Non-probabilistic reliability-based topology optimization for two-material structure based on convex set and bounded field mixed model

This study addresses the inherent uncertainties impacting the manufacturing and application of multi-material structures. Due to limited sample sizes, the need for non-probabilistic reliability-based optimization designs in these structures is crucial. We developed a novel topology optimization method for multi-material structures that is based on non-probabilistic reliability, in which uncertainties are characterized by a convex set and a non-probability bounded field model for parameter and field uncertainties respectively. For practical implementation, we focused on a two-material structure. We formulated the two-material non-probability reliability-based topology optimization (TNRBTO) with an uncertain field and uncertain parameters to maximize the non-probabilistic reliability index of the structure under two candidate material volume constraints. A gradient-based optimization algorithm is used to solve the TNRBTO problems. The validity of our proposed TNRBTO method was assessed through four numerical examples, considering uncertainties in parameters such as the Young's modulus uncertainties of two candidate materials and a field uncertainty in the form of an uncertain distributed loading field.

Automated summary

This study focuses on addressing the uncertainties inherent in the manufacturing and application of multi-material structures. A novel topology optimization method based on non-probabilistic reliability is developed, which characterizes uncertainties using a convex set and a non-probability bounded field model. The proposed method is validated through numerical examples considering uncertainties in parameters and field loading.