A new hybrid fuzzy-goal programming scheme for multi-objective topological optimization of static and dynamic structures under multiple loading conditions

This work presents a hybrid fuzzy-goal multi-objective programming scheme for topological optimization of continuum structures, in which both static and dynamic loadings are considered. The proposed methodology fortopological optimization first employs a fuzzy-goal programming scheme at the top level for multi-objective problems with static and dynamic objectives. For the static objective with multi-stiffness cases in the fuzzy-goal formulation, a hybrid approach, involving a hierarchical sequence approach or a hierarchical sequence approach coupled with a compromise programming method, is especially suggested for the statically loaded multi-stiffness structure at the sublevel. Concerning dynamic optimization problems of freevibration cases, nonstructural mass, oscillation of the objective function, and repeated eigenvalues are also discussed. Solid Isotropic Material with Penalization density–stiffness interpolation scheme is used to indicate the dependence ofmaterial modulus upon regularized element densities. The globally convergent version of the method of moving asymptotes and the sequential linear programming method areboth employed as optimizers. Several applications have been applied to demonstrate the validation of the presented methodologies.