Reliability-based topology optimization of structures considering stress constraints
Abstract
The primary contributions and objectives of this article are to propose an enhanced proportional topology optimization algorithm with strong global optimization capability and high computational efficiency, as well as a novel reliability-based topology optimization method that is capable of decreasing sensitivity analysis. First of all, the structural topology optimization problem with minimum volume under stress constraints is studied, and the enhanced proportional topology optimization algorithm is developed by applying an improved material interpolation model, the density filtering method based on a Gaussian distribution weighting function, and a composite projection operator to modify the proportional topology optimization algorithm. Subsequently, to explore the reliability-based topology optimization problem with minimum volume under stress constraints, a novel reliability-based topology optimization method is devised by combining the enhanced proportional topology optimization algorithm with the sequential optimization and reliability assessment method, the first-order reliability method, and the response surface method. Among these, the sequential optimization and reliability assessment method and the first-order reliability method are employed to decouple the reliability-based topology optimization problem and implement structural reliability analysis, respectively, and the response surface method is applied to simulate the limit state function related to stress. Finally, numerical examples are employed, and their results are analyzed and discussed, thereby evaluating the effectiveness of the enhanced proportional topology optimization algorithm and the new reliability-based topology optimization method. The results show that, compared to the proportional topology optimization algorithm, the enhanced proportional topology optimization algorithm has the advantages of strong global optimization capability, fast convergence speed, and high computational efficiency. In addition, the reliability-based topology optimization method can generate optimized structures with high reliability.