Hybrid method of SIMP and SAIP for reliability-based topology optimization considering strength failure under load uncertainty

Reliability-based topology optimization (RBTO) considering strength failure under load uncertainty can yield the optimum topological designs that significantly enhance the structural safety. By employing stress-based performance functions, this study formulates the problem as minimizing an objective function subject to a system reliability constraint. Load uncertainty is characterized by treating both the direction and magnitude of loads as independent random variables. To enhance the convergence speed of density-based topology optimization in achieving binary designs, we propose a hybrid method of solid isotropic material with penalization (SIMP) and sequential approximate integer programming (SAIP). Initially, the SIMP method is employed to determine an initial structural design with a stable path of force transmission. Subsequently, the SAIP incorporating with an intermediate density variation strategy is utilized to obtain a clear topology design. The direct probability integral method is suggested to accurately and efficiently estimate the failure probability of the series system and to calculate its sensitivity with respect to design variables. Several numerical examples demonstrate that the proposed method achieves distinct binary topology configurations in fewer iterations. Moreover, the optimized designs exhibit high sensitivity to variations in load conditions. By accounting for the load uncertainties in both magnitude and direction, the designs generated by RBTO are more suitable for practical applications.