A novel method for concurrent thickness and material optimization of non-laminate structures

Abstract

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.