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Shape and material optimization for buckling behavior of functionally graded toroidal shells
Thin-Walled Structures ( IF 6.4 ) Pub Date : 2020-09-18 , DOI: 10.1016/j.tws.2020.107129
Pham Toan Thang , T. Nguyen-Thoi , Jaehong Lee

For the first time, an investigation on the shape and material optimization for buckling behavior of functionally graded (FG) toroidal shells using differential evolution (DE) algorithm is presented in this paper. For buckling analysis, an analytical approach is used to derive governing equations, then combining with the Galerkin procedure to obtain the critical buckling load. In the optimization problem, the material distribution of functionally graded material is described by interpolated points whose coordinates of these interpolated points are located along the thickness direction of the toroidal shell using Hermite cubic functions. The design variables are volume fraction at the interpolated points. The DE algorithm is employed to find maximum critical buckling loads with ceramic volume fraction constraints. In the section of numerical results, the reliability of the current formulation is validated by several examples. Furthermore, a comprehensive examination of the influences of geometric and material parameters, etc., on the buckling behavior of the FG toroidal shells are performed. Besides, the study sets out to explore current optimal results to its effectiveness and robustness, in particular distributions, in order to examine its impact on critical buckling loads.



中文翻译:

功能梯度环形壳体屈曲行为的形状和材料优化

本文首次使用微分演化(DE)算法研究功能梯度(FG)环形壳的屈曲行为的形状和材料优化。对于屈曲分析,使用一种分析方法来导出控制方程,然后与Galerkin程序结合以获得临界屈曲载荷。在优化问题中,使用Hermite三次函数通过插值点描述了功能渐变材料的材料分布,这些插值点的坐标沿环形壳的厚度方向定位。设计变量是插值点处的体积分数。采用DE算法查找具有陶瓷体积分数约束的最大临界屈曲载荷。在数值结果部分,通过几个示例验证了当前公式的可靠性。此外,还对几何和材料参数等对FG环形壳的屈曲行为的影响进行了全面检查。此外,该研究着手探讨其有效性和鲁棒性的当前最佳结果,特别是分布,以检查其对临界屈曲载荷的影响。

更新日期:2020-09-20
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