Abstract: Two optimization algorithms are presented that are capable of finding a global optimum in a computationally efficient manner: a gradient-based multistart algorithm based on Sobol sampling and a hybrid optimizer combining a genetic algorithm with a gradient-based algorithm. The optimizers are used to investigate multimodality in aerodynamic-shape-optimization problems. The performance of each algorithm is tested on an analytical test function as well as several aerodynamic-shape-optimization problems in two and three dimensions. In each problem the primary objectives are to classify the problem according to the degree of multimodality and to identify the preferred optimization algorithm for the problem. The results show that multimodality should not always be assumed in aerodynamic-shape-optimization problems. Typical two-dimensional airfoil-optimization problems are unimodal. Three-dimensional shape-optimization problems may contain local optima. The number of local optima tends to increase with increasin...

Abstract: In the isogeometric analysis framework, a computational domain is exactly described using the same representation as the one employed in the CAD process. For a CAD object, various computational domains can be constructed with the same shape but with different parameterizations; however one basic requirement is that the resulting parameterization should have no self-intersections. Moreover we will show, with an example of a 3D thermal conduction problem, that different parameterizations of a computational domain have different impacts on the simulation results and efficiency in isogeometric analysis. In this paper, a linear and easy-to-check sufficient condition for the injectivity of a trivariate B-spline parameterization is proposed. For problems with exact solutions, we will describe a shape optimization method to obtain an optimal parameterization of a computational domain. The proposed injective condition is used to check the injectivity of the initial trivariate B-spline parameterization constructed by discrete Coons volume method, which is a generalization of the discrete Coons patch method. Several examples and comparisons are presented to show the effectiveness of the proposed method. During the refinement step, the optimal parameterization can achieve the same accuracy as the initial parameterization but with less degrees of freedom.

Abstract: Large-scale three-dimensional aerodynamic shape optimization based on the compressible Euler equations is considered. Shape calculus is used to derive an exact surface formulation of the gradients, enabling the computation of shape gradient information for each surface mesh node without having to calculate further mesh sensitivities. Special attention is paid to the applicability to large-scale three dimensional problems like the optimization of an Onera M6 wing or a complete blended-wing–body aircraft. The actual optimization is conducted in a one-shot fashion, in which the tangential Laplace operator is used as a Hessian approximation, thereby also preserving the regularity of the shape.

Abstract: Purpose – The purpose of this paper is to propose a novel contribution to adaptive sampling strategies for non‐intrusive reduced order models based on Proper Orthogonal Decomposition (POD). These strategies aim at reducing the cost of optimization by improving the efficiency and accuracy of POD data‐fitting surrogate models to be used in an online surrogate‐assisted optimization framework for industrial design.Design/methodology/approach – The effect of the strategies on the model accuracy is investigated considering the snapshot scaling, the design of experiment size and the truncation level of the POD basis and compared to a state‐of‐the‐art radial basis function network surrogate model on objectives and constraints. The selected test case is a Mach number and angle of attack domain exploration of the well‐known RAE2822 airfoil. Preliminary airfoil shape optimization results are also shown.Findings – The numerical results demonstrate the potential of the capture/recapture schemes proposed for adequately...

Abstract: In this research, Method of Moving Asymptotes (MMA) is utilized for simultaneous shape and topology optimization of shell structures. It is shown that this approach is well matched with the large number of topology and shape design variables. The currently practiced technology for optimization is to find the topology first and then to refine the shape of structure. In this paper, the design parameters of shape and topology are optimized simultaneously in one go. In order to model and control the shape of free form shells, the NURBS (Non Uniform Rational B-Spline) technology is used. The optimization problem is considered as the minimization of mean compliance with the total material volume as active constraint and taking the shape and topology parameters as design variables. The material model employed for topology optimization is assumed to be the Solid Isotropic Material with Penalization (SIMP). Since the MMA optimization method requires derivatives of the objective function and the volume constraint with respect to the design variables, a sensitivity analysis is performed. Also, for alleviation of the instabilities such as mesh dependency and checkerboarding the convolution noise cleaning technique is employed. Finally, few examples taken from literature are presented to demonstrate the performance of the method and to study the effect of the proposed concurrent approach on the optimal design in comparison to the sequential topology and shape optimization methods.

Abstract: The subject of this work is numerical shape optimization in fluid mechanics, based on isogeometric analysis. The generic goal is to design the shape of a 2-dimensional flow domain to minimize some prescribed objective while satisfying given geometric constraints. As part of the design problem, the steady-state, incompressible Navier-Stokes equations, governing a laminar flow in the domain, must be solved. Based on isogeometric analysis, we use B-splines as the basis for both the design optimization and the flow analysis, thereby unifying the models for geometry and analysis, and, at the same time, facilitating a compact representation of complex geometries and smooth approximations of the flow fields. To drive the shape optimization, we use a gradient-based approach, and to avoid inappropriate parametrizations during optimization, we regularize the optimization problem by adding to the objective function a measure of the quality of the boundary parametrization. A detailed description of the methodology is given, and three different numerical examples are considered, through which we investigate the effects of the regularization, of the number of geometric design variables, and of variations in the analysis resolution, initial design and Reynolds number, and thereby demonstrate the robustness of the methodology.

Abstract: The performance of a homogeneous T-mixer can be enhanced significantly by the stimulation of secondary/transverse flows in the microchannel. The groove-based micromixers generate helical flows within the microchannel to augment the mixing performance. These micromixers are extensively studied with respect to planar geometric parameters such as groove width, groove spacing, channel height, etc. The effect of groove shape on mixing performance has not been systematically studied. Previous studies have focused on two or three different predefined groove shapes, typically involving slanted grooves, asymmetric herringbone grooves, and their variations. In this computational study, we analyze the effect of groove shape on micromixing performance and search for the optimal groove shape for a pressure-driven flow across the microchannel. The groove shape is parametrically represented by Bezier curves which could take any shape within a constrained plane. The control points of the Bezier curve are chosen as optimization parameters to identify the optimal groove shape which maximizes the mixing for given operating conditions. The optimization is carried out for pressure-driven flow with and without staggered arrangement of grooves. The resulting single groove optimal design improves the mixing efficiency from 0.18 for T-mixer to 0.85 for the same operating conditions (Re ~0.42, Pe ~4,200). Unlike previous studies, axial mixing index profiles are presented for different micromixers which clearly distinguish the effect of flow field on the mixing performance. Various parametric studies are carried out to compare the optimal groove structure with other common groove type (staggered, herringbone, etc.) micromixers for a range of Pe between 400 and 6,200. The improved mixing performance in optimal designs is due to a continuously growing finger-like structure of the interface which enhances the overall mass transfer.

Abstract: The present paper introduces a numerical solution to shape optimization problems of domains in which boundary value problems of partial differential equations are defined. In the present paper, the finite element method using NURBS as basis functions in the Galerkin method is applied to solve the boundary value problems and to solve a reshaping problem generated by the H1 gradient method for shape optimization, which has been developed as a general solution to shape optimization problems. Numerical examples of linear elastic continua illustrate that this solution works as well as using the conventional finite element method.

Abstract: Multi-objective shape optimization of a row of laidback fan-shaped film cooling holes has been performed using a hybrid multi-objective evolutionary approach in order to achieve an acceptable compromise between two competing objectives: the enhancement of film cooling effectiveness and the reduction of aerodynamic loss. In order to perform comprehensive optimization of a film cooling hole shape, the injection angle of the hole, lateral expansion angle of the diffuser, forward expansion angle of the hole, and pitch-to-hole diameter ratio are chosen as design variables. Forty experimental designs within the design spaces are selected using the Latin hypercube sampling method. The response surface approximation method is used to construct the surrogate using objective function values calculated at the experimental points using Reynolds-averaged Navier-Stokes analysis. The shear stress transport turbulence model is used as a turbulence closure. The optimization results are processed using the Pareto-optimal m...

Abstract: Certain natural geometric evolution flows for Kahler metrics have been interpreted as anisotropic filtering operators. These flows are typically given by highly non linear PDE and involve usually transcendental and non-constructive techniques. The main objective of this note is to show that in certain cases, Geometric Quantization theory helps to overcome these difficulties and provides new algorithms based on S.K. Donaldson’s ideas.

Abstract: This paper proposes the optimization of an anisotropic ferrite magnet shape and magnetization direction to maximize back-EMF of IPM BLDC motor. Firstly, four different models of general magnet shapes are selected, and then FEM analysis is carried out with four different magnetization directions for each of four models. The best magnet shape and magnetization direction from each model are selected as an initial model for optimization. Secondly, based on the initial model, optimization design for maximum back-EMF and minimum cogging torque and THD is performed. Finally, validity and superiority of the optimization design are confirmed by manufacturing the prototype motor and performing the experiment.

Abstract: Computational fluid dynamic (CFD) models are ubiquitous in aerodynamic design. Variable-fidelity optimization algorithms have proven to be computationally efficient and therefore suitable to reduce high CPU-cost related to the design process solely based on accurate CFD models. A convenient way of constructing the variable-fidelity models is by using the high-fidelity solver, but with a varying degree of discretization and reduced number of flow solver iterations. So far, selection of the appropriate parameters has only been guided by the designer experience. In this paper, an automated low- fidelity model selection technique is presented. By defining the problem as a constrained nonlinear optimization problem, suitable grid and flow solver parameters are obtained. Our approach is compared to conventional methods of generating a family of variable-fidelity models. Comparison of the standard and the proposed approaches in the context of aerodynamic design of a transonic airfoil indicates that the automated model generation can yield significant computational savings.

Abstract: The complicated problem of truss shape and size optimization with multiple frequency constraints is investigated in this paper. A recently developed metaheuristics called teachinglearning-based optimization (TLBO) algorithm is used for the first time to solve this kind of problem. Contrary to other metaheuristics, the procedure of TLBO is simple to implement since no tuning parameters need to be adjusted. Analyses of structures are performed by a finite element code in MATLAB which is used in conjunction with an optimization code based on TLBO. Various benchmark problems are solved with this technique and the results are compared with those found by other methods including metaheuristics such as PSO, HS and FA. In all test cases, the results show that TLBO leads to very satisfactory results i.e. lighter structures which satisfy all frequency constraints. The results of this study indicate excellent inherent capacity of the approach in dealing with complicated dynamic non-linear optimization problems. Keywords– Truss structures, non-linear dynamic optimization, frequency constraints, teaching-learning-based optimization (TLBO)

Abstract: This work explores the interdependencies between the topological design of a compliant flapping mechanism and that of a flight-loaded elastic membrane-wing skeleton. This is done via a monolithic aeroelastic framework that encompasses the compliant-mechanism deformation, the motion of a flexible wing, and the transmission of aerodynamic and inertial forces back into the mechanism. A cellular-based evolutionary topology optimization scheme is used for mechanism design, wing design, or both simultaneously. The latter approach is shown to provide superior performance as this allows the tightly coupled nature of the two structures to be fully exploited. The results presented here also demonstrate potential issues that arise during wing design if the flapping kinematics are assumed to be prescribed. Finally, the mechanism topology is further improved via a gradient-based sizing/shape optimization to decrease actuator requirements as well as the time-dependent elastic stresses.

Abstract: Cable-braced grid shells, being a new type of single-layer reticulated shell, are widely used in glass roofs. However, research on the shape optimization of free-form cable-braced grid shells is relatively lacking. This paper describes a shape optimization method for cable-braced free-form grid shells, with strain energy used as the optimization object, structural height used as the optimization variable, and the conjugate gradient method used as the optimization algorithm. According to the shape forming method for grid shells, their shape optimization can be realized only by adjusting the generatrix and directrix, not by optimizing the whole surface. The B-spline curve method is used to model the generatrix and directrix and maintain an optimized surface fairing. The following conclusions can be drawn from this study. First, the structural mechanical behavior of grid shells can be significantly improved with rapid convergence using the proposed shape optimization method. Second, the plane quadrilateral mesh is maintained and fewer optimization variables are needed during the proposed shape optimization method. Finally, the optimized surface is fairing and the mechanical properties of the optimized surface are somewhat decreased when using the B-spline curve method.

Abstract: Design-dependent loads related to boundary shape, such as pressure and convection loads, have been a challenging issue in optimization. Isogeometric analysis, where the analysis model has smooth boundaries described by spline functions can handle design-dependent loads with ease. In the present study, shape optimization based on isogeometric analysis is applied to the Stokes flow problems such as minimizing energy dissipation and drag force. The drag force objective is based on accurate integration of boundary pressures. Local control point insertion schemes are employed for accurate representation of geometry in an adaptive manner.

Abstract: The purpose of this work is to analyse and study an efficient parametrization technique for a 3D shape optimization problem. After a brief review of the techniques and approaches already available in literature, we recall the Free Form Deformation parametrization, a technique which proved to be efficient and at the same time versatile, allowing to manage complex shapes even with few parameters. We tested and studied the FFD technique by establishing a path, from the geometry definition, to the method implementation, and finally to the simulation and to the optimization of the shape. In particular, we have studied a bulb and a rudder of a race sailing boat as model applications, where we have tested a complete procedure from Computer-Aided-Design to build the geometrical model to discretization and mesh generation.

Abstract: A shape optimization method by using combination of stress and electromagnetic field analyses has been developed for the design of high-speed motors. In the stress analysis, the mechanical stress caused by centrifugal force in the rotor is estimated. In the electromagnetic field analysis, the loss and torque of the motor are estimated. The permeability and the core-loss coefficients used in the electromagnetic field analysis are modified due to the results of the stress analysis. The validity of the optimization is confirmed by the measurement of a prototype motor. The measured and calculated results are found to be in good agreement. The proposed method is useful for high-speed motor designs.