Topology optimization of microplates considering size effect based on consistent couple stress theory for minimizing the mean compliance

Abstract

This paper aims to optimize the topology of microplates to achieve minimum compliance considering consistent couple stress theory (C-CST). Material properties interpolation scheme is constructed based on the modified solid isotropic material with penalization (SIMP). An updating scheme is developed based on the generalized optimality criteria method (G-OCM). Three problems are addressed. First problem involves the size-dependent topology design of a plate to minimize the compliance while adhering to a volume constraint. As compliance decreases, the eigenfrequencies of the plate generally increase, which can cause them to shift into undesirable ranges. To address this, in the second problem, the plate topology design is carried out to minimize compliance, considering the volume and frequency band constraints. In the third problem, the nano-reinforcement phase distribution is optimized to minimize the compliance of the nanocomposite plates. In this respect, the element reinforcement volume fraction is considered as the design variable, and a homogenization scheme is employed to interpolate the material properties. The size-dependent effects are examined through benchmark examples. The results reveal that imposing constraints on the eigenfrequencies leads to a redistribution of optimized compliance, which becomes more pronounced as the characteristic length ratio increases. Moreover, applying a frequency constraint to the nano-reinforcement phase results in an optimized compliance and topology that differ significantly from those of the homogeneous configuration.