The study of reactive silencers by shape and parametric optimization techniques

A novel approach to the three-dimensional optimal design of magnetic shields is presented, in which both shape optimization and topology optimization are achieved with the aid of numerical magnetic-field analysis. These numerical procedures are implemented by means of the hybrid finite element and boundary element method combined with the genetic algorithm. This results in an overall increase in the optimization speed with acceptable computational accuracy. Finally, some numerical results that demonstrate the validity of the proposed approach are presented.

The torpedo is a vital component of the naval arsenal, and efforts are continually directed toward improving the technology to make the torpedo more lethal and more stealthy. Recently, a new direction of research is considering the high-speed torpedo, which is capable of reaching up to 200 mph underwater. When a torpedo travels at this speed, the flow around the body separates and a cavity is formed. This cavity generation due to high speeds is called supercavitation. And the drag force acting on this supercavitating torpedo dictates the thrust requirements for the propulsion system, to maintain a required cavity at the operating speed. Therefore, any reduction in the drag force, obtained by modifying the shape of the cavitator or the nose of the torpedo, would result in lower propulsion requirements. In this work, shape optimization techniques were employed to determine the optimum (minimum-drag) shape of the cavitator given certain operating conditions. Shape optimization was also used to determine the shape of the cavity for any given cavitator, using potential flow theory. Analytical sensitivities were derived for various parameters in order to implement a gradient-based optimization algorithm. The developed methodology is an optimization process where the cavity and cavitator shapes are determined simultaneously. The cavitator shape that induces minimum drag and the corresponding cavity shape can be used to model a supercavitating torpedo that fits in the generated cavity and satisfies the required performance characteristics.

This paper presents a performance index for topology and shape optimization of plate bending problems with displacement constraints. The performance index is developed based on the scaling design approach. This performance index is used in the Performance-Based Optimization (PBO) method for plates in bending to keep track of the performance history when inefficient material is gradually removed from the design and to identify optimal topologies and shapes from the optimization process. Several examples are provided to illustrate the validity and effectiveness of the proposed performance index for topology and shape optimization of bending plates with single and multiple displacement constraints under various loading conditions. The topology optimization and shape optimization are undertaken for the same plate in bending, and the results are evaluated by using the performance index. The proposed performance index is also employed to compare the efficiency of topologies and shapes produced by different optimization methods. It is demonstrated that the performance index developed is an effective indicator of material efficiency for bending plates. From the manufacturing and efficient point of view, the shape optimization technique is recommended for the optimization of plates in bending.

In this paper, a technique to determine effectively an optimum shape of two-dimensional and axisymmetric bodies under body force is proposed. This technique is based on the iteration of a sequential search method consisting of the following steps. In the first step, the superiority or inferiority of a given shape, which satisfies the constrained conditions of design, is judged by the deviation from the design object stress value. In the second step, this given shape is modified to an optimum shape by the proportional transformation method of the finite elements, which is considered an effect of body force. By using this technique the optimum shapes of the basic problems under gravity load or centrifugal force are obtained and the results are compared with the corresponding shapes given by elementary theory. Moreover and optimum shape of the rotating disk with a rim and a bored hole is obtained by applying the optimization technique. The validity of this shape is examined experimentally by comparing with the fracture strength of a bored, uniform thickness disk.

The design of a centrifugal compressor for supercritical carbon dioxide power cycle must consider non-ideal gas effects and the possible occurrence of two-phase flows. Shape optimization techniques, combined with computational fluid-dynamic (CFD) simulations, can produce optimized designs while inherently coping with such peculiar flow characteristics. This study presents a three-dimensional shape optimization of a compressor stage composed of the impeller and the vaneless diffuser, whose compression starts close to the critical point. Impeller blade angle distributions and meridional channel are parameterized with Bezier control points, enabling local shape control within the optimization routine. The pinch of the vaneless diffuser is also optimized. The experimentally validated CFD solver considers both non-ideal effects and two-phase homogeneous flows, assuming thermodynamic equilibrium and a barotropic fluid. The constrained optimization problem is addressed using genetic algorithms. To mitigate computational costs, Kriging surrogates for the objective function and constraints are trained using a limited number of CFD results. The optimized geometry shows an appreciable efficiency increase (1.1 percentage points) while delivering the design pressure ratio. Although performing better at the design condition, the operating range of the compressor is altered by the optimization. Future optimizations that include both design and off-design operating points in the definition of the objective function and constraints may mitigate this problem.

The population of the world is increasing day by day. Accordingly, the amount of production and consumption are increasing. Due to the continuous and rapid development of technology, the duration of the use of some products becomes shorter. That is why the more efficient use of limited resources is even more important. In the developing and growing automotive industry, companies are currently focusing on weight and cost reduction methods to compete. In this study, the optimum design has been achieved by using topology and shape optimization in the suspension cover used in suspension systems. As a result of the topology and shape optimization efforts, The mass of the optimum design achieved was reduced by 35.203 % according to the first design.

This work relies on constructal design to perform the geometric optimization of the V-shaped pathways of highly conductive materials (inserts) that remove a constant heat generation rate from a body and deliver it to isothermal heat sinks. It is shown numerically that the global thermal resistance of the V-shaped pathway can be minimized by geometric optimization subject to total volume and V-shaped pathways material constraints. Constructal design and genetic algorithm (GA) optimization showed the emergence of an optimal architecture that minimizes the global thermal resistance: an optimal external shape for the assembly of pathways and optimal geometry features for the V-shaped pathway. Parametric study was performed to show the behavior of the minimized global thermal resistance as function of the volume fraction of the V-shaped pathways. First achieved results for ϕ = 0.3 indicated that when freedom is given to the geometry, the thermal performance is improved. Afterward, the employment of GA with constructal design allowed the achievement of the optimal shapes of V-shaped pathways for different volume fractions (0.2 ≤ ϕ ≤ 0.4). It was not realized the occurrence of one universal optimal shape for the several values of ϕ investigated, i.e., the optimal design was dependent on the degrees of freedom and the parameter ϕ and it is reached according to constructal principle of optimal distribution of imperfections.

In the paper the global optimization problem of truss systems is studied. The genetic algorithms are employed for the optimization. As the objective function the structure mass is treated; the constraints include equilibrium, local stability and other requirements. All the truss system characteristics needed for genetic algorithm are obtained via finite element solution. Topology optimization of truss system is performed using original modified genetic algorithm, while the shape optimization – using ordinary genetic algorithm. Numerical solutions are presented. The obtained solutions are compared with global extremes obtained using full search algorithm. All the numerical examples are solved using original software.

Design and analysis of auto-balancer of an optical disk drive using speed-dependent vibration absorbers

In this paper, shape optimization is employed to improve the stability of the flow past an elastically mounted circular cylinder at subcritical Reynolds numbers (Re < 47). As a key criterion for the stability of fluid-structure interaction system, dynamic derivative is adopted as the object of the optimization. The parametrization of the cross section is based on the class-shape function transformation technique. Then, shape optimization is conducted using the differential evolution algorithm. To improve the optimization efficiency, a surrogate model is constructed to replace the direct numerical simulation in the optimization process. Research shows that through the shape optimization, vortex-induced vibration is significantly suppressed and the stability of the fluid-structure interaction system is remarkably improved. In addition, the critical Reynolds number of the optimized cross section is also improved compared with that of the circular cylinder.

Shape design of a structure plays a significant part in deciding its least weight. In this paper, a fuzzy controlled genetic-based search technique for structural shape optimization is investigated. An automated optimal procedure based on the proposed approach is developed and used in the least-weight design of truss structures, which include their geometry as a design variable to be optimized. To increase the performance of the genetic-based approach for shape optimization problems, the design constraints related to member stress, joint displacement, and member buckling are described by using fuzzy set theory. A fuzzy rule-based system representing expert knowledge and experience is incorporated in the approach to control its optimal search process. Four examples for shape designs are presented to demonstrate the effectiveness and efficiency of the proposed hybrid approach in comparison with the use of pure genetic algorithms and other numerical methods. The examples show that the approach is flexible enough to deal with rigidly jointed structures.

Shape optimization (with topological changes) has become a de facto standard approach for synthesizing new designs. Current approaches heavily rely on voxelized modifications of the initial domain, followed by heuristic reconstruction procedures that result in a detailed shape design. The initial domain is almost always conservatively estimated so that the design space spans a sufficiently large set of possible solutions. We propose a novel approach to shape optimization that exploits the geometric and topologic properties of medial zones and a new shape modification paradigm to synthesize shapes with topological guarantees. The medial zone is a ‘thick skeleton’ of the domain induced by prescribed boundary conditions, and represents an initial solution that is topologically valid. We modify such an initial solution by adding or subtracting ‘bubbles’ of material defined via prescribed shape functions. The proposed approach has many advantages in terms of topological guarantees, shape control, and computational cost, supports parametric optimization of free-form geometry, and can be implemented in any geometric representation that supports distance computations.

Shape optimization of multi-chamber cross-flow mufflers by SA optimization

In structural optimization, static loads are generally utilized although real external forces are dynamic. Dynamic loads have been considered only in small-scale problems. Recently, an algorithm for dynamic response optimization using transformation of dynamic loads into equivalent static loads has been proposed. The transformation is conducted to match the displacement fields from dynamic and static analyses. This algorithm can be applied to large-scale problems. However, the application has been limited to size optimization. The present study applies the algorithm to shape optimization. Because the number of degrees of freedom of finite element models is usually very large in shape optimization, it is difficult to conduct dynamic response optimization with conventional methods that directly treat dynamic response in the time domain. The optimization process is carried out by interfacing an optimization system and an analysis system for structural dynamics. Various examples are solved to verify the algorithm. The results are compared to the results from static loads. It is found that the algorithm using static loads transformed from dynamic loads based on displacement is valid for very large-scale shape optimization problems. Copyright © 2005 John Wiley & Sons, Ltd.

Chapter 4 - Massive Parallelization as Prinicipal Technology for Constrained Optimization of Aerodynamic Shapes