Constructal Design Associated to Genetic Algorithm of Asymmetric V-Shaped Pathways

The study of reactive silencers by shape and parametric optimization techniques

An optimal shape of two-dimensional asymmetric diffuser with maximum pressure recovery at the exit is numerically obtained using a mathematical theory based on the variational calculus and gradient algorithm. The initial diffuser is taken to be a two-dimensional asymmetric diffuser for which much experimental and numerical data are available. The Reynolds number based on the bulk mean velocity and the channel height at the diffuser entrance is 1.8 × × 10 4 .F rom this initial shape, optimal diffuser shapes are designed for six different geometric constraints, such as the streamwise length and height of the diffuser. The optimality condition for maximum pressure recovery is obtained to be zero skin friction along the diffuser wall. The turbulent flow inside the diffuser is predicted using the k‐� ‐v2‐f model, and optimal shapes are obtained through iterative procedures to satisfy the optimality condition. With the shape design, flow separation that appeared in the initial diffuser is completely removed or significantly reduced. For one of the optimal diffuser shapes obtained, large-eddy simulation is carried out to validate the result of the shape design. The wall shear stress, wall pressure, mean velocity, and turbulence quantities obtained from large-eddy simulation are in good agreement with those from the simulation using the turbulence model.

The Simulated Annealing is a widely used metaheuristic to combinatorial and optimization problems studied since 1983, when it was first proposed. This algorithm has a particular parameter, the cooling schedule (specifically the decrease of temperature) which is still defined for each problem empirically. This study has the aim to find the best cooling schedule(s) for geometric optimization of a heat transfer problem. More specifically it is performed the geometrical evaluation of an isothermal Y-shaped cavity intruded into conducting solid wall with internal heat generation. In this research, Constructal Design is employed to determine the constraints and objectives for geometric evaluation of this problem. The cooling schedule(s) recommended here will contribute for future applications of Simulated Annealing heuristic in association with Constructal Design to seek for the optimal shapes of complex geometries in heat transfer problems, as well as, evaluate the influence of geometric parameters over thermal performance of the problem. Six different methods of decrease of temperature are evaluated in twenty samples of thirty simulations for each cooling schedule. From these simulations, it was extracted the percentage of convergence to the global optimal point. Results showed that the Fast cooling schedule led to the worst performance in the seek for the global optimal shapes, while the three hybrid cooling schedules proposed here are the most recommended to find the optimal geometrical configurations in heat transfer problems in association with Constructal Design ( BoltzExp , ConstExp1 and ConstExp2 )

Radar cross section (RCS) reduction technologies are very important in survivability of the military naval vessels. Ship appearance shaping as an effective countermeasure of RCS reduction redirects the scattered energy from one angular region of interest in space to another region of little interest. To decrease the scattering electromagnetic signals from ship scientifically, optimization methods should be introduced in shaping design. Based on the assumption of the characteristic section design method, mathematical formulations for optimal shaping design were established. Because of the computation-intensive analysis and singularity in shaping optimization, the response surface method (RSM) combined genetic algorithm (GA) was proposed. The polynomial response surface method was adopted in model approximation. Then genetic algorithms were employed to solve the surrogate optimization problem. By comparison RCS of the conventional and the optimal design, the superiority and effectiveness of proposed design methodology were verified.

Shape optimization of automotive body frame using an improved genetic algorithm optimizer

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.

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.

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

Optimal designs of arches under multiple load cases using an automated design routine are presented. The design variables consist of geometric (arch shape) as well as member sizing variables (cross-sectional dimensions). The members are sized on the basis of working stress design procedure, and all the relevant provisions of the AISC specifications are met. The optimal arch shapes produced by the present method for a uniformly distributed load case show a good agreement with the theoretical results. The optimal designs under two and three load cases are also obtained. Under two load cases, the optimal shapes are not very different than a parabolic curve passing through the supports and crown of the arch.

This chapter is the printed matter of a series of lectures on shape optimization given in Udine (Italy) in June 2012. It is mainly focused on the optimal design problem in elasticity.It is well known, since the pioneer work of Tartar and Murat in the late 70’s, that this problem – as well as the scalar shape optimization problem in conductivity – is ill posed and does not always admit solutions. If the goal is to construct numerical methods to address this optimal design problem, this illposedness will lead to algorithms showing instabilities and erratic behaviours.Two ways are possible to slightly change the initial problem so that it may be solved in an efficient and reliable way by numerical methods. The first one consists in enlarging the set of admissible shapes and allow, as solutions, “generalized shapes” that may contain fine mixtures of the initial material and void. This process is called “relaxation” and the main mathematical tool involved is the homogenization theory. It leads to the so called “homogenization method for shape optimization”. It is described in Section 2, both from theoretical and numerical point of views, including practical issues necessary to write a numerical code.The second approach consists in restricting the set of admissible solutions. A few theorems prove the existence of solutions under further geometrical, topological or regularity constraints. The classical domain variation method is revisited using the level set representation, that may be seen as a constraint on the set of admissible solutions. The main tool is here the shape derivative. The level set algorithm is presented in Section 3.Of course this chapter is too short to develop new results and methods and present extensive proofs. Its goal is rather to give an overview on different parts of our work on this topics. Interested readers should check the references cited to have further details.KeywordsTopology OptimizationShape OptimizationHomogenization MethodAdmissible SolutionOptimal Design ProblemThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

In response to the problems of traditional genetic algorithms in evaluating English compositions, the stability of automatic grading of English compositions has been further enhanced. This article evaluates the teaching effectiveness of automatic grading of English compositions using an optimization fusion algorithm combined with genetic optimization algorithm and CNN model. By analyzing genetic content and optimization algorithms, a corresponding fusion optimization model was obtained, and the automatic evaluation of English compositions was analyzed and predicted through experimental verification. The results indicate that the curves corresponding to different parameters exhibit typical segmentation features through the variation curves of individual numbers under different scale factors. And through quantitative description and analysis of the curve, it can be seen that the change in proportion factor has an absolute advantage in the impact of genetic algorithm on the number of children. As the number of samples increases, the performance of genetic optimization algorithms under the f function shows an upward trend. Research has shown that the writing content index has the greatest impact on English writing, while the corresponding grammar errors have the smallest impact on English writing. Finally, the accuracy of the optimized model was verified by comparing the model curve with experimental data. This study provides theoretical support for the use of genetic optimization algorithms and CNN models in English, and provides ideas for the use of optimization algorithms in other fields.

Constructal design for blast furnace wall based on the entransy theory

Mathematical shape optimization of hip prosthesis design

Aerodynamic shape optimisation technology is presented, comprising an efficient variable fidelity shape parameterisation method, an efficient andhigh quality mesh deformation scheme, and a parallel optimisation algorithm. The objective of the research presented here is the comparison of truly three-dimensional optimisations of aircraft wings in both aerodynamic and aeroelastic environments. The novel shape parameterisation technique allows various fidelities of design parameters, ranging from detailed surface changes to novel truly three-dimensional planform adjustments. An efficient interpolation scheme, using radial basis functions, transfers domain element movements into direct deformations of the design surface and corresponding CFD mesh, thus allowing total independence from the grid generation package and type (structured or unstructured). Optimisation is independent from the CFD flow solver by obtaining sensitivity information for an advanced parallel gradient-based optimiser by finite-differences. This ‘wrap-around’ optimisation technique is applied to a modern large transport aircraft wing in the cruise flight condition for minimum drag with stringent constraints in lift, volume, and two root moments. The objective of all optimisations is aerodynamic, however the static aeroelastic deflection provided by an aeroelastic solver will give that particular optimisation increased accuracy and real world relevance. The result of a constrained inviscid aerodynamic optimisation is presented and has a significant reduction in drag when compared to the initial wing with no violation of any constraints. The shape parameterisation method demonstrates that only a low number of design variables are necessary to achieve innovative planform and surface geometries with dramatically improved performance. Computational fluid dynamics (CFD) methods are now commonplace in aerospace industries, and at the forefront of analysis capabilities, providing a fast and effective method of predicting a design’s aerodynamic performance. However, with ever increasing complexity of designs, engineers can often struggle to interpret the intricacies of the CFD results sufficiently to be able to manually alter the geometry to improve performance. Hence, there has been an increase in demand for intelligent and automatic shape optimisation schemes. This requires combining geometry control methods with numerical optimisation algorithms, to provide a mechanism to mathematically seek improved and optimum designs, using CFD as the analysis tool. Optimisation requires consideration of three issues, each of which have numerous solutions: shape parameterisation including CFD surface and volume mesh deformation, computation of design variable derivatives, and effective use of these derivatives to improve design. Geometry parameterisation is critical for effective shape optimisation. This is the method of representing the design surface, and defines the degrees of freedom in which the geometry can be altered and, ideally, this should be linked with an effective method of deforming the CFD surface and volume mesh in a corresponding fashion. Parameterising complex shapes is a problem that remains a serious obstacle to both manual and automatic CFD-based optimisation. A wide variety of shape control and morphing methods have been developed, but many do not allow sufficiently

Finite-element approximation of 2D elliptic optimal design