An integrated optimization method for the damper placements, shape and size of truss structures

This work extends the application of the approximation concept in dynamic topology optimization for truss structures. The corresponding problem contains both continuous and discrete variables, encompassing damper placements, truss shape and cross-sectional area. First, the utilization of a branched multipoint approximation (BMA) function establishes sequential approximation problems that also involve such mixed variables, marking its innovative application in dynamic optimization. Then, a modified genetic algorithm (GA) is used to optimize discrete variables. To enhance convergence stationarity, the concept of 'adjacent individuals' is proposed to control the degree of difference in topology configuration between initial population members and the current optimal. Additionally, adjustments to the sequence-based crossover process ensure compliance with damper quantity constraints. Examples demonstrate that the introduction of adjacent individuals is beneficial to convergence stationarity, and the shape change of the truss increases the mode damping ratio by more than 20%. The created optimization platform can also tackle other mixed variables optimization problems.