9.6 Topological Optimization with Maximized Stiffness and Heat Transfer
359
On the other hand, in many cases, the heat transfer and elastic properties of
materials compete with each other [68]. Hence, it is often difficult to achieve both
high heat transfer and high stiffness simultaneously. For this reason, it is important to
develop a procedure that would work effectively in spite of the conflicting objectives.
In general, the multi-target optimization is difficult or even impossible to obtain a
global optimum for all expected design targets. However, in the optimization process,
it can be seen that at some stage, any further improvement of one criterion requires a
compromise with at least one other criterion. A set of such solutions determines the
Pareto space which consists of a series of points within the solution space [69], where
for each of the mentioned solutions it is impossible to further improve some target
functions without worsening at least one of the remaining target functions. Thus,
it is necessary to gather as much information about the Pareto space as possible to
choose the best solution.
Torquato et al. [70] combined heat transfer and electrical transfer with equal
weight to propose the optimal design of manufacturable 3D composites with multifunctional characteristics. Yoo and Lee [71] used various weight coefficients to find
optimal topologies of the Pareto solution of a swing arm type actuator in accordance
with the flexibility criteria and eigenfrequency. The mentioned works show that the
use of the weight functions is the best method to obtain a set of Pareto solutions.
Seresta et al. [104] considered a wing box design optimization by employing composite laminates with blending constraints based on the inclusion of fibre orientation
angle of the layers and the total thickness of the laminate as design optimization
variables. They have shown that the optimum design has better continuity of the
laminate lay-ups.
The multi-criteria (multi-objective) optimization of laminated composite structures under technological constraints was discussed by Bassir et al. [105]. The main
method based on the NSGA-II program exhibited its efficiency in obtaining a uniform
spray of the Pareto solutions.
Lee et al. [106] developed a multi-objective approach using a parallel multiobjective generic algorithm to study a stacking sequence design optimization for a
multilayer composite plate. The used methodology matched a robust multi-objective
evolutionary algorithm and a finite element analysis with a parallel optimization
system. It has been shown analytically that Pareto optimal solutions offer a set of
selections for engineers to improve the composite structure in terms of the industrial
needs (cost) and mechanical properties (weight and stiffness).
Ning et al. [107] developed an experimental method of additive manufacturing
using the fused deposition modelling, which affected the tensile strength, Young’s
modulus, yield strength, flexural stresses and toughness of reinforced thermoelastic
composites.
Madeira et al. [108] proposed the optimal design of laminated composite panels
with constrained layer damping aimed at minimization of weight and maximization
of model damping. In particular, trade-off Pareto optimal solutions and the respective
treatment configurations were obtained and analyzed.
Salem and Donaldson [109] developed and studied a methodology for a combined
weight and cost optimization of sandwich plates with hybrid composite face sheets
359
On the other hand, in many cases, the heat transfer and elastic properties of
materials compete with each other [68]. Hence, it is often difficult to achieve both
high heat transfer and high stiffness simultaneously. For this reason, it is important to
develop a procedure that would work effectively in spite of the conflicting objectives.
In general, the multi-target optimization is difficult or even impossible to obtain a
global optimum for all expected design targets. However, in the optimization process,
it can be seen that at some stage, any further improvement of one criterion requires a
compromise with at least one other criterion. A set of such solutions determines the
Pareto space which consists of a series of points within the solution space [69], where
for each of the mentioned solutions it is impossible to further improve some target
functions without worsening at least one of the remaining target functions. Thus,
it is necessary to gather as much information about the Pareto space as possible to
choose the best solution.
Torquato et al. [70] combined heat transfer and electrical transfer with equal
weight to propose the optimal design of manufacturable 3D composites with multifunctional characteristics. Yoo and Lee [71] used various weight coefficients to find
optimal topologies of the Pareto solution of a swing arm type actuator in accordance
with the flexibility criteria and eigenfrequency. The mentioned works show that the
use of the weight functions is the best method to obtain a set of Pareto solutions.
Seresta et al. [104] considered a wing box design optimization by employing composite laminates with blending constraints based on the inclusion of fibre orientation
angle of the layers and the total thickness of the laminate as design optimization
variables. They have shown that the optimum design has better continuity of the
laminate lay-ups.
The multi-criteria (multi-objective) optimization of laminated composite structures under technological constraints was discussed by Bassir et al. [105]. The main
method based on the NSGA-II program exhibited its efficiency in obtaining a uniform
spray of the Pareto solutions.
Lee et al. [106] developed a multi-objective approach using a parallel multiobjective generic algorithm to study a stacking sequence design optimization for a
multilayer composite plate. The used methodology matched a robust multi-objective
evolutionary algorithm and a finite element analysis with a parallel optimization
system. It has been shown analytically that Pareto optimal solutions offer a set of
selections for engineers to improve the composite structure in terms of the industrial
needs (cost) and mechanical properties (weight and stiffness).
Ning et al. [107] developed an experimental method of additive manufacturing
using the fused deposition modelling, which affected the tensile strength, Young’s
modulus, yield strength, flexural stresses and toughness of reinforced thermoelastic
composites.
Madeira et al. [108] proposed the optimal design of laminated composite panels
with constrained layer damping aimed at minimization of weight and maximization
of model damping. In particular, trade-off Pareto optimal solutions and the respective
treatment configurations were obtained and analyzed.
Salem and Donaldson [109] developed and studied a methodology for a combined
weight and cost optimization of sandwich plates with hybrid composite face sheets