Velocity fields using NURBS with distortion control for structural shape optimization

The paper presents methods for the calculation of design velocity fields and mesh updating in the context of shape optimization. Velocity fields have a fundamental role in the integration of the main conceptual and software components in shape design optimization. Nonuniform rational B-splines are used to parameterize the domain boundary. A Newton/Raphson procedure is used to calculate the curve and surface internal parameters. A preconditioning iterative conjugate gradient method with low precision is used to improve the solution performance of the auxiliar problem in the calculation of the velocity fields. The velocity fields are also used to perturb the finite element mesh and element distortion measures are introduced. Finally, examples of two- and three-dimensional elastic problems are presented to illustrate the application of the algorithms.     

基于免疫遗传算法优化的模糊控制方法及其应用

在模糊控制器的设计过程中,为了使模糊控制器的性能达到全局优化,应用免疫遗传算法对模糊控制器参数进行优化设计;在综合考虑各种参数对控制器性能影响的基础上,给出了一种全面优化隶属度函数、比例因子和量化因子的优化方法;利用了免疫算法能保持个体的多样性和能对学习过程进行引导的特点,对模糊控制器的多个参数同时进行优化,从而显著提高了系统的收敛性、稳定性。应用该方法对数控铣削加工过程的模糊控制器的设计进行了仿真,并与其他方法进行比较和控制实例的验证,表明了该基于免疫遗传算法优化的模糊器能获得更优良的控制性能。     

Analytical derivatives technology for structural shape design

The ability to perform and evaluate the effect of shape changes on the stress and modal responses of components is an important ingredient in the “design” of aircraft engine components. The classical design of experiments (DOE)-based approach that is motivated from statistics (for physical experiments) is one of the possible approaches for the evaluation of the component response with respect to design parameters [Myers, Montgomery. Response surface methodology, process and product optimization using design of experiments. John Wiley and Sons, NY (1995)]. As the underlying physical model used for the component response is deterministic and understood through a computer simulation model, one needs to re-think the use of the classical DOE techniques for this class of problems. In this paper, we explore an alternate sensitivity-analysis-based technique where a deterministic parametric response is constructed using exact derivatives of the complex finite-element (FE)-based computer models to design parameters. The method is based on a discrete sensitivity analysis formulation using semi-automatic differentiation (Griewank, SIAM (2000), ADIFOR, Automatic Differentiation of FORTRAN codes ) to compute the Taylor series or its Pade equivalent for finite-element-based responses. Shape design or optimization in the context of finite element modeling is challenging because the evaluation of the response for different shape requires the need for a meshing consistent with the new geometry. This paper examines the differences in the nature and performance (accuracy and efficiency) of the analytical derivatives approach against other existing approaches with validation on several benchmark structural applications. The use of analytical derivatives for parametric analysis is demonstrated to have accuracy benefits on certain classes of shape applications.     

Review of formulations for structural and mechanical system optimization

Alternative formulations for optimization and simulation of structural and mechanical systems and other related fields are reviewed. The material is divided roughly into two parts. Part 1 focuses on the developments in structural and mechanical systems, including configuration and topology optimization. Here the formulations are classified into three broad categories: (i) the conventional formulation where only the structural design variables are treated as optimization variables, (ii) simultaneous analysis and design (SAND) formulations where design and some of the state variables are treated as optimization variables, and (iii) a displacement-based two-phase approach where the displacements are treated as unknowns in the outer loop and the design variables as the unknowns in the inner loop. Part 2 covers more general formulations that are applicable to diverse fields, such as economics, optimal control, multidisciplinary problems and other engineering disciplines. In these fields, SAND-type formulations have been called mathematical programs with equilibrium constraints (MPEC), and partial differential equations (PDE)-constrained optimization problems. These formulations are viewed as generalizations of the SAND formulations developed in the structural optimization field. Based on the review, it is concluded that the basic ideas of the formulations presented in diverse fields can be integrated to conduct further research and develop alternative formulations and solution procedures for practical engineering applications. The paper lists 187 references on the subject.     

Multilevel optimization of composite panels under complex load and boundary conditions

Due to their complexity and large numbers of design variables, aerospace structures, such as aircraft wings, are best optimized using a multi-level process. In addition to simplifying the optimization procedure, such an approach allows a combination of different methods to be used, increasing the efficiency of the analysis. This paper presents a technique based on the usage of exact finite strip software, VICONOPT, with the finite element analysis package, ABAQUS. The computer programme VICONOPT is computationally efficient but provides solutions for a restricted range of geometries and loading conditions. Finite element analysis allows accurate models of structures with complex geometries to be created but is computationally expensive. By combining the two, these limitations are minimised, whilst the strengths of each are exploited. The fundamental principles of this multi-level procedure are demonstrated by optimizing a series of curved composite panels under combined shear and in-plane bending subject to buckling constraints. Presented at the 7th World Congress on Computational Mechanics, LA, USA, July 2006.     

Genetic algorithms in mesh optimization for visualization and finite element models

This paper investigates the use of a genetic algorithm (GA) to perform the large-scale triangular mesh optimization process. This optimization process consists of a combination of mesh reduction and mesh smoothing that will not only improve the speed for the computation of a 3D graphical or finite element model, but also improve the quality of its mesh. The GA is developed and implemented to replace the original mesh with a re-triangulation process. The GA features optimized initial population, constrained crossover operator, constrained mutation operator and multi-objective fitness evaluation function. While retaining features is important to both visualization models and finite element models, this algorithm also optimizes the shape of the triangular elements, improves the smoothness of the mesh and performs mesh reduction based on the needs of the user.     

Evolutionary structural optimization for stress minimization problems by discrete thickness design

Stress minimization is a major aspect of structural optimization in a wide range of engineering designs. This paper presents a new evolutionary criterion for the problems of variable thickness design whilst minimizing the maximum stress in a structure. On the basis of finite element analysis, a stress sensitivity number is derived to estimate the stress change in an element due to varying the thickness of other elements. Following the evolutionary optimization procedure, an optimal design with a minimum maximum stress is achieved by gradually removing material from those elements, which have the lowest stress sensitivity number or adding material onto those elements, which have the highest stress sensitivity number. The numerical examples presented in this paper demonstrate the capacity of the proposed method for solving stress minimization problems. The results based on the stress criterion are compared with traditional ones based on a stiffness criterion, and an optimization scheme based on the combination of both the stress minimization and the stiffness maximization criteria is presented.     

带孔等厚薄壳荷重传感器弹性元件的形状优化

建立带孔等厚薄壳荷重传感器弹性元件的优化参数模型、有限单元计算模型及优化数学模型,确定电阻应变计的粘贴位置,用结构分析软件ANSYS5.7及一阶优化方法优化弹性元件的形状,提高弹性元件在贴片位置的应变响应。     

Integration of topology and shape optimization for design of structural components

This paper presents an integrated approach that supports the topology optimization and CAD-based shape optimization. The main contribution of the paper is using the geometric reconstruction technique that is mathematically sound and error bounded for creating solid models of the topologically optimized structures with smooth geometric boundary. This geometric reconstruction method extends the integration to 3-D applications. In addition, commercial Computer-Aided Design (CAD), finite element analysis (FEA), optimization, and application software tools are incorporated to support the integrated optimization process. The integration is carried out by first converting the geometry of the topologically optimized structure into smooth and parametric B-spline curves and surfaces. The B-spline curves and surfaces are then imported into a parametric CAD environment to build solid models of the structure. The control point movements of the B-spline curves or surfaces are defined as design variables for shape optimization, in which CAD-based design velocity field computations, design sensitivity analysis (DSA), and nonlinear programming are performed. Both 2-D plane stress and 3-D solid examples are presented to demonstrate the proposed approach. Received January 27, 2000 Communicated by J. Sobieski     

Low cost integration of additive and subtractive processes for hybrid layered manufacturing

While CNC machining (subtractive method) is the only option when it comes to high quality components, it demands greater human intervention to generate the CNC programs, making it a slow and costly route. On the other hand, Rapid Prototyping (additive method) is able to convert the design into the physical objects without any human intervention. But its total automation comes with compromises in the qualities of geometry and material. A hybrid layered manufacturing process presented here combines the best features of both these approaches. In this process the near-net shape of the object is first built using weld-deposition; the near-net shape is then finish machined subsequently. Time and cost saving of this process can be attributed to reduction in NC programming effort and elimination of rough machining. It is envisioned as a low cost retrofitment to any existing CNC machine for making metallic objects without disturbing its original functionalities. Near-net shape building and finish machining happening at the same station is the unique feature of this process. A customized software generates the NC program for near-net shape building. The intricate details of integrating arc welding unit with a CNC milling machine are presented in this paper.     

远程数控仿真系统的设计与实现

由于几何建模的复杂性和消隐算法的低效性,目前的数控仿真系统大多只能实现数控加工结果显示,而在数控加工过程实时仿真方面功能还很弱,对于基于Internet的远程数控仿真的研究则更少。为解决以上问题,提出了实现远程数控仿真的技术框架,即采用VRML建立几何模型,采用Java建立通信接口,构造虚拟环境与操作者之间的通信机制。通过构造EAI接口控制Eleva-tion Grid结点,实现工件动态建模,采用Java applet构造NC代码解释器,并阐述了干涉校验的实现方法。实现了远程数控仿真系统。     

Combining genetic algorithms with BESO for topology optimization

This paper proposes a new algorithm for topology optimization by combining the features of genetic algorithms (GAs) and bi-directional evolutionary structural optimization (BESO). An efficient treatment of individuals and population for finite element models is presented which is different from traditional GAs application in structural design. GAs operators of crossover and mutation suitable for topology optimization problems are developed. The effects of various parameters used in the proposed GA on the optimization speed and performance are examined. Several 2D and 3D examples of compliance minimization problems are provided to demonstrate the efficiency of the proposed new approach and its capability of obtaining convergent solutions. Wherever possible, the numerical results of the proposed algorithm are compared with the solutions of other GA methods and the SIMP method.     

A phase-field method for shape optimization of incompressible flows

In this paper, we present a phase-field method applied to the fluid-based shape optimization. The fluid flow is governed by the incompressible Navier–Stokes equations. A phase field variable is used to represent material distributions and the optimized shape of the fluid is obtained by minimizing the certain objective functional regularized. The shape sensitivity analysis is presented in terms of phase field variable, which is the main contribution of this paper. It saves considerable amount of computational expense when the meshes are locally refined near the interfaces compared to the case of fixed meshes. Numerical results on some benchmark problems are reported, and it is shown that the phase-field approach for fluid shape optimization is efficient and robust.     

Structural optimization of as-built parts using reverse engineering and evolution strategies

In industry, some parts are prone to failures or their design is simply sub-optimal. In those critical situations, one would like to be able to make changes to the part, making it lighter or improving its mechanical resistance. The problem of as-built parts is that the original computer-aided design (CAD) model is not available or is lost. To optimize them, a reverse engineering process is necessary to capture the shape and topology of the original design. This paper describes how to capture the original design geometry using a semi-automated reverse engineering process based on measurement provided by an optical 3D sensor. Following this reverse engineering process, a Fixed Grid Finite Element method and evolutionary algorithms are used to find the optimum shape that will minimize stress and weight. Several examples of industrial parts are presented. These examples show the advantages and disadvantages of the proposed method in an industrial scenario. Presented at the 7th World Congress on Computational Mechanics, Los Angeles 2006.     

Simultaneous optimization of photostrictive actuator locations,numbers and light intensities for structural shape control using hierarchical genetic algorithm

The present paper introduces an investigation into simultaneous optimization of the PbLaZrTi-based actuator configuration and corresponding applied light intensity for morphing beam structural shapes. A finite element formulation for multiphysics analysis of coupled opto-electro-thermo-mechanical fields in PbLaZrTi ceramics is derived and verified with the theoretical solution and the commercial software ANSYS. This element is then used to simulate beam bending shape control using the orthotropic PbLaZrTi actuators and the simultaneous optimization. In this procedure, the controlling and geometrical variables are simultaneously optimized via a hierarchical genetic algorithm. A bi-coded chromosome is proposed in a hierarchical mode, which consists of some control genes (i.e. actuator location and number) and parametric genes (i.e. applied light intensity). Whether the parametric gene is activated or not is managed by the value of the first-grade control genes. The numerical results demonstrate that the achieved beam bending shapes correlate remarkably well with the expected ones and the simultaneous optimization of photostrictive actuator locations, numbers and light intensities can result in optimal actuator layout with less PbLaZrTi actuators and irradiated light energy. The simulation results also show that the hierarchical genetic algorithm has more superior performance over the conventional real-coded genetic algorithm.     

Discrete variable optimization of frames using a strain energy criterion

This paper reports on recent advances concerning a new method for the weight (discrete variable) optimization of frames under both stress and multi-displacement constraints using a criterion based on the distribution of the virtual strain energy density. The proposed methodology is based on an idea that has been previously demonstrated and successfully applied on truss structures. The influence of each participating beam is defined through properly normalized sensitivity factors. An iterative formula, similar to that used for trusses, is proposed for updating the second moment of inertia followed by an improvement of shape variables (e.g. height, width, thickness) on the cross-section. The proposed method is successfully compared with the sequential quadratic programming method and other techniques published in the most recent literatures.     

面向性能分析和优化的多业务过程仿真方法研究

针对业务过程性能分析和优化多侧重于对已部署的业务过程进行事后的性能监控、管理和数据分析等问题,详细分析了业务过程性能和仿真优化的研究进展,提出了一种与企业模型和工作流模型相兼容的集成化业务过程仿真建模方法（IBPSM）,并设计了支持IBPSM的多业务过程仿真工具（MBPST）原型系统。最后给出了一个具体的应用案例。实践表明这种事前的基于多业务过程仿真方法提供了业务过程性能的仿真分析与优化;同时可对优化后的业务过程进行快速部署,有利于业务过程的信息化实现。     

A sequential coupling of optimal topology and multilevel shape design applied to two-dimensional nonlinear magnetostatics

In this paper, a sequential coupling of two-dimensional (2D) optimal topology and shape design is proposed so that a coarsely discretized and optimized topology is the initial guess for the following shape optimization. In between, we approximate the optimized topology by piecewise Bézier shapes via least square fitting. For the topology optimization, we use the steepest descent method. The state problem is a nonlinear Poisson equation discretized by the finite element method and eliminated within Newton iterations, while the particular linear systems are solved using a multigrid preconditioned conjugate gradients method. The shape optimization is also solved in a multilevel fashion, where at each level the sequential quadratic programming is employed. We further propose an adjoint sensitivity analysis method for the nested nonlinear state system. At the end, the machinery is applied to optimal design of a direct electric current electromagnet. The results correspond to physical experiments. This research has been supported by the Austrian Science Fund FWF within the SFB “Numerical and Symbolic Scientific Computing” under the grant SFB F013, subprojects F1309 and F1315, by the Czech Ministry of Education under the grant AVČR 1ET400300415, by the Czech Grant Agency under the grant GAČR 201/05/P008 and by the Slovak Grant Agency under the project VEGA 1/0262/03.     

Three dimensional shape optimization of total knee replacements for reduced wear

This paper presents the design optimization of a total knee replacement (TKR) using a parametric three-dimensional finite element (FE) model, considering wear of the ultra high molecular weight polyethylene (UHMWPE) insert. A framework has been developed to generate three-dimensional FE models of the femoral component and UHMWPE insert of a TKR design in a batch mode process, then simulate an ISO standard TKR wear test. A modified version of Archard’s wear model calculates abrasive wear as a function of contact pressure, sliding distance and an experimentally determined wear factor. The UHMWPE wear was reduced by modifying the contact geometry of both components in the frontal and sagittal planes. Wear was reduced by 18.5%, from 55.248 to 45.013 mm³ per year by reducing the radii of curvature of the femoral condyles in the sagittal planes, increasing the radii in the frontal plane, and reducing conformity between the implant components.