Inversion of the source and vorticity equations for supercavitating hydrofoils

The problem of a supercavitating hydrofoil of general shape with leading edge cavity detachment is addressed in linear theory in terms of unknown source and vorticity distributions on the foil and cavity. The related singular integral equations are inverted analytically and the cavitation number, the source and vorticity distributions are expressed in terms of integrals of quantities which depend only on the hydrofoil shape and the cavity length. Numerical algorithms for computing these integrals accurately and efficiently are given.     

Shape optimization of preform tools in forging of aerofoil using a metamodel-assisted multi-island genetic algorithm

Preform design plays an important role in improving the material flow, mechanical properties and reducing defects for forgings with complex shapes. In this paper, a study on shape optimization of preform tools in forging of an airfoil is carried out based on a multi-island genetic algorithm combined with a metamodel technique. An optimal Latin hypercube sampling technique is employed for sampling with the expected coverage of parameter space. Finite element (FE) simulations of multistep forging processes are implemented to obtain the objective function values for evaluating the forging qualities. For facilitating the optimization process, a radial basis function surrogate model is established to predict the responses of the hot forging process to the variation of the preform tool shape. In consideration of the compromise between different optimal objectives, a set of Pareto-optimal solutions are identified by the suggested genetic algorithm to provide more selections. Finally, according to the proposed fitness function, the best solution of multi-objective optimization on the Pareto front is confirmed and the corresponding preform tool shape proves optimal performances with substantially improved forging qualities via FE validation.     

A smart repair embedded memetic algorithm for 2D shape matching problems

Shape representation plays a major role in any shape optimization exercise. The ability to identify a shape with good performance is dependent on both the flexibility of the shape representation scheme and the efficiency of the optimization algorithm. In this article, a memetic algorithm is presented for 2D shape matching problems. The shape is represented using B-splines, in which the control points representing the shape are repaired and subsequently evolved within the optimization framework. The underlying memetic algorithm is a multi-feature hybrid that combines the strength of a real coded genetic algorithm, differential evolution and a local search. The efficiency of the proposed algorithm is illustrated using three test problems, wherein the shapes were identified using a mere 5000 function evaluations. Extension of the approach to deal with problems of unknown shape complexity is also presented in the article.     

Topology optimization of a magnetic field in a three-dimensional finite region

This article describes the method of magnetic field topology optimization in an axisymmetric three-dimensional finite region. It is assumed that the region of interest is surrounded by a cylindrical solenoid with an electrical current. The solenoid’s inner and outer surfaces are built-up by rotating plane Bezier curves around the symmetry axis. As a global minimizer a genetic algorithm method is used. Optimal configurations are provided under given constraints.     

Unification of parametric and implicit methods for shape sensitivity analysis and optimization with fixed mesh

Parametric and implicit methods are traditionally thought to be two irrelevant approaches in structural shape optimization. Parametric method works as a Lagrangian approach and often uses the parametric boundary representation (B‐rep) of curves/surfaces, for example, Bezier and B‐splines in combination with the conformal mesh of a finite element model, while implicit method relies upon level‐set functions, that is, implicit functions for B‐rep, and works as an Eulerian approach in combination with the fixed mesh within the scope of extended finite element method or finite cell method. The original contribution of this work is the unification of both methods. First, a new shape optimization method is proposed by combining the features of the parametric and implicit B‐reps. Shape changes of the structural boundary are governed by parametric B‐rep on the fixed mesh to maintain the merit in computer‐aided design modeling and avoid laborious remeshing. Second, analytical shape design sensitivity is formulated for the parametric B‐rep in the framework of fixed mesh of finite cell method by means of the Hamilton–Jacobi equation. Numerical examples are solved to illustrate the unified methodology. Copyright © 2016 John Wiley & Sons, Ltd.     

Accelerating global optimization of aerodynamic shapes using a new surrogate-assisted parallel genetic algorithm

An efficient strategy is presented for global shape optimization of wing sections with a parallel genetic algorithm. Several computational techniques are applied to increase the convergence rate and the efficiency of the method. A variable fidelity computational evaluation method is applied in which the expensive Navier–Stokes flow solver is complemented by an inexpensive multi-layer perceptron neural network for the objective function evaluations. A population dispersion method that consists of two phases, of exploration and refinement, is developed to improve the convergence rate and the robustness of the genetic algorithm. Owing to the nature of the optimization problem, a parallel framework based on the master/slave approach is used. The outcomes indicate that the method is able to find the global optimum with significantly lower computational time in comparison to the conventional genetic algorithm.     

A parametric study on achieving the same final shape by numerical experimentation using a shape optimization process subject to different initial conditions

A finite element based shape optimization program has been developed for three-dimensional shell structures which allows for multiple edge movement and large shape changes. This program automatically performs shape optimization by linking together adaptive mesh generation, substructuring and optimization algorithms with a commercial finite element analysis program, MSC/NASTRAN. This paper examines the robustness of the shape optimization program by varying the initial shape and design parameters for three examples. This is performed to determine the conditions under which similar optimum shapes will be generated for different initial conditions.     

Shape optimization for general two-dimensional structures

Summary The growth-strain method was used for general two-dimensional shape optimization. It was verified in previous papers that the growth-strain method is very effective for shape optimization of structures with only one free surface to be deformed. But it could not provide reasonable optimized shapes for structures with two or more free surfaces such as structures with holes inside. Problems occurred, as the growth-strain method was applied to structures with two or more free surfaces. Then, an improved method was suggested. Finally, an automatic shape optimization system was built by the improved growth-strain method with commercial software using the finite element method. The effectiveness and practicability of the developed shape optimization system was verified by some examples.     

Microwave imaging of parallel perfectly conducting cylinders

This paper considers microwave imaging of parallel perfectly conducting cylinders using a solution of the scattering problem by the point‐matching method. A cubic B‐spline, real‐coded genetic algorithm and an adaptive hybrid algorithm are proposed to solve the inverse problem. Previous shape functions in trigonometric series with arbitrary coefficients are nondefinite, which intensify the ill‐posedness and slow the early time convergence of the algorithm. A novel shape function based on cubic B‐splines is developed and the real‐coded genetic algorithm is modified accordingly. Numerical simulation examples show that the early time convergence of the real‐coded genetic algorithm is improved significantly. Next, the adaptive hybrid algorithm is developed to improve the late time convergence of the cubic B‐spline real‐coded genetic algorithm. © 2001 John Wiley & Sons, Inc. Int J Imaging Syst Technol 11, 365–371, 2000     

Shape optimization using a NURBS‐based interface‐enriched generalized FEM

This study presents a gradient‐based shape optimization over a fixed mesh using a non‐uniform rational B‐splines‐based interface‐enriched generalized finite element method, applicable to multi‐material structures. In the proposed method, non‐uniform rational B‐splines are used to parameterize the design geometry precisely and compactly by a small number of design variables. An analytical shape sensitivity analysis is developed to compute derivatives of the objective and constraint functions with respect to the design variables. Subtle but important new terms involve the sensitivity of shape functions and their spatial derivatives. Verification and illustrative problems are solved to demonstrate the precision and capability of the method. Copyright © 2016 John Wiley & Sons, Ltd.     

基于Hough变换的三次方Bezier曲线检测算法研究

类似经典Hough变换中对直线(段)、圆(弧)、椭圆、抛物线等解析曲线的检测,论文研究了三次方Bezier曲线的检测算法,提出了离散Bezier曲线的特征建模方法和使用R函数的Hough变换曲线检测快速算法。该算法能够根据所给出的待检测目标点阵图像建立形状参数模型,然后检测该曲线在复杂图像中出现的位置、大小和方向。实验表明,该法能够有效地检测任意三次方Bezier曲线,且精确度优于目前广泛用于曲线检测的广义Hough变换。     

基于虚载荷变量的无网格法形状优化的研究

将选择施加在"虚结构"控制点上的虚载荷作为形状优化的设计变量,并将它与无网格Galerkin法相结合来开展结构形状优化研究,采用罚函数法来施加边界条件,通过直接微分法建立了结构形状优化的离散型灵敏度分析算法,利用无网格法研究了节点坐标关于设计变量导数的计算。所提出的算法简单明了,它不仅解决了网格的畸变问题,而且简化了优化模型和迭代流程,并可使结构的受力特性得到进一步的改善。最后用2个工程实例验证了所建立的算法,并得到了形状优化结果。     

A multiscale flaw detection algorithm based on XFEM

We present a novel multiscale algorithm for nondestructive detection of multiple flaws in structures, within an inverse problem type setting. The key idea is to apply a two‐step optimization scheme, where first rough flaw locations are quickly determined, and then, fine tuning is applied in these localized subdomains to obtain global convergence to the true flaws. The two‐step framework combines the strengths of heuristic and gradient‐based optimization methods. The first phase employs a discrete‐type optimization in which the optimizer is limited to specific flaw locations and shapes, thus converting a continuous optimization problem in the entire domain into a coarse discrete optimization problem with limited number of choices. To this end, we develop a special algorithm called discrete artificial bee colony. The second phase employs a gradient‐based optimization of the Broyden–Fletcher–Goldfarb–Shanno type on local well‐defined and bounded subdomains determined in the previous phase. A semi‐analytical approach is developed to compute the stiffness derivative associated with the evaluation of objective function gradients. The eXtended FEM (XFEM), with both circular and elliptical void enrichment functions, is used to solve the forward problem and alleviate the costly remeshing of every candidate flaw, in both optimization steps. The multiscale algorithm is tested on several benchmark examples to identify various numbers and types of flaws with arbitrary shapes and sizes (e.g., cracks, voids, and their combination), without knowing the number of flaws beforehand. We study the size effect of the pseudo grids in the first optimization step and consider the effect of modeling error and measurement noise. The results are compared with the previous work that employed a single continuous optimization scheme (XFEM–genetic algorithm and XFEM–artificial bee colony methods). We illustrate that the proposed methodology is robust, yields accurate flaw detection results, and in particular leads to significant improvements in convergence rates compared with the previous work. Copyright © 2014 John Wiley & Sons, Ltd.     

Effect of wavelength of fish-like undulation of a hydrofoil in a free-stream flow

Fish-like undulating body was proposed as an efficient propulsion system, and various mechanisms of thrust generation in this type of propulsion are found in the literature—separately for undulating and pitching fishes/foil. The present work proposes a unified study for undulating and pitching foil, by varying wavelength \(\lambda \) (from 0.8 to 8.0) of a wave travelling backwards over the NACA0012 hydrofoil in a free-stream flow; the larger wavelength is shown to lead to the transition from the undulating motion to pitching motion. The effect of wavelength of undulation is studied numerically at a Reynolds number \(Re=4000\), maximum amplitude of undulation \(A_{max}=0.1\) and non-dimensional frequency of undulation \(St=0.4\), using level-set immersed-boundary-method based in-house 2D code. The Navier–Stokes equation governing the fluid flow is solved using a fully implicit finite-volume method, while level-set equation governing the movement of the hydrofoil is solved using an explicit finite-difference method. It is presented here that the thrust generation mechanism for the low wavelength case undulating \((\lambda =0.8)\) foil is different from the mechanism for the high wavelength pitching foil. With increasing wavelength, mean thrust coefficient of the undulating foil increases and asymptotes to value for the pure pitching foil. Furthermore, the ratio of maximum thrust coefficient to maximum lateral force coefficient is found to be larger for the smaller wavelength undulating foil as compared with the larger wavelength pitching foil.     

A variant space search method and its application to the optimization design of compressor profiles

Optimization methods have been widely used in practical engineering, with search efficiency and global search ability being the main evaluation criteria. In this article, the Bezier curve equivalent recursion is used in a genetic algorithm (GA) to realize the variant space search to improve the search efficiency and global search ability. The parameters related to this method are investigated by an optimization test of the simple curve approximation, which is then used for optimization designs of supersonic and transonic profiles. The results show that the GA can be improved if the variant space search method is added.     

保形几何Hermite插值

本文将保形概念引入到几何:Hermite插值,利用三次Bezier曲线段构造了一条GC2连续的保形参数三次几何:Hermite插值曲线,曲线在相邻两个型值点之间,由两段三次:Bezier曲线组成。该曲线的所有Bezier点由型值点及相应的曲率信息直接计算产生,无需求解矢量方程组,因此该曲线计算简单,局部修改方便。     

Comparison between rectangular and trapezoidal bonded composite repairs in aircraft structures: A numerical analysis

The optimization of the patch shape of bonded composite repair in aircraft structures is a good way to improve the repair performance. In this study, the three-dimensional finite element method is used to compare the repair performance of patches with rectangular and trapezoidal shapes in aircraft structures. The comparison is done by analysing the stress intensity factor (SIF) at the tip of repaired crack and the distribution of the adhesive stresses for the two patch shapes. The obtained results show that, when the crack length is ranged from 5 to 20 mm, the trapezoidal shape presents lower stress intensity factor at the crack tip, which is beneficial for the fatigue life and lower adhesives stresses, which is beneficial for the repair durability. These advantages disappear when the crack length reaches the value of 40 mm. It is also shown that the use of the trapezoidal shape reduce the mass of the patch, which can reduce the repair cost.     

Evolutionary optimization in thermoelastic problems using the boundary element method

 The paper is devoted to application of evolutionary algorithms and the boundary element method to shape optimization of structures for various thermomechanical criteria, inverse problems of finding an optimal distribution of temperature on the boundary and identification of unknown boundary. Design variables are specified by Bezier curves. Several numerical examples of evolutionary computation are presented. Received 6 November 2000     

Shape design of internal cooling passages within a turbine blade

The article concerns the optimization of the shape and location of non-circular passages cooling the blade of a gas turbine. To model the shape, four Bezier curves which form a closed profile of the passage were used. In order to match the shape of the passage to the blade profile, a technique was put forward to copy and scale the profile fragments into the component, and build the outline of the passage on the basis of them. For so-defined cooling passages, optimization calculations were carried out with a view to finding their optimal shape and location in terms of the assumed objectives. The task was solved as a multi-objective problem with the use of the Pareto method, for a cooling system composed of four and five passages. The tool employed for the optimization was the evolutionary algorithm. The article presents the impact of the population on the task convergence, and discusses the impact of different optimization objectives on the Pareto optimal solutions obtained. Due to the problem of different impacts of individual objectives on the position of the solution front which was noticed during the calculations, a two-step optimization procedure was introduced. Also, comparative optimization calculations for the scalar objective function were carried out and set up against the non-dominated solutions obtained in the Pareto approach. The optimization process resulted in a configuration of the cooling system that allows a significant reduction in the temperature of the blade and its thermal stress.     

Topology optimization of fluid problems using genetic algorithm assisted by the Kriging model

A non‐gradient‐based approach for topology optimization using a genetic algorithm is proposed in this paper. The genetic algorithm used in this paper is assisted by the Kriging surrogate model to reduce computational cost required for function evaluation. To validate the non‐gradient‐based topology optimization method in flow problems, this research focuses on two single‐objective optimization problems, where the objective functions are to minimize pressure loss and to maximize heat transfer of flow channels, and one multi‐objective optimization problem, which combines earlier two single‐objective optimization problems. The shape of flow channels is represented by the level set function. The pressure loss and the heat transfer performance of the channels are evaluated by the Building‐Cube Method code, which is a Cartesian‐mesh CFD solver. The proposed method resulted in an agreement with previous study in the single‐objective problems in its topology and achieved global exploration of non‐dominated solutions in the multi‐objective problems. © 2016 The Authors International Journal for Numerical Methods in Engineering Published by John Wiley & Sons Ltd