In the ever-expanding fields of thickness and topology optimization, there is a research gap for simultaneous and direct optimization of thickness and material for complex shell structures using fully analytical sensitivities, with prevention of coincident material layers. This paper introduces a novel method to fill this gap: concurrent thickness and material optimization (CTMO) based on a gradient-based approach. This proposed formulation determines optimal thickness and material choice for shell elements within a finite element (FE) model design space. The method of moving asymptotes (MMA) is used for optimization, and material interpolation is handled with solid isotropic material with penalization (SIMP). The behavior of this solver is demonstrated with several academic examples, through a series of extensive parameter sweeps of mass fraction, and minimum and maximum designable thickness, for the compliance minimization objective function. The proposed methodology is geared towards practical design of complex structures, allowing for feasible interpretation into actual engineering solutions. As such, optimization of a small aerobatic aircraft wing is conducted with study of several key design factors. The effects of design restriction and filter size are studied to determine best practices for design procedures. To demonstrate the practical utility of this algorithm, a selected wing optimization result is interpreted into a set of complete, industry style designs, verified through finite element analysis (FEA) to determine deviation from the ideal optimum. It is demonstrated that designs can be interpreted faithfully from optimization results with mass and compliance errors of less than 2%, alongside a discussion of pertinent factors. Finally, several areas with potential for future work are explored.

在不断扩大的厚度和拓扑优化领域中，利用完全的分析灵敏度同时防止材料层重合的同时，对复杂壳体结构的厚度和材料进行直接和直接优化存在研究空白。本文介绍了一种填补这一空白的新颖方法：基于基于梯度的方法的同时厚度和材料优化（CTMO）。此提议的公式确定了有限元（FE）模型设计空间内壳单元的最佳厚度和材料选择。使用移动渐近线（MMA）的方法进行优化，并使用带有罚分的固体各向同性材料（SIMP）处理材料插值。通过一系列广泛的质量分数参数扫描，通过几个学术示例证明了该求解器的行为，最小和最大可设计厚度，用于最小化法规遵从性目标功能。所提出的方法适用于复杂结构的实际设计，可以对实际的工程解决方案进行可行的解释。因此，通过研究几个关键设计因素，进行了小型特技飞机机翼的优化。研究了设计限制和过滤器尺寸的影响，以确定设计程序的最佳实践。为了演示该算法的实用性，将选定的机翼优化结果解释为一组完整的工业风格设计，并通过有限元分析（FEA）进行验证，以确定与理想最优值的偏差。结果表明，通过对优化结果的忠实解释，质量和合规误差小于2％，并且可以对相关因素进行讨论。最后，探讨了一些有潜力开展未来工作的领域。