Vulnerability-based robust design optimization of imperfect shell structures

A stochastic vulnerability-based robust design procedure of isotropic shell structures possessing uncertain initial geometric as well as material and thickness properties that are modeled as random fields is assessed against conventional and reliability-based robust design procedures. The main idea of the vulnerability-based design philosophy is to achieve robust optimum designs while allowing designers to determine explicitly accepted probabilities that various performance objectives will not be exceeded, by introducing additional probabilistic (vulnerability) constraints. For this purpose, a stochastic finite element methodology is incorporated into the framework of an efficient two-objective robust design optimization formulation. This combined approach is then implemented in order to obtain optimum designs of an “imperfect” shell structure involving random geometric deviations from its perfect geometry as well as a spatial variability of its modulus of elasticity and thickness. Two-objective functions, the material volume of the structure and the coefficient of variation of the buckling load of the shell, are used for the description of the optimization problem, subject to deterministic, reliability and vulnerability constraints.