Robust reliability-based topology optimization for stress-constrained continuum structures using polynomial chaos expansion

To achieve an ideal balance between cost and robustness, reliability and structural safety, this paper presents a unified robust reliability-based topology optimization (RRBTO) approach for continuum structures considering loading uncertainty for the first time. An optimization model of minimizing a linear combination of mean and standard deviation of compliance response subject to stress-based reliability constraint is established. To accelerate the computational efficiency of the proposed unified framework for RRBTO, polynomial chaos expansion-based surrogate modeling technique is adopted to calculate the mean and standard deviation of compliance response and construct the stress response surface function used in reliability analysis. The derivation of compliance means and its standard deviations with respect to design variables are detailed based on polynomial chaos expansion approach (PCE). 2D and 3D benchmark design examples are optimized and the Monte Carlo simulation is also implemented to verify the effectiveness of the proposed PCE-based RRBTO approach for the design problems of stress-constrained continuum structures under load uncertainty.