Topology optimization for the computationally poor: efficient high resolution procedures using beam modeling

Abstract

A structural optimization approach based on beam modeling is formulated and investigated. Its computational efficiency and enhanced design freedom place it as a computationally cheap alternative to continuum topology optimization. The optimization uses a ground structure parametrization and consists of alternating shape and sizing-topology design phases. The sizing-topology phase controls the thicknesses of tapered beams. Linear constraints applied in the shape phase provide regularity and consistency to the structure and enable the shape design variables to benefit from large freedom of movement. A direct comparison to continuum-based topology optimization shows that the beam-based optimization can offer significant computational savings while generating designs that perform similarly to continuum designs. The result of the beam optimization can be utilized also as an effective starting point for further design iterations on a refined continuum model. The reduced computational effort facilitates the optimization of high resolution structures without separating to micro and macro scales, hence non-uniform and non-periodic porous structures can be designed in a single-level optimization process. Furthermore, the beam modeling allows to impose minimum and maximum length scales explicitly without any additional constraints. The applicability of the suggested approach is demonstrated on several cases of stiffness maximization and mechanism design.