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Structural and material optimization based on thermodynamic principles
Author(s) -
Jantos Dustin Roman,
Hackl Klaus,
Junker Philipp
Publication year - 2019
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201900112
Subject(s) - topology optimization , dissipative system , affine transformation , ordinary differential equation , topology (electrical circuits) , mathematics , material properties , differential equation , mathematical optimization , mathematical analysis , finite element method , geometry , physics , thermodynamics , combinatorics
In our previous work, we developed a variational approach for topology optimization based on thermodynamic principles, i.e. Hamilton's principle for dissipative processes. Hamilton's principle yields a closed set of differential equations for a variety of problems in continuum mechanics, which include microstructural processes described by internal variables (e.g. plasticity, damage modeling, crystallographic transformations, etc.). These internal variables can also be used to describe design variables for an optimization, i.e. structural compliance minimization. The resulting differential equations yield evolution equations as known from material modeling that can be used as update scheme for an iterative optimization procedure. With this method, we derived differential equations for different design variables: 1) the topology, which is described by a continuous density distribution with penalization of intermediate densities (SIMP); 2) the local material orientation of a anisotropic base material, for which we introduce a filtering technique to control the fiber path smoothness; 3) the material distribution for tension and a compression affine materials, e.g. steel and concrete, in which tension affine material is applied in regions predominant to tension and compression affine material in regions predominant to compression.