Efficient optimization of integrated aerodynamic–structural design

The introduction of composite materials is having a profound effect on the design process. Because these materials permit the designer to tailor material properties to improve structural, aerodynamic and acoustic performance, they require a more integrated multidisciplinary design process. Because of the complexity of the design process numerical optimization methods are required. The present paper is focused on a major difficulty associated with the multidisciplinary design optimization process—its enormous computational cost. We consider two approaches for reducing this computational burden: (i)development of efficient methods for cross-sensitivity calculation using perturbation methods; and (ii) the use of approximate numerical optimization procedures. Our efforts are concentrated upon combined aerodynamic-structural optimization. Results are presented for the integrated design of a sailplane wing. The impact of our computational procedures on the computational costs of integrated designs is discussed.     

Optimum Structural and Manufacturing Design of a Braided Hollow Composite Part

Simultaneous material consolidation and shaping, as performed in manufacturing of composite materials, causes a strong interconnection between structural and manufacturing parameters which makes the design process complicated. In this paper, the design of a carbon fiber bicycle stem is examined through the application of a multi-objective optimization method to illustrate the interconnection between structural and manufacturing objectives. To demonstrate the proposed method, a test case dealing with the design of composite part with complex geometry, small size and hollow structure is described. Bladder-assisted Resin Transfer Molding is chosen as the manufacturing method. A finite element model of the stem is created to evaluate the objectives of the structural design, while a simplified 2D model is used to simulate the flow inside the preform during the injection process. Both models are formulated to take into account the variation of fiber orientation, thickness and fiber volume fraction as a function of braid diameters, injection pressure and bladder pressure. Finally, a multiobjective optimization method, called Normalized Normal Constraint Method, is used to find a set of solutions that simultaneously optimizes weight, filling time and strength. The solution to the problem is a set of optimum designs which represent the Pareto frontier of the problem. Pareto frontier helps to gain insight into the trade-off among objectives, whose presence and importance is confirmed by the numerical results presented in this paper.     

Multimaterial multijoint topology optimization

In this paper, a methodology that solves multimaterial topology optimization problems while also optimizing the quantity and type of joints between dissimilar materials is proposed. Multimaterial topology optimization has become a popular design optimization technique since the enhanced design freedom typically leads to superior solutions; however, the conventional assumption that all elements are perfectly fused together as a single piece limits the usefulness of the approach since the mutual dependency between optimal multimaterial geometry and optimal joint design is not properly accounted for. The proposed methodology uses an effective decomposition approach to both determine the optimal topology of a structure using multiple materials and the optimal joint design using multiple joint types. By decomposing the problem into two smaller subproblems, gradient‐based optimization techniques can be used and large models that cannot be solved with nongradient approaches can be solved. Moreover, since the joining interfaces are interpreted directly from multimaterial topology optimization results, the shape of the joining interfaces and the quantity of joints connecting dissimilar materials do not need to be defined a priori. Three numerical examples, which demonstrate how the methodology optimizes the geometry of a multimaterial structure for both compliance and cost of joining, are presented.     

CONSTRUCTIVE DESIGN MODELS FOR THE OPTIMIZATION OF COMPOSITE PLATES AND SHELLS

The paper presents the basic ideas of so-called constructive design models and their special formulation for the material layup and the geometry of plane and curved composite load-bearing structures (plates, shells) without and with stiffeners. Constructive models additionally facilitate the consideration of manufacturing requirements and limitations of a fully integrated tape-laying process. Within the constructive design models, the constructive layout is described by means of a parametric model which is independent from the analysis model, and constructive (geometric) parameters are denned as design variables for the optimization process instead of the commonly used analysis variables. The application of constructive design models leads to a better representation of the design variables and makes the optimization process more efficient.     

Design of Electrical Rotating Machines by Associating Deterministic Global Optimization Algorithm With Combinatorial Analytical and Numerical Models

This paper presents a new methodology of design of electrical rotating machines. The methodology is an extension of previous works of the second author. Indeed, associating combinatorial analytical models with exact global optimization algorithms leads to rational solutions of predesign. These solutions need to be validated by a numerical tool (using a finite-element method) before the expansive phase of hand-making a prototype. Such an automatic numerical tool for computing some characteristic values, such as the torque, was previously developed. The idea of this paper is to extend the exact global optimization algorithm by inserting the direct use of this automatic numerical tool. This new methodology makes it possible to solve design problems more rationally. Some numerical examples validate the usefulness of this new approach.     

Optimizing process parameters for laser beam micro-marking using genetic algorithm and particle swarm optimization

Laser micro-marking is an efficient technique for permanent marking and logo printing on materials. This study details the selection of an optimal parametric combination for laser micro-marking. In this work, markings were performed on Gallium Nitride (GaN) with varying the levels of marking parameters. The parameters considered in the present work are current (A), pulse frequency (Hz), and scanning speed (mm/sec). This experiment was designed using a “central composite design,” grounded in the response surface methodology. Mark intensity, which is a prominent response in laser marking, was considered the output response. The data interpretation involved analysis of variance (ANOVA) and mathematical modelling between the input parameters. It is essential to determine the relationship and significance of input-output variation. The interaction effect of various input parameters on mark intensity was also studied. Finally, two techniques, namely genetic algorithm (GA) and particle swarm optimization (PSO), were applied, and the optimal settings of input constraints were predicted.     

Challenges in materials and process selection

Recent developments are outlined of materials and process selection methods leading towards industrial applications. The systematic implementation of selection for multiple criteria and multiple design elements is presented as a natural extension of Ashby's method. The importance of a “pre-defined questionnaire” approach in process selection is illustrated for casting, joining and surface treatments. The use of materials selection methods for materials and multi-materials development is described for the case of glass, composite materials and sandwich structures, and the application of various optimization techniques adapted to each problem is given. In conclusion, possible new developments toward a better integration of materials and process selection in the whole design procedure are proposed.     

Geometric Design of Scalable Forward Scatterers for Optimally Efficient Solar Transformers

It will be ideal to deliver equal, optimally efficient “doses” of sunlight to all cells in a photobioreactor system, while simultaneously utilizing the entire solar resource. Backed by the numerical scattering simulation and optimization, here, the design, synthesis, and characterization of the synthetic iridocytes that recapitulated the salient forward‐scattering behavior of the Tridacnid clam system are reported, which presents the first geometric solution to allow narrow, precise forward redistribution of flux, utilizing the solar resource at the maximum quantum efficiency possible in living cells. The synthetic iridocytes are composed of silica nanoparticles in microspheres embedded in gelatin, both are low refractive index materials and inexpensive. They show wavelength selectivity, have little loss (the back‐scattering intensity is reduced to less than ≈0.01% of the forward‐scattered intensity), and narrow forward scattering cone similar to giant clams. Moreover, by comparing experiments and theoretical calculation, it is confirmed that the nonuniformity of the scatter sizes is a “feature not a bug” of the design, allowing for efficient, forward redistribution of solar flux in a micrometer‐scaled paradigm. This method is environmentally benign, inexpensive, and scalable to produce optical components that will find uses in efficiency‐limited solar conversion technologies, heat sinks, and biofuel production.     

飞行器机翼气动/结构耦合优化设计研究

基于CFD/CSD耦合数值计算,以升力特性为优化目标,采用响应面算法优化光固化树脂材料的轻质F4风洞模型构型,寻得6个优化解,并采用光固化快速成型技术(SL)制作这6个F4风洞实验模型。实验结果表明:6个模型升力特性与国外静气动弹性修正后的结果较接近(特别是6#模型最为接近机翼弹性变形的三维效果),初步证明该文发展的气动/结构耦合优化设计方法基本可行,既为基于SL技术的轻质模型高速风洞应用提供了支持,又为多气动参数的飞行器气动/结构耦合优化和风洞试验数据静弹性修正建立了工作基础。     

Automated design of threats and shields under hypervelocity impacts by using successive optimization methodology

In this study, predictive hydrocode simulations are coupled with approximate optimization (AO) methodology to achieve successive design automation for a projectile-Whipple shield (WS) system at hypervelocity impact (HVI) conditions. Successive design methodology is first applied to find the most dangerous threat for a given WS design by varying the shape and orientation of a projectile while imposing constraints on the total projectile mass and radar cross section (RCS). Subsequent optimization procedure is then carried on to improve the baseline WS design parameters. A parametric multi-layered stuffed WS model is considered with varying thicknesses of each layer and variable positions of the inter-layers while having a constraint on the areal density. HVI simulations are conducted by using a non-linear explicit dynamics numerical solver, LS-DYNA. Coupled finite element and smoothed particle hydrodynamics (SPH) parametric models are developed for the predictive numerical simulations. LS-OPT is employed to implement the design optimization process based on response surface methodology. It is found that the ideal spherical projectiles are not necessarily presenting the most dangerous threat compared to the ones with irregular shapes and random orientations, which have the same mass and RCS. Therefore, projectiles with different shapes and orientations should be considered while designing a WS. It is also shown that, successive AO methodology coupled with predictive hydrocode simulations can easily be utilized to enhance WS design.     

Parameter identification and shape optimization

Simulation of metal forming processes using the Finite Element Method (FEM) is a well established procedure, being nowadays possible to develop alternative approaches, such as inverse methodologies, in solving complex problems. In the present paper, two types of inverse approaches will be discussed, namely the parameter identification and the shape optimization problems. The aim of the former is to evaluate the input parameters for material constitutive models that would lead to the most accurate set of results respecting physical experiments. The second category involves determining the initial geometry of a given specimen leading to a desired final geometry after the forming process. The purpose of the present work is then to formulate these inverse problems as optimization problems, introducing a straightforward methodology of process optimization in engineering applications such as metal forming and structural analysis. To reach this goal, an integrated optimization approach, using a finite element code together with a numerical optimization program, was employed. A gradient-based optimization method, as a combination of the steepest-descent method and the Levenberg-Marquardt techniques, was used. Numerical applications in the parameter optimization category include, namely, the characterization of a non-linear elasto-plastic hardening model and the determination of the parameters for a nonlinear hyperelastic model. It is also discussed the simultaneous identification of both constitutive material model parameters and the friction coefficient parameters. From the point of view of shape optimization problems, the determination of the initial geometry of a specimen in a upsetting billing problem as well as a methodology for defining the most suited blank shape to be formed in a square cup, are discussed. The final results for both categories show that this kind of algorithms have great potential for future developments in more demanding and realistic benchmarks. It is also worth noting that the presented integrated methodology can be easily applied to a first introduction of optimization techniques and numerical simulation to undergraduate courses in engineering.     

Bayesian Design of Experiments Using Approximate Coordinate Exchange

The construction of decision-theoretical Bayesian designs for realistically complex nonlinear models is computationally challenging, as it requires the optimization of analytically intractable expected utility functions over high-dimensional design spaces. We provide the most general solution to date for this problem through a novel approximate coordinate exchange algorithm. This methodology uses a Gaussian process emulator to approximate the expected utility as a function of a single design coordinate in a series of conditional optimization steps. It has flexibility to address problems for any choice of utility function and for a wide range of statistical models with different numbers of variables, numbers of runs and randomization restrictions. In contrast to existing approaches to Bayesian design, the method can find multi-variable designs in large numbers of runs without resorting to asymptotic approximations to the posterior distribution or expected utility. The methodology is demonstrated on a variety of challenging examples of practical importance, including design for pharmacokinetic models and design for mixed models with discrete data. For many of these models, Bayesian designs are not currently available. Comparisons are made to results from the literature, and to designs obtained from asymptotic approximations. Supplementary materials for this article are available online.     

A framework for data-driven structural analysis in general elasticity based on nonlinear optimization: The dynamic case

In this article, we present an extension of the formulation recently developed by the authors to the structural dynamics setting. Inspired by a structure-preserving family of variational integrators, our new formulation relies on a discrete balance equation that establishes the dynamic equilibrium. From this point of departure, we first derive an “exact” discrete-continuous nonlinear optimization problem that works directly with data sets. We then develop this formulation further into an “approximate” nonlinear optimization problem that relies on a general constitutive model. This underlying model can be identified from a data set in an offline phase. To showcase the advantages of our framework, we specialize our methodology to the case of a geometrically exact beam formulation that makes use of all elements of our approach. We investigate three numerical examples of increasing difficulty that demonstrate the excellent computational behavior of the proposed framework and motivate future research in this direction.     

A strategy based on the strain-to-kinetic energy ratio to ensure stability and convergence in topology optimization of globally resonating one-material structures

The authors propose a new formulation of SIMP-based topology optimization problems aiming to obtain resonating one-material structures through a stable maximization process. The new formulation is capable of achieving globally resonant lightly damped “0-1” structures for frequencies close to those of interest. The proposed strategy successfully deals with known issues like design “degeneration” and instability of the gradient-based optimization process around the resonance frequency (which is a local maximum when maximizing vibration responses) at which harmonic excitation forces shall be applied. In this work, the authors use the concept of complex input power to overcome the mentioned issues. It is proposed a topology optimization procedure where a weighted sum between the active input power (real part of the complex input power) and the static compliance is minimized with a constraint on the reactive input power (imaginary part of the complex input power), which is converted to a ratio between the time-averaged potential and kinetic energies of the system named quotient R. By this way, it is possible to ensure viability to the procedure by preventing the resonance frequency from reaching exactly the excitation frequency throughout the process, which otherwise causes difficulties on convergence. The process achieves resonance frequencies very close to given values of interest by keeping the “side” of R<1 or R>1. Several examples are presented to illustrate the potential of the proposed method.     

Tube hydroforming optimization using a surrogate modeling approach and Genetic Algorithm

ABSTRACT

The quality of a product obtained by hydroforming process is influenced by the geometrical, material and process parameters. In this paper, to predict an acceptable T-shaped tube with minimum wall thickness variations, and accomplishes the industrial requirements, a methodology based on the coupling of three-dimensional finite element incremental simulation based on Explicit Dynamic approach and an automatic surrogate model are proposed. The surrogate model is based on an adaptive moving target zone, and both Moving Least Square (MLS) and the Kriging technique. The optimization results are presented and compared in term of efficiency. Five quality criteria are used, an objective function defining the thickness variation with four nonlinear constraints functions, to reduce the risk of necking and to fulfil the industrial requirements. The proposed approach will provide a numerical estimation of the “best” tool dimensions and ideal punch stroke in order to obtain a final feasible workpiece.     

Design sensitivity analysis and optimization for minimizing springback of sheet‐formed part

The springback is a manufacturing defect in the stamping process and causes difficulty in product assembly. An impediment to the use of lighter‐weight, higher‐strength materials in manufacturing is relative lack of understanding about how these materials respond to complex forming processes. The springback can be reduced by using an optimized combination of die, punch, and blank holder shapes together with friction and blank‐holding force. An optimized process can be determined using a gradient‐based optimization to minimize the springback. For an effective optimization of the stamping process, development of an efficient design sensitivity analysis (DSA) for the springback with respect to these process parameters is crucial. A continuum‐based shape and configuration DSA method for the stamping process has been developed using a non‐linear shell model. The material derivative is used to develop the continuum‐based design sensitivity. The design sensitivity equation is solved without iteration at each converged load step in the finite deformation elastoplastic non‐linear analysis with frictional contact, which makes sensitivity calculation very efficient. Numerical implementation of the proposed shape and configuration DSA method is performed using the meshfree method. The accuracy and efficiency of the proposed method are illustrated by minimizing the springback in a benchmark S‐rail problem. Copyright © 2007 John Wiley & Sons, Ltd.     

Blank design optimization on deep drawing of square shells

A numerical scheme for improving the drawability in the deep drawing of square shells by blank design optimization is presented. The numerical scheme is formulated as an optimization problem whose objective is to maximize the drawability, subject to the constraint that fracture failure and draw-in failure do not occur. Appropriate blank design parameters are used as the design variables of the formulation. To enable the numerical scheme to work models predicting the onset of fracture failure and draw-in failure are required. Numerical models simulating the onset of these failures under the given process conditions are thus discussed. Optimal designs for three cases are then presented. Finally, by considering both the drawability and the non-uniformity of the final flange profile it is shown that the circular profile can be considered to be the optimal blank shape for square cup drawing.     

Multi-objective Optimization of Sheet Metal Forming Die Using Genetic Algorithm Coupled with RSM and FEA

Present study describes the approach of applying response surface methodology (RSM) with a Pareto-based multi-objective genetic algorithm to assist engineers in optimization of sheet metal forming. In many studies, finite element analysis and optimization technique have been integrated to solve the optimal process parameters of sheet metal forming by transforming multi-objective problem into a single-objective problem. This paper aims to minimize objective functions of fracture and wrinkle simultaneously. Design variables are blank-holding force and draw-bead geometrical parameters (length and diameter). RSM has been used for design of experiment and finding relationship between variables and objective functions. Forming limit diagram has been used to define objective functions. Finite element analysis applied for simulating the process. Proposed approach has been investigated on a fuel tank drawing part and it has been observed that it is more effective and accurate than traditional finite element analysis method and the “trial and error” procedure.     

Particle swarm-based structural optimization of laminated composite hydrokinetic turbine blades

Composite blade manufacturing for hydrokinetic turbine application is quite complex and requires extensive optimization studies in terms of material selection, number of layers, stacking sequence, ply thickness and orientation. To avoid a repetitive trial-and-error method process, hydrokinetic turbine blade structural optimization using particle swarm optimization was proposed to perform detailed composite lay-up optimization. Layer numbers, ply thickness and ply orientations were optimized using standard particle swarm optimization to minimize the weight of the composite blade while satisfying failure evaluation. To address the discrete combinatorial optimization problem of blade stacking sequence, a novel permutation discrete particle swarm optimization model was also developed to maximize the out-of-plane load-carrying capability of the composite blade. A composite blade design with significant material saving and satisfactory performance was presented. The proposed methodology offers an alternative and efficient design solution to composite structural optimization which involves complex loading and multiple discrete and combinatorial design parameters.     

Combining iterative heuristic optimization and uncertainty analysis methods for robust parameter design

A number of investigators have pointed out that products and processes lack quality because of performance inconsistency, which is often due to uncontrollable parameters in the manufacturing process or product usage. Robust design methods are aimed at finding product/process designs that are less sensitive to parameter variation. Robust design of computer simulations requires a large number of runs, which are very time consuming. A novel methodology for robust design is presented in this article. It integrates an iterative heuristic optimization method with uncertainty analysis to achieve effective variability reductions, exploring a large parameter domain with an accessible number of simulations. To demonstrate the effectiveness of this methodology, the robust design of a 0.15 μm CMOS device is shown.