A Proposal of a Shape-0ptimization Method Using a Constitutive Equation of Growth : In the Case of a Static Elastic Body

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Abstract

A simple method for analysis of uniform-strength shape is newly proposed. In this paper, the most fundamental case of a static elastic body is considered. The idea of the present method came from the growth behavior of living organisms by which they changed their own shapes to adapt themselves to the mechanical living environment. The scheme consists of the iteration of the two analytical steps : (1) conventional elastic analysis for evaluation of stress distribution, and (2) incremental growth analysis using a constitutive equation of growth. In the latter step, a shape is deformed with an incremental bulk strain which is generated according to an objective stress indicating strength of the material. Two examples of a cantilever beam under top shear loading and a column under top compressive loading and gravity are analyzed to show the effectiveness of the proposed method.

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