9.2 Literature Review
337
More recently, the optimal microstructure of materials has been worked out in the
problems of achieving maximum value and shear moduli [44, 67]. The mentioned
methods allow to design novel composites with negative Poisson’s coefficient [57]
as well as materials with extreme or even negative heat transfer coefficient [60],
which demonstrates a huge ability of the mentioned method while designing either
elastic or thermoelastic composites. It is evident that in many cases heat transfer and
elastic material properties are coupled [68]. Therefore, it is difficult to achieve the
composite material with high heat transfer and stiffness ability simultaneously. This
is why it is worthy to develop a novel procedure working effectively while designing
the composite materials with a few inversely required targets. However, the multicriteria optimization is difficult and sometimes impossible to be realized in order
to obtain a global optimum for all design targets. In the optimization process, one
may observe that the improvement of one criterion requires compromise with regard
to another criterion. A set of the obtained solutions is defined by the Pareto space
consisting of a series of points in the solutions space, where each of the included
solutions cannot be improved via the used target function without deterioration of the
remaining target functions [69]. This means that it is required to gather a sufficient
choice of the best solutions. Torquato et al. [70] proposed an optimal design of
manufacturable 3D composites with multifunctional characteristics including heat
transfer and electricity transfer with the same weights [70].
Yoo and Lee [71] employed various weight coefficients while searching for optimal topology of the Pareto solution with regard to the stiffness and frequency criteria
mainly using a swing arm type actuator by computing the response surface method.
For many years, as it follows from the literature overview, the microstructure design
of the beam-type structural members was based on the designer intuition and experience with the support of the optimization methods.
In this chapter, we solve a multistep optimization problem of reinforcement of a
beam made from composite material to improve its resistance to the acting loads. The
approach consists of a few steps. In the first step, using the methods of topological
optimization, a microstructure of two-component composite being optimized with
regards to stiffness and heat transfer is obtained. The second step relies on topological
optimization of the reinforced beam structure under the criterion of minimum flexibility (maximum stiffness) for the given boundary conditions and loading conditions
of the beam embedded into temperature field. In each of the considered cases, the
optimal structure of the reinforced beam becomes original for the given conditions
of loading and the employed boundary conditions. In result, the designed beam with
the optimal microstructure exhibits non-homogeneity along the two directions, i.e.
its thickness and length.
The third step is aimed at investigation of the static and dynamic beam behaviour
with its mathematical model derived on a basis of the Euler-Bernoulli hypotheses,
the modified couple stress theory and with an account of the geometric von Kármán
non-linearity. The influence of the temperature fields is taken into account by using
the Duhamel-Neumann relations.
337
More recently, the optimal microstructure of materials has been worked out in the
problems of achieving maximum value and shear moduli [44, 67]. The mentioned
methods allow to design novel composites with negative Poisson’s coefficient [57]
as well as materials with extreme or even negative heat transfer coefficient [60],
which demonstrates a huge ability of the mentioned method while designing either
elastic or thermoelastic composites. It is evident that in many cases heat transfer and
elastic material properties are coupled [68]. Therefore, it is difficult to achieve the
composite material with high heat transfer and stiffness ability simultaneously. This
is why it is worthy to develop a novel procedure working effectively while designing
the composite materials with a few inversely required targets. However, the multicriteria optimization is difficult and sometimes impossible to be realized in order
to obtain a global optimum for all design targets. In the optimization process, one
may observe that the improvement of one criterion requires compromise with regard
to another criterion. A set of the obtained solutions is defined by the Pareto space
consisting of a series of points in the solutions space, where each of the included
solutions cannot be improved via the used target function without deterioration of the
remaining target functions [69]. This means that it is required to gather a sufficient
choice of the best solutions. Torquato et al. [70] proposed an optimal design of
manufacturable 3D composites with multifunctional characteristics including heat
transfer and electricity transfer with the same weights [70].
Yoo and Lee [71] employed various weight coefficients while searching for optimal topology of the Pareto solution with regard to the stiffness and frequency criteria
mainly using a swing arm type actuator by computing the response surface method.
For many years, as it follows from the literature overview, the microstructure design
of the beam-type structural members was based on the designer intuition and experience with the support of the optimization methods.
In this chapter, we solve a multistep optimization problem of reinforcement of a
beam made from composite material to improve its resistance to the acting loads. The
approach consists of a few steps. In the first step, using the methods of topological
optimization, a microstructure of two-component composite being optimized with
regards to stiffness and heat transfer is obtained. The second step relies on topological
optimization of the reinforced beam structure under the criterion of minimum flexibility (maximum stiffness) for the given boundary conditions and loading conditions
of the beam embedded into temperature field. In each of the considered cases, the
optimal structure of the reinforced beam becomes original for the given conditions
of loading and the employed boundary conditions. In result, the designed beam with
the optimal microstructure exhibits non-homogeneity along the two directions, i.e.
its thickness and length.
The third step is aimed at investigation of the static and dynamic beam behaviour
with its mathematical model derived on a basis of the Euler-Bernoulli hypotheses,
the modified couple stress theory and with an account of the geometric von Kármán
non-linearity. The influence of the temperature fields is taken into account by using
the Duhamel-Neumann relations.