Free vibration analysis and shape optimization of variable thickness plates, prismatic folded plates and curved shells: Part 2: shape optimization

Abstract A robust computational tool which integrates FS analysis, parametric cubic spline geometry definition, sensitivity analysis and mathematical programming is developed for the optimization of the shape and thickness variation of prismatic folded plates and curved shell structures. The objective of the optimization process is to maximize the fundamental frequency. Both thickness and shape variables defining the cross-section of the structure are considered. The analysis is carried out by using curved, variable thickness finite strips, formulated and tested in Part 1 of this paper. To obtain the optimal shapes, semi-analytical sensitivity calculations are used in conjunction with a sequential quadratic programming optimization algorithm. Optimal shapes are presented for several shells and folded plates of variable thickness.