Engineering Transactions, 65, 1, pp. 3–9, 2017

On Shape and Material Optimization of Isotropic Bodies

Sławomir CZARNECKI
Warsaw University of Technology
Poland

Tomasz LEWIŃSKI
Warsaw University of Technology
Poland

Paweł WAWRUCH
Warsaw University of Technology
Poland

This paper deals with the free material design and its two constrained versions constructed by imposing isotropy with (i) independent bulk and shear moduli, and (ii) fixed Poisson’s ratio. In the latter case, the Young modulus is the only design variable. The moduli are viewed as non-negative, thus allowing for the appearance of void domains within the design domain. The paper shows that all these methods reduce to one stress-based problem in which the norm involved reflects the type of the constraints imposed.
Keywords: optimum design; elastic moduli; free material design
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