9.6 Topological Optimization with Maximized Stiffness and Heat Transfer
357
9.6 Topological Optimization of Thermoelastic Composites
with Maximized Stiffness and Heat Transfer
The topological optimization of composite structures is widely used while tailoring
materials to achieve the required engineering physical properties. In this section, the
problem of topological optimization of the microstructure of a composite aimed at the
construction of a material with most effective values of the bulk modulus of elasticity
and thermal conductivity taking into account the competing mechanical and thermal
properties of the materials included in the composite is defined and solved [100]. A
two-phase composite consists of two base materials, one of which has a higher Young
modulus but lower thermal conductivity, while the other has a lower Young modulus
but higher thermal conductivity. A new class of problems for composites containing
material pores or technological inclusions of different shapes is considered. Effective
thermoelastic properties are obtained using the asymptotic homogenization method.
A modified solid isotropic material with penalization (SIMP) model is used to regularize the problem. The problem of the isoperimetric constraints is solved by the
method of moving asymptotes (MMA). The influence on the optimal topology of the
composite in the presence of two competing materials, and optimality criteria using
linear weight functions are investigated. Pareto spaces that provide a deep understanding of how these goals compete in achieving optimal topology are constructed.
9.6.1 Introduction
The use of new composite materials requires a theoretical background to predict
microscopic/effective properties of composites based on the knowledge of their material components. It is well known and documented that cell bulk fractions, shapes
and orientation are important factors in the manufacturing of composite materials
with effective properties.
The topological optimization of composite structures is a widely employed
method of tailoring materials, which is used to achieve their improved and required
physical properties. In the recently published papers and monographs, one can find
that the asymptotic homogenization approach plays a key role in achieving reliable
averaging of the complex microstructural behaviour of an elastic medium [44–46,
101]. An interesting way to compute modified Young modules in both directions for
a two-dimensional crystal body with a square lattice using the continuum approach
of continuum mechanics is described in reference [102].
It appears that the most widely recognized and used methods for the topological
optimization of structures are explicit parametrization methods, which are known
as density-based methods. These methods are based on the subdivision of the analyzed mechanical object into finite elements. Instead of a set of properties, each finite
element contains only one design variable, which is often understood as the finite element material density ρ e . The main idea of this approach is to define the finite element
357
9.6 Topological Optimization of Thermoelastic Composites
with Maximized Stiffness and Heat Transfer
The topological optimization of composite structures is widely used while tailoring
materials to achieve the required engineering physical properties. In this section, the
problem of topological optimization of the microstructure of a composite aimed at the
construction of a material with most effective values of the bulk modulus of elasticity
and thermal conductivity taking into account the competing mechanical and thermal
properties of the materials included in the composite is defined and solved [100]. A
two-phase composite consists of two base materials, one of which has a higher Young
modulus but lower thermal conductivity, while the other has a lower Young modulus
but higher thermal conductivity. A new class of problems for composites containing
material pores or technological inclusions of different shapes is considered. Effective
thermoelastic properties are obtained using the asymptotic homogenization method.
A modified solid isotropic material with penalization (SIMP) model is used to regularize the problem. The problem of the isoperimetric constraints is solved by the
method of moving asymptotes (MMA). The influence on the optimal topology of the
composite in the presence of two competing materials, and optimality criteria using
linear weight functions are investigated. Pareto spaces that provide a deep understanding of how these goals compete in achieving optimal topology are constructed.
9.6.1 Introduction
The use of new composite materials requires a theoretical background to predict
microscopic/effective properties of composites based on the knowledge of their material components. It is well known and documented that cell bulk fractions, shapes
and orientation are important factors in the manufacturing of composite materials
with effective properties.
The topological optimization of composite structures is a widely employed
method of tailoring materials, which is used to achieve their improved and required
physical properties. In the recently published papers and monographs, one can find
that the asymptotic homogenization approach plays a key role in achieving reliable
averaging of the complex microstructural behaviour of an elastic medium [44–46,
101]. An interesting way to compute modified Young modules in both directions for
a two-dimensional crystal body with a square lattice using the continuum approach
of continuum mechanics is described in reference [102].
It appears that the most widely recognized and used methods for the topological
optimization of structures are explicit parametrization methods, which are known
as density-based methods. These methods are based on the subdivision of the analyzed mechanical object into finite elements. Instead of a set of properties, each finite
element contains only one design variable, which is often understood as the finite element material density ρ e . The main idea of this approach is to define the finite element