Reflections on Truss and Continuum Topology Optimal Designs

摘要

In continuum topology optimization the resulting optimal designs are highly depending on the amount of material available, relative to the size of the possible design space. To obtain black and white solutions (material or no material), penalization's are applied, and for the problems of low density we see a clear tendency toward solutions which more or less are truss or frame structures. Often the accuracy of the finite element models for the continuum is then at the limits with respect to accuracy. The purpose of the presented project is to make a comparison between optimal designs found by known methods for topology optimization of continuum structures and optimal designs of structures modeled as trusses. For a statically determined truss each bar can be designed independently and therefore must be fully stressed in an optimal design. We want to put focus on the basic knowledge which gives optimality criteria for single load cases with only a single constraint. Truss and continuum examples are analyzed, optimized, and evaluated to get further insight into the influence from the basic modeling, being truss or continuum. Stiffness as well as strength are important aspects of optimal design, and elastic energy density is a general measure of these constraints.