Optimal design of periodic functionally graded composites with prescribed properties |
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Authors: | Glaucio H Paulino Emílio Carlos Nelli Silva Chau H Le |
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Affiliation: | 1.Department of Civil and Environmental Engineering,University of Illinois at Urbana-Champaign,Urbana,USA;2.Department of Mechatronics and Mechanical Systems,Escola Politécnica da Universidade de S?o Paulo,S?o Paulo,Brazil |
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Abstract: | The computational design of a composite where the properties of its constituents change gradually within a unit cell can be
successfully achieved by means of a material design method that combines topology optimization with homogenization. This is
an iterative numerical method, which leads to changes in the composite material unit cell until desired properties (or performance)
are obtained. Such method has been applied to several types of materials in the last few years. In this work, the objective
is to extend the material design method to obtain functionally graded material architectures, i.e. materials that are graded
at the local level (e.g. microstructural level). Consistent with this goal, a continuum distribution of the design variable
inside the finite element domain is considered to represent a fully continuous material variation during the design process.
Thus the topology optimization naturally leads to a smoothly graded material system. To illustrate the theoretical and numerical
approaches, numerical examples are provided. The homogenization method is verified by considering one-dimensional material
gradation profiles for which analytical solutions for the effective elastic properties are available. The verification of
the homogenization method is extended to two dimensions considering a trigonometric material gradation, and a material variation
with discontinuous derivatives. These are also used as benchmark examples to verify the optimization method for functionally
graded material cell design. Finally the influence of material gradation on extreme materials is investigated, which includes
materials with near-zero shear modulus, and materials with negative Poisson’s ratio. |
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Keywords: | Material design Functionally graded materials Optimization Homogenization Extreme materials Zero shear-modulus materials Negative Poisson’ s ratio materials |
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