Young's Modulus Control in Material and Topology Optimization

Grzegorz Michał Dzierżanowski , Tomasz Denis Lewiński


We discuss compliance minimization from the broad perspective of Free Material Design (FMD) with Young’s moduli in place of Hooke’s tensor. By this, we attempt to optimize these elastic moduli which tightly correspond to principal components of stress at each point in the design space. The optimization task under study takes a form of the following constrained variational problem: In a given design space, fix two variables for which the total stored energy functional is minimal: (i) design variable - the directional Young modulus field restricted by an isoperimetric condition, and (ii) state variable - the statically admissible stress field. The functional is parametrically dependent on the Poisson ratios; these moduli are not optimized in the proposed approach. Similarly to FMD, our problem also reduces to minimizing a functional of linear growth in stresses. A characteristic feature is that the functional to be minimized is Michell-like, i.e. it takes a form of an integral of absolute values of principal components of stress tensor if the Poisson ratios are set to zero.
Author Grzegorz Michał Dzierżanowski IIB
Grzegorz Michał Dzierżanowski,,
- The Institute of Civil Engineering
, Tomasz Denis Lewiński IIB
Tomasz Denis Lewiński,,
- The Institute of Civil Engineering
Publication size in sheets0.55
Book Schumacher A., Vietor T., Fiebig S., Bletzinger K., Maut K. (eds.): Advances in Structural and Multidisciplinary Optimization :Proceedings of the 12th World Congress of Structural and Multidisciplinary Optimization (WCSMO12), 2018, Springer, ISBN 978-3-319-67987-7, [978-3-319-67988-4], 2115 p., DOI:10.1007/978-3-319-67988-4
Keywords in EnglishYoung’s modulus Material optimization, Topology optimization, Michell-like structures
Languageen angielski
10.1007_978-3-319-67988-4_103.pdf 183.69 KB
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