Minimization of maximum failure criterion of laminated composite shell structure by optimizing distributed-material orientation
Minimization of maximum failure criterion of laminated composite shell structure by optimizing distributed-material orientation
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DOI：
10.1007/s00158-019-02435-z
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发表时间：
2020-04
影响因子：
3.9
通讯作者：
M. Shimoda;Yoshiaki Muramatsu;Ryosuke Tsukihara
中科院分区：
文献类型：
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作者：
M. Shimoda;Yoshiaki Muramatsu;Ryosuke Tsukihara
本文提出了一种基于层合板理论的各向异性复合材料层合壳体结构强度最大化的分布参数优化方法。本文采用修正的Tsai-Hill准则作为失效准则，并在状态方程约束下使其最大值最小。通过使用Kreisselmeier-Steinhauser函数将奇异局部测度转化为光滑的可微积分泛函，避免了这个极小-极大问题所固有的不可微性问题。将优化设计问题描述为一个分布参数优化问题，并基于变分方法从理论上推导了该问题对材料取向变化的灵敏度函数。用H1梯度法结合泊松方程确定了最优材料取向变化量，其中灵敏度函数作为Robin条件来改变和优化材料取向分布。我们将灵敏度函数转化为内部产热，并利用泊松方程来确定材料取向的变化，以确保材料取向的连续分布。优化设计算例表明，该优化方法能有效、高效地获得最优材料取向，使破坏准则所测得的最大强度最小，且具有光滑的曲线分布。
In this study, we propose a distributed-parameter optimization method for the material-orientation design aiming at maximizing the strength of a laminated composite shell structure with anisotropic material, which is homogenized based on a laminate theory. The modified Tsai–Hill criterion is employed as a failure criterion in this study, and its maximum value is minimized with the state equation constraint. The issue of non-differentiability inherent in this min–max problem is avoided by transforming the singular local measure to a smooth differentiable integral functional using the Kreisselmeier–Steinhauser function. The optimum design problem is formulated as a distributed-parameter optimization problem, and the sensitivity function with respect to the material-orientation variation is theoretically derived based on a variational method. The optimal material-orientation variation is determined using the H1gradient method with Poisson’s equation proposed by the authors, where the sensitivity function are applied as Robin condition to vary and optimize the material-orientation distribution. We transfer the sensitivity function to the internal heat generation and determine the material-orientation variation using Poisson’s equation to ensure continuous distribution of material orientation. The optimum design examples show that the proposed optimization method can effectively and efficiently obtain the optimum material orientation with the smooth curvilinear distribution and minimize the maximum strength measured by a failure criterion.