Reliability-based topology optimization of double layer grids using a two-stage optimization method

This paper presents a two-stage optimization method for reliability-based topology optimization (RBTO) of double layer grids that considers uncertainties in applied loads. The optimization is performed using a two-stage optimization by employing the method of moving asymptotes (MMA) and ant colony optimization (ACO), which is called MMA-ACO method. For implementation of MMA-ACO, the structural stiffness is maximized using MMA, first. Then, the results of MMA are used to enhance ACO through the following four modifications: (I) finding the structural importance rate of elements or joints and using this to achieve a better topology, (II) determining the number of compressive and tensile element types, (III) changing the lower limit of available cross-sectional areas for the elements of each group and (IV) modifying the generation of random stable structures. In reliability analysis, multiple criteria i.e. stiffness and eigenvalue are considered where the probability of failure in each mode is calculated by Monte Carlo simulation (MCS). To reduce the computational time, the eigenvalues are evaluated using the third order approximation (TOA). Through numerical examples, reliability-based topology designs of typical double layer grids are obtained by ACO and MMA-ACO methods. The numerical results reveal the computational advantages and effectiveness of the proposed MMA-ACO method for the RBTO of double layer grids. Also, the importance of considering uncertainties is then demonstrated by comparing the results obtained by those of other failure probabilities.