Justification of a certain algorithm for shape optimization in 3D elasticity.

The trabecular bone adapts its form to mechanical loads and is able to form structures that are both lightweight but very stiff. In this sense, it is a problem (for the Nature or living entities) similar to the structural optimization, especially the topology optimization. The structural optimization system developed by the authors previously was based directly on the bio-mechanical models. The paper aims to clarify the approach of using the bio-mechanical models of the trabecular bone remodelling phenomenon as a base for the structural optimization. The justified algorithm for shape optimization mimics the natural phenomenon to satisfy the condition of constant value of the strain energy density on the structural surface, issuing from the considerations in the area of mechanics. The main body of the paper contains the analysis of the stiffness optimization problem in the framework of speed method approach to shape optimization. The given numerical example (cantilever beam in bending) includes the influence of the structural surface curvature on the optimization procedure. The presented in the paper approach can be used as a method of structural optimization unrelated already to trabecular bone remodelling phenomenon. [ABSTRACT FROM AUTHOR]