Topology Optimization of Integral Rib Reinforcement of Plate and Shell Structures with Weighted-Sum and Max-Min Objectives

This paper deals with the problem of determining the optimum integral rib reinforcement of statically loaded or freely vibrating plate and shell structures. The problem is treated as one of topology optimization where the rib reinforcement is considered as an orthotropic microstructure with continuously varying orientation and concentration of a two-way system of reinforcing ribs attached symmetrically with respect to the mid-surface of the base plate or shell structure. Multiobjective weighted-sum and max-min formulations are considered for problems of stiffness optimization of plates and shells subjected to several static load cases and problems of optimization of eigenfrequencies of free vibrations. Special emphasis is devoted to the occurrence of multiple eigenfrequencies in max-min formulations of vibration problems. Illustrative examples of optimum rib reinforcement are presented for the problems considered.

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