Uncertainty-oriented topology optimization of dynamic structures considering hybrid uncertainty of probability and random field

This article introduces a novel reliability-based topology optimization (RBTO) method to tackle the design challenges of dynamic structures under uncertain harmonic loads. The method considers hybrid uncertainty, incorporating both probability and random field. The amplitude of loads is characterized as a random field using the expansion optimal linear estimation, and the excitation frequency is modeled as a normally distributed random variable. An optimization model of minimizing the structural volume ratio of dynamic structures with a constraint on the square of the dynamic compliance is established. To simplify the derivatives of strongly nonlinear implicit functions with respect to random parameters, the polynomial chaotic expansion-based surrogate model is introduced to construct an explicit function for reliability analysis. Morevoer, the mode superposition method (MSM) is adopted to deal with high computational costs involved in RBTO of dynamics problems. Four design examples are tested to demonstrate the computational advantage and effectiveness of the method presented. The optimized results indicate that the proposed method can effectively design dynamic structures that meet the specified reliability level, with a relative error of reliability index not exceeding 2 %.