Biomimetic Structural Optimization Method: New paradigm for shape and topology optimization

Abstract

The trabecular bone adapts its form to mechanical loads and is able to form lightweight but very stiff structures. In this sense, it is a problem (for the Nature) similar to the structural optimization, especially the topology optimization. The structural optimization system based on shape modification using shape derivative [1] will be presented. Structural evolution during the structural optimization procedure is based on the adaptive remodeling of the trabecular bone and is independent of domain selection. In general the problem of stiffest design (compliance minimization) has no solution. If the volume of the object is increasing, the compliance is decreasing. Thus, in the standard approach to the energy based topology optimization the additional constraint has to be added. Usually the volume of the material is limited. But with such an assumption the optimization procedure does not include any criteria for stress. In case of the biomimetic approach presented here, the role of the additional constraint plays the strain energy density on the structural surface (which is between two assumed levels forming the insensitivity zone) and the volume or structural mass results from the optimization procedure. The variational approach to shape optimization in linearized elasticity is used in order to improve convergence of a heuristic algorithm. The method is enhanced to handle the problem of structural optimization under multiple loads [2]. The new approach does not require volume constraints. Instead of imposing volume constraints, shapes are parameterized by the assumed strain energy density on the structural surface.