Multi-objective optimization of membrane structures

A multi-objective optimization model is proposed for membrane structures. Three objectives are established according to the characteristics of membrane structures, including maximum stiffness, most uniform stress and minimum value of reaction. Mathematical formulations are presented for these objectives. Especially, three types of functions for stiffness, respectively based on strain energy, maximum displacement and average displacement, are investigated to show their different aspects in mechanical concepts and optimization solutions. Further more, weighting method is introduced to combine the three objectives into a single objective and a genetic algorithm is applied to solve this optimization problem. Finally, several numerical examples are provided to illustrate the proposed model and method. The study shows that the proposed multi-objective optimization model is feasible and efficient for membrane structures; the differences in stiffness functions result in different optimization solutions, and comparing with the others, the strain energy is more comprehensive and apt to reveal the essence of stiffness, which in turn leads to better results; the desired optimal membrane structures can be obtained by the weighting method and genetic algorithm.