳层片方向。