Fuzzy Controlled Genetic Algorithm Search for Shape Optimization

The study of reactive silencers by shape and parametric optimization techniques

Structural design optimization in precise or imprecise environment plays an important role in civil engineering as well as in mathematics. Conventionally in most of the situation structural designs are treated as single objective optimization problem with cost as objective function. Practically there exists some real life problems where multiple and conflicting objects frequently exist.So a methodology known as Multi-objective Four Valued Refined Neutrosophic Optimization (MOFVRNO) technique has been introduced in this paper.This optimization technique is generalization of fuzzy set (FS)theory,Intuitionistic Fuzzy Set (IFO)Theory and above all Single Valued  Neutrosophic Set Optimization (SVNSO)theory.In this problem cost and deflection of the beam have been considered as objective functions. Also in this welded beam design problem maximum shear stress in the weld group, maximum bending stress in the beam, buckling load of the beam have been considered as constraints. The design variables are length ,depth ,height,width in this optimization problem.Now from the mathematical point of view indeterminacy is again refined as uncertain(U),Contradiction(Truth∧Falsity,T) in Four valued Refined Neutrosophic Optimization technique.The results obtained by different methods like nonlinear optimization technique,Fuzzy optimization technique ,Intuitionistic Fuzzy Optimization technique ,Single Valued Neutrosophic Optimization technique andFour Valued Refined Neutrosophic Optimization technique have been discussed in the perspective of welded beam design problem in this paper. It helps to make comparison among them to find most cost effective method.

During the last 20 years, structural optimization has become one of the most important topics of engineering applications. Design optimization of structure has been an interesting area of research in the field of engineering design for its ability to short the design cycle and to enhance product quality. Significant research activity has occurred in the area of structural optimization in the last decade. Especially for topology optimization of structure, many new theoretical, algorithmic, and computational contributions have resulted by researchers and engineers. Topology optimization is a powerful tool for global and multi-scale design of macrostructures, microstructures, and the cell of prescribed composite materials. The population based evolutionary algorithms have emerged as powerful mechanism for finding optimum solutions of complex optimization problems in engineering during the last two decades. Evolutionary computation is the study of computational systems which use ideas and get inspiration from natural evolution and adaptation [1]. The thinking has wide application in various engineering fields, such as computer science, artificial intelligence, operations research. Genetic algorithm is another kind of bio-inspired optimization method and it is playing an increasingly important role in studies of complex adaptive systems. Its application ranges from adaptive agents in economic theory to the use of machine learning techniques in the design of complex devices and structures, such as aircraft turbines and integrated circuits [2]. Optimization of structures can be classified into three categories: sizing, shaping, and topology optimization. In the topology optimization, it is concerned with the structure members and connectivity between members. In general, it is easily represented by discrete variables rather than by those used for continuous optimization problems. Topology optimization is the most difficult and complex among three categories and it is special useful in developing innovative conceptual designs. Structural optimization, in particular the topology optimization, has been identified as one of the most challenging tasks in structural design. Various techniques and approaches have been established during the last two decades. Topology optimization usually referred to as layout optimization or general shape optimization [3]. It lets engineers get the optimal topology of structure or new configurations during product design phase, as they are implementing the design of the size

Because of their superior mechanical, structural, and electronic properties, graphene sheets (GSs) are supposed to be components of nanoelectromechanical systems (NEMS). In this study, we carry out shape and structural optimization of GSs with topological defects in natural vibration problem to enhance their fundamental frequencies. At first, we model GSs as continuum frame models based on the molecular mechanics method. Then, we carry out shape design optimization of GSs by using a developed free-form optimization method for frame structures. In the shape design optimization, we use the fundamental frequency as objective function and enhance it considering volume constraint and repeated eigenvalues. Next, we derive the optimal atom structures of GSs with topological defects using a combination of the Phase-Field-Crystal method, the Voronoi tessellation method, and molecular dynamics simulation. The numerical results show that the fundamental frequencies of GSs can be significantly increased according to the shape and structural design optimization, and we can get their optimal atom structures with defects, which is helpful for designing GSs as components in NEMS.

Swarm intelligence hybridized with genetic search in multi-objective design optimization under constrained-Pareto dominance

Surface shape design in fluid flow problems via hybrid optimization algorithms

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.

Structural topology optimization.- On basic properties of Michell's structures.- Validation of numerical method by analytical benchmarks and verification of exact solutions by numerical methods.- Introduction to shape and topology optimization.- Homogenization method for shape and topology optimization.- Level set method for shape and topology optimization.- Compliance minimization of two-material elastic structures.- Some notes on topology optimization of vibrating continuum structures.- Topology optimization of vibrating continuum structures for maximum values of simple and multiple eigenfrequencies and frequency gaps.- On optimum shape design and periodicity of band-gape beam structures.- Topological design for minimum dynamic compliance of continuum structures subjected to forced vibration.- Topological design for minimum sound emission from bi-material structures subjected to forced vibration.- Discrete material optimization of vibrating laminated composite plates for minimum sound emission.- Optimization of diffusive transport problems.- Fluid topology optimization: stokes and Navier-stokes models.- Topology optimization of coupled multi-physics problems.- Topology optimization based on the extended finite element method.- Topology optimization of meso- and nano-scale problems.- Topology optimization under uncertainty.- A brief review of numerical methods of structural topology optimization.- The free material design in planar elasticity.

One of the major difficulties in structural shape optimal design is to create a design model by parameterizing a geometric model. Shape design parameterization is more complicated and difficult to handle than sizing design parameterization. First, the optimum shape is highly dependent on the design parameterization selected. An inappropriate design parameterization may result in an impractical design. On the other hand, changing the geometric shape of the design model to reflect successive changes in design parameters is a tedious, complicated, and inefficient process. Manual updates of geometric shape and finite element meshes are quite impractical. In this paper, a shape design parameterization method that is built on the geometric modeler PATRAN is presented. Using this method, a number of geometric entities that represent structural design boundaries are parameterized, and a design parameter linking process can be performed to create geometric features from geometric entities. To support the proposed method in structural shape design, a unified velocity computation method using geometric parametric mapping and an elliptic equation solver is developed for shape design sensitivity computation. The design parameterization and associated velocity Held computation methods are general enough to handle a broad range of engineering applications. Finally, automatic finite element mesh and geometric shape update methods are presented, which can be used to easily perform design changes.

PurposeThis paper aims to summarize design rules based on the process characteristics of selective laser melting (SLM) and structural optimization and apply the design rules in the lightweight design of an aluminum alloy antenna bracket. The design goal is to reduce 30 per cent of the weight while maintaining the stress levels in the original part.Design/methodology/approachTo reduce weight as much as possible, the titanium alloy with higher specific strength was selected during the process of optimization. The material distribution of the bracket was improved by the topology optimization design. The redesign for SLM was used to obtain an optimization model, which was more suitable for SLM. The component performance was improved by shape optimization. The modal analysis data of the structural optimization model were compared with those of the stochastic lightweight model to verify the structural optimization model. The scanning data were compared with those of the original model to verify whether the model was suitable for SLM.FindingsStructural optimization design for antenna bracket realized the mass decrease of 30.43 per cent and the fundamental frequency increase of 50.18 per cent. The modal analysis data of the stochastic lightweight model and the structural optimization model indicated that the optimization performance of structural optimization method was better than that of the stochastic lightweight method. The comparison results between the scanning data of the forming part and the original data confirmed that the structural optimization design for SLM lightweight component could achieve the desired forming accuracy.Originality/valueThis paper summarizes geometric constraints in SLM and derives design rules of structural optimization based on the process characteristics of SLM. SLM design rules make structural optimization design more reasonable. The combination of structural optimization design and SLM can improve the performance of lightweight antenna bracket significantly.

To obtain reliable designs, aleatory and epistemic uncertainties are considered recently in the structural analysis and design optimization. The reliability based de-sign optimization (RBDO) method [1] is used when the amount of input data is sufficient enough to create accurate statistical distribution. On the other hand, when the sufficient input data are not available due to limitations in time, human, and facility resources, the optimum design may not be reliable if RBDO method is used. To deal with the situation that input uncertainties have insufficient information, a possibility (or fuzzy set) method can be used for structural analysis and possibility based design optimization (PBDO) [2]. However, in many industry design problems, we may have to deal with design problems that involve with the mixed input statistical random and fuzzy variables simultaneously. For these problems, RBDO may yield unreliable optimum designs because of insufficient data. On the other hand, treating the random variables as fuzzy variables and invoking PBDO to solve the mixed design variable problem may yield too conservative designs with higher optimum costs. This paper proposes a new mixed variable design optimization (MVDO) problem based on the performance measure approach (PMA) [1]. To evaluate the possibilistic constraint in MVDO, a sub-optimization problem for inverse analysis is carried out using a hyper-cylinder domain. To solve this sub-problem efficiently and effectively, a new numerical algorithm, maximum failure search (MFS) method, is proposed in this paper by combining the enhanced hybrid mean value (HMV+) method [3] for the inverse reliability analysis in RBDO and the maximal possibility search (MPS) method [2] for the inverse possibility analysis in PBDO. Some mathematical examples are used to demonstrate the efficiency and effectiveness of the proposed numerical MFS method. Some physical design examples are used to compare the proposed MVDO results with RBDO and PBDO results.

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.

In excavation design, optimizing the reinforcement and finding the optimal shape ofthe opening are two significant challenges. Both ofthese problems can be viewed as searching for the optimum distribution of material in the design domain. In structural design, topology optimization techniques have been successfully used to deal with such problems. One ofthese techniques, known as bi-directional evolutionary structural optimization (BESO), is employed here to improve the shape and reinforcement designs of underground openings. The BESO algorithm is extended to simultaneously optimize the shape of the opening and the topology of the reinforcement. The capability of the proposed approach is illustrated via numerical examples.

A shape design sensitivity analysis and optimization procedure is proposed using a meshfree method. A CAD tool connection is established to facilitate the seamless integration of structural modeling, simulation, and design optimization. A new CAD-based method for design velocity computation is proposed, applicable to both the meshfree method and the finite element method. A shape design variable can be chosen among the geometric parameters defined in the CAD model in order to support a concurrent engineering environment. A new CAD-based method for updating the discrete model is proposed, such that the meshfree model is automatically updated in a continuous and consistent way during design optimization. The proposed method is applied to 2D and 3D linear elastic problems, as well as to a large deformation hyperelastic problem.

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.