On compliance minimization by biomimetic regularization method

Abstract

The standard approach to mechanical design is based on strength hypotheses. However, the structural optimization methods do not take into account this important condition determining the correctness of the engineering solution. The situation is different in the case of biological systems, where reference to material strength is a basic condition for the formation of functional mechanically loaded systems. The team developed an optimization system modeled on the phenomenon of bone remodeling, based on rigorous theoretical studies in the field of material continuum optimization, where the condition for achieving the optimal solution is the equalization of strain energy density on the structural surface. The new idea presented in this paper is to link this condition with the strength properties of the material. Furthermore the strength hypotheses are expressed in terms of strain energy. The aim of the research presented in this paper is to precisely estimate the relationship between the condition of a constant value of the strain energy density on the structural surface and the material strength, according to yield criteria. The given numerical examples contain a reference to the analytical results and indicate a unique feature of the presented method. The use of the notion of insensitivity zone concept for building the biomimetic structural optimization system allows regularization without focusing on the existence of the Lagrange multiplier correspondence to the volume constraint. The approach presented in the paper can be used by engineers as a method for structural optimization no longer bound to the phenomenon of trabecular bone remodeling. Also discussed is the problem of numerical implementation and the necessary modification of the position and size of the insensitivity zone to ensure that the result is achieved by numerical means. These results require the development of appropriate heuristics but allow us to achieve similar results regardless of the initial configuration. However, the discussion of the use of observations of Nature in mechanical design remains open.