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Multi-objective optimization of functionally graded thick shells for thermal loading

机译：功能梯度厚壳热载荷的多目标优化

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Presented herein is a methodology for the multi-objective optimization of material distribution of functionally graded cylindrical shells for steady thermomechanical processes. The proposed approach focuses on isotropic metal/ceramic and metal/metal functionally graded materials, which offer great promise in high temperature and high heat flux applications. The material composition is assumed to vary only in the thickness direction. The volume fractions of the constituent material phases at a point are obtained through piecewise cubic interpolation of volume fractions defined at a finite number of evenly spaced control points. The effective material properties are estimated using the self-consistent homogenization scheme. The volume fractions at the control points, which are chosen as the design variables, are optimized using an elitist, non-dominated sorting multi-objective genetic algorithm. Candidate designs are evaluated using an exact power-series solution to the two-dimensional quasi-static heat conduction and plane strain thermoelasticity problems. The formulation, which is applicable to both thin and thick functionally graded shells, can also be used to analyze and optimize functionally graded plates in the limit that the midsurface radius of the shell approaches infinity. The proposed methodology is illustrated by optimizing the material composition profile for two model problems. In the first model problem, both the mass and the peak hoop stress of Zirconia/Titanium alloy plates and shells are simultaneously minimized for a prescribed temperature load with a constraint on the maximum temperature experienced by the metal. The goal of the second model problem is to simultaneously minimize the mass and maximize the factor of safety of Tungsten/Copper alloy functionally graded plates and shells under an applied heat flux, subject to a constraint on the factor of safety.
机译：本文介绍的是一种用于稳定热机械过程的功能梯度圆柱壳材料分布的多目标优化方法。拟议的方法侧重于各向同性的金属/陶瓷和金属/金属功能梯度材料，在高温和高热通量应用中具有广阔的前景。假定材料组成仅在厚度方向上变化。通过在有限数量的均匀间隔的控制点处定义的体积分数的分段三次插值，可以获得某一点上组成材料相的体积分数。使用自洽均质方案估算有效材料性能。选择控制点的体积分数作为设计变量，使用精英，非支配的排序多目标遗传算法进行优化。使用精确的幂级数解来评估候选设计，以解决二维准静态热传导和平面应变热弹性问题。该配方适用于薄的和厚的功能梯度壳，也可用于分析和优化功能梯度板，以使壳的中表面半径接近无穷大。通过针对两个模型问题优化材料成分轮廓来说明所提出的方法。在第一个模型问题中，对于规定的温度负载，同时限制了金属所经历的最高温度，同时使氧化锆/钛合金板和壳体的质量和峰值环向应力均最小。第二个模型问题的目的是在施加热通量的同时，将钨/铜合金功能梯度板材和壳体的质量同时最小化，并将其安全系数最大化，但要严格考虑安全系数。

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