Development of Boundary-Based Topology Optimization Approaches for Smart Structures Under Finite Strain

Abstract

Designing smart structures capable of responding to external stimuli requires a rigorous consideration of multi-physics interactions, large deformations, and multi-material distributions. While topology optimization provides a systematic design methodology, conventional density-based approaches often face challenges in defining the clear boundaries necessary for accurately modeling the complex multi-material interfaces inherent in these systems. This dissertation addresses these critical gaps by establishing a unified boundary-based topology optimization framework, specifically focusing on structural nonlinearity, thermoelastic objective formulations, and numerical stability in multi- material design. First, an explicit topology optimization approach is proposed for multi-material structures considering both geometric and material nonlinearities. By integrating the Moving Morphable Components-based topology optimization with hyperelastic constitutive models, this study overcomes the limitations of linear assumptions in boundary-based multi-material topology optimization. The proposed method yields crisp structural boundaries and reveals that multi-material designs outperform single-material counterparts by strategically distributing materials with distinct nonlinear behaviors. Furthermore, the applicability of this framework to smart structure design is demonstrated through the realization of a programmable structure capable of exhibiting prescribed deformation behaviors. Second, this research investigates the distinct characteristics of objective functions under nonlinear thermoelastic conditions. A comparative study between end compliance and strain energy minimization reveals that, unlike in linear elasticity, these objectives diverge significantly in a finite strain setting. The results indicate that minimizing end compliance effectively leverages the direction of thermal expansion to minimize displacement, whereas minimizing strain energy contributes to the strength of the structure by limiting the thermal contribution to the overall stress. These findings also provide essential design guidelines for selecting appropriate objectives in thermally driven smart structures. Furthermore, by introducing a generalized eigenstrain-based formulation for thermal expansion, this framework demonstrates its versatility to readily extend to other multi-physics phenomena such as swelling and photostrain. Finally, to overcome the convergence issues in multi-material Level Set Topology Optimization (LSTO), a discrete adjoint sensitivity analysis is introduced. Previous works relying on continuous adjoint sensitivities often necessitate artificial regularization, which can degrade accuracy and hinder convergence in multi-phase problems. The proposed approach alleviates this issue by explicitly evaluating shape sensitivities at the boundary without smoothing filters. This method ensures accurate sensitivity computation and stable convergence, enabling the precise design of complex multi-material interfaces. Furthermore, the integration of this approach with existing LSTO formulations for multi- physics and large deformations facilitates its extension into a unified framework capable of simultaneously addressing large deformations, multi-physics interactions, and multi-material distributions. Collectively, the numerical examples presented in this dissertation demonstrate the validity and robustness of the proposed framework. By integrating finite strain theory, multi-physics, and multi- material modeling into boundary-based topology optimization, this research establishes a solid foundation for the innovative design of next-generation smart structures.