Optimal design of rib structures using the topology optimization technique

Abstract

The objective of this work is to search the optimal shapes and locations of ribs in order to increase the stiffness of structures using the topology optimization technique. In this approach, an initial rib structure consisting of many discrete shell elements is added to the existing structure and the optimization procedure is applied to determine the density of each element for the minimal mean compliance of the whole system. The remaining shell elements determined to have higher densities by an optimization procedure will remain attached to the structure and become the rib structure. This is different from the existing approach which tries to derive the rib design from the optimized thickness distribution of the structure. A penalty term is also introduced in the objective function in addition to the mean compliance to prohibit the intermediate densities. The mean compliance is computed by the finite element method in which each element has a variable density. Young's modulus of each element is derived by assuming a quadratic relation between the density and Young's modulus. The optimization is performed by the feasible direction method using the densities of elements as the design variables. The total material usage is used as a constraint in the optimization to provide lightweight structures.