基于密度分布曲线法的复合材料变刚度铺层优化

基于梯度的优化方法对复合材料层合板进行了变刚度铺层优化设计。在优化过程中需确定铺层中各单元的密度以及角度。为了使优化结果具有可制造性,优化结果需满足制造工艺约束并且铺层角度需从预定角度中选取。为了避免在优化问题中引入过多的约束并减少设计变量的数目,提出密度分布曲线法(DDCM)对层合板中各单元的密度进行参数化。根据各单元的密度以及角度设计变量并基于Bi-value Coding Parameterization(BCP)方法中的插值公式确定各单元的弹性矩阵。优化过程中以结构柔顺度作为优化目标,结构体积作为约束,优化算法采用凸规划对偶算法。对碳纤维复合材料的算例结果表明:采用DDCM可得到较理想的优化结果,并且收敛速率较快。     

Optimal design of composite shells based on minimum weight and maximum feasibility robustness

A robust design optimization (RDO) approach for minimum weight and safe shell composite structures with minimal variability into design constraints under uncertainties is proposed. A new concept of feasibility robustness associated to the variability of design constraints is considered. So, the feasibility robustness is defined through the determinant of variance–covariance matrix of constraint functions introducing in this way the joint effects of the uncertainty propagations on structural response. A new framework considering aleatory uncertainty into RDO of composite structures is proposed. So, three classes of variables and parameters are identified: deterministic design variables, random design variables and random parameters. The bi-objective optimization search is performed using on a new approach based on two levels of dominance denoted by Co-Dominance-based Genetic Algorithm (CoDGA). The use of evolutionary concepts together sensitivity analysis based on adjoint variable method is a new proposal. The examples with different sources of uncertainty show that the Pareto front definition depends on random design variables and/or random parameters considered in RDO. Furthermore, the importance to control the uncertainties on the feasibility of constraints is demonstrated. CoDGA approach is a powerfully tool to help designers to make decision establishing the priorities between performance and robustness.     

Design of laminated piezocomposite shell transducers with arbitrary fiber orientation using topology optimization approach

Sensor and actuator based on laminated piezocomposite shells have shown increasing demand in the field of smart structures. The distribution of piezoelectric material within material layers affects the performance of these structures; therefore, its amount, shape, size, placement, and polarization should be simultaneously considered in an optimization problem. In addition, previous works suggest the concept of laminated piezocomposite structure that includes fiber‐reinforced composite layer can increase the performance of these piezoelectric transducers; however, the design optimization of these devices has not been fully explored yet. Thus, this work aims the development of a methodology using topology optimization techniques for static design of laminated piezocomposite shell structures by considering the optimization of piezoelectric material and polarization distributions together with the optimization of the fiber angle of the composite orthotropic layers, which is free to assume different values along the same composite layer. The finite element model is based on the laminated piezoelectric shell theory, using the degenerate three‐dimensional solid approach and first‐order shell theory kinematics that accounts for the transverse shear deformation and rotary inertia effects. The topology optimization formulation is implemented by combining the piezoelectric material with penalization and polarization model and the discrete material optimization, where the design variables describe the amount of piezoelectric material and polarization sign at each finite element, with the fiber angles, respectively. Three different objective functions are formulated for the design of actuators, sensors, and energy harvesters. Results of laminated piezocomposite shell transducers are presented to illustrate the method. Copyright © 2012 John Wiley & Sons, Ltd.     

基于遗传算法的离散型结构拓扑优化设计

采用遗传算法求解包括桁架结构和框架结构的离散型结构拓扑优化问题。在遗传算法的基础上,通过引入拓扑变量并修改被删除杆件的材料弹性模量,提出了一个受多工况荷载作用,能同时考虑应力、稳定及位移等约束的离散型结构拓扑优化问题统一数学模型。该模型不但能同时适用于桁架结构和框架结构等离散型结构拓扑优化问题,而且还能解决奇异最优解问题。结合上述统一数学模型和遗传算法,给出了求解离散型结构拓扑优化问题的优化方法。算例结果表明,采用该文提出的拓扑优化方法可有效、方便地对桁架结构、框架结构等离散型结构进行拓扑优化设计。     

离散变量结构优化设计的最优综合效能法

针对结构优化问题的位移约束,引入关键约束的界约参数,提出了结构位移统一约束的缩减形式,从而简化了结构优化模型。根据离散变量结构优化问题的特点,提出了效能系数的概念,它衡量设计变量在离散邻域范围内变化对目标函数与约束函数值的影响,并研究了基于效能系数取值分类的四种主要调整方式。根据结构应力和位移约束的影响区域属性,以综合效能最大化为引导,提出了求解离散变量结构优化问题的最优综合效能法。算例结果显示该算法具有良好的优化效率,可求得问题的最优解或获得历史上的最优记录。     

基于遗传算法的复合材料层合板削层结构铺层优化

针对应力变化较大的碳纤维增强复合材料层合板,提出削层结构铺层分级优化模式。通过将结构分解为若干子铺层并对各子铺层的位置、尺寸、铺层数以及铺层顺序进行优化,得到了满足强度和可制造性要求且质量最小的结构设计方案。该模式的第1、2级优化利用参考层对各子铺层位置及尺寸进行优化,第3级优化通过引入3次样条插值参数化方法对各子铺层层数和铺层顺序进行优化。参考层的引入可减少设计变量的数量,3次样条插值参数化方法可解决以铺层角为设计变量时设计变量数目不确定的问题。利用有限元方法对结构进行力学分析计算,并依据Tsai-Wu准则确定结构强度。在第2、3级优化中利用遗传算法对优化问题进行求解。算例计算表明:削层结构铺层分级优化模式结果合理可信。与均匀铺层方法结果比较可知:削层结构可有效减少结构质量。     

基于铺层设计特征的碳纤维增强复合材料悬架控制臂结构优化

基于铺层设计特征,提出一种使用碳纤维复合材料对承载结构件进行结构优化设计的方法和流程.该方法综合考虑结构几何特征、材料铺层方式、铺层厚度及铺层角度在设计环节中的序列关系,通过几何设计空间构建、离散变量多目标优化、基于工艺可行性的最优决策等方法实现结构设计.以碳纤维增强复合材料悬架控制臂的轻量化设计为例:首先,以钢质控制臂结构为参考建立复合材料控制臂的几何设计空间;然后,以复合材料铺层便利性为原则对其进行结构设计,采用准各向同性铺层对控制臂的铺层厚度进行设计;进而,以提高控制臂刚度和1阶固有频率为目标,使用优化算法对铺层角度进行多目标优化设计;最后,以工艺可行性为约束对优化结果进行筛选并最终完成结构设计.结果表明,所设计复合材料结构具有更大的刚度和1阶固有频率,并且与钢质结构相比减重47.9%.所提出的方法能够较好地兼顾结构特征和复合材料设计要求之间的关系,为复合材料结构优化设计理论与方法的发展提供有益参考.     

Topology optimization of structures under multiple load cases using a fiber-reinforced composite material model

This paper presents a method to optimize the topology of structures under multiple load cases with stress constraints. Fiber-reinforced orthotropic composite is employed as the material model to simulate the constitutive relation of truss-like continua. The fiber densities and orientations at the nodes are taken as design variables. First, for each load case, the fiber orientations are aligned with the orientations of principal stress and the fiber densities are adjusted according to the strains along the fiber orientations. Then, to optimize the structure, the fiber densities and orientations under multiple load cases are determined by constraining its elastic matrix to approach the elastic matrix of the optimum structures defined for each single load case. Finally the member distribution in the optimal structure is suggested by the continuous lines formed according to the fiber densities and orientations. Several examples are presented to demonstrate the effectiveness of the proposed approach.     

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.     

基于几何因子的复合材料气动弹性剪裁设计

实现了基于几何因子的复合材料层合板建模,解决了几何因子与Natran的参数输入问题,并根据工艺约束中的最小铺层比例对几何因子可行空间进行了推导补充。在此基础上,提出了一种基于几何因子和Nastran的复合材料气动弹性剪裁优化设计方法。首先以总厚度和几何因子作为设计变量以及以Nastran作为求解器,以强度、刚度、颤振和发散速度以及几何因子相关性约束作为约束条件进行结构寻优,得到最优的铺层总厚度和几何因子。其次,以最优几何因子作为目标,进行铺层结构逆问题求解,约束条件为复合材料铺层工艺约束。因几何因子为铺层厚度和铺层顺序的表达式,与传统的多级优化相比,以几何因子作为设计变量可以避免铺层厚度和铺层顺序的解耦,进而获得更大的设计空间,且得到的铺层结构可以满足工艺约束。最后,对一矩形悬臂复合材料层合板进行剪裁设计,使得铺层结构满足气动弹性约束且质量最小。结果显示,运用该优化方法可以得到质量更小且满足工艺约束的铺层结构。     

Efficient handling of stability problems in shell optimization by asymmetric ‘worst‐case’ shape imperfection

The paper presents an approach to shape optimization of proportionally loaded elastic shell structures under stability constraints. To reduce the stability‐related problems, a special technique is utilized, by which the response analysis is always terminated before the first critical point is reached. In this way, the optimization is always related to a precritical structural state. The necessary load‐carrying capability of the optimal structure is assured by extending the usual formulation of the optimization problem by a constraint on an estimated critical load factor. Since limit points are easier to handle, the possible presence of bifurcation points is avoided by introducing imperfection parameters. They are related to an asymmetric shape perturbation of the structure. During the optimization, the imperfection parameters are updated to get automatically the ‘worst‐case’ pattern and amplitude of the imperfection. Both, the imperfection parameters and the design variables are related to the structural shape via the design element technique. A gradient‐based optimizer is employed to solve the optimization problem. Three examples illustrate the proposed approach. Copyright © 2007 John Wiley & Sons, Ltd.     

An algorithm for optimization of non-linear shell structures

An algorithm for optimal design of non-linear shell structures is presented. The algorithm uses numerical optimization techniques and nonlinear finite element analysis to find a minimum weight structure subject to equilibrium conditions, stability constraints and displacement constraints. A barrier transformation is used to treat an apparent non-smoothness arising from posing the stability constraints in terms of the eigenvalues of the Hessian of the potential energy of the structure. A sequential quadratic programming strategy is used to solve the resulting non-linear optimization problem. Matrix sparsity in the constraint Jacobian is exploited because of the large number of variables. The usefulness of the proposed algorithm is demonstrated by minimizing the weight of a number of stiffened thin shell structures.     

A global single-loop deterministic approach for reliability-based design optimization of truss structures with continuous and discrete design variables

A single-loop deterministic method (SLDM) has previously been proposed for solving reliability-based design optimization (RBDO) problems. In SLDM, probabilistic constraints are converted to approximate deterministic constraints. Consequently, RBDO problems can be transformed into approximate deterministic optimization problems, and hence the computational cost of solving such problems is reduced significantly. However, SLDM is limited to continuous design variables, and the obtained solutions are often trapped into local extrema. To overcome these two disadvantages, a global single-loop deterministic approach is developed in this article, and then it is applied to solve the RBDO problems of truss structures with both continuous and discrete design variables. The proposed approach is a combination of SLDM and improved differential evolution (IDE). The IDE algorithm is an improved version of the original differential evolution (DE) algorithm with two improvements: a roulette wheel selection with stochastic acceptance and an elitist selection technique. These improvements are applied to the mutation and selection phases of DE to enhance its convergence rate and accuracy. To demonstrate the reliability, efficiency and applicability of the proposed method, three numerical examples are executed, and the obtained results are compared with those available in the literature.     

Multiobjective stacking sequence optimization for laminated composite structures

A Pareto-based multiobjective evolutionary algorithm is presented for stacking sequence optimization of composite structural parts. Special attention has been paid to engineering design guidelines for stacking sequence design. These guidelines are included into the formulation of the optimization problem as constraints or additional objectives. A new initialization strategy is proposed following mechanical considerations. The method is applied to the optimal design of a composite plate for weight minimization and maximization of the buckling margins under three hundred load cases that make also the originality of this work. It is shown that the introduction of new ply orientations compared to the classical 0°, ±45° and 90° plies can lead to significantly improved optimal designs.     

Modelling and design of adaptive structures using B-spline strip models

The aim of this paper is to present a family of laminated plate/shell B-spline finite strip models based on higher order displacement fields applied to the optimal design of laminated composite plate/shell structures with embedded and/or surface bonded piezoelectric actuators and sensors. Simulated annealing, as a stochastic global optimisation technique, is used to improve the performance of composite adaptive structures subjected to behavioural functions and/or constraints, with continuous and discrete design variables. To show the applicability of the proposed optimisation models, two illustrative examples are presented and discussed.     

Design Optimization of Composite Prosthetic Tubes Using GA-ANN Algorithm Considering Tsai-Wu Failure Criteria

The investigation of possible failures in composite materials is a matter of very great importance, and the Tsai-Wu criterion is an effective criterion for analyzing those flaws in anisotropic materials and defining whether the material at a given load will or will not suffer structural failure. In this study, an optimization procedure is proposed to minimize the maximum value of Tsai-Wu of laminated composite tubes subject to axial loading. Artificial neural networks and genetic algorithms are chosen as optimization tools. The results of this study show that the developed algorithm converges faster. Then, the maximum Tsai-Wu value is used as the objective function and the fiber orientations are the constraints in the optimization process. The results yielded by them are compared and discussed. Optimal results are compared with respect to the usual initial design. The design approach is recommended for structures where composites are the key load-carrying members such as orthopedic prosthesis.     

离散变量结构优化设计的拟满应力遗传算法

以力学准则法为基础,提出了一种求解离散变量结构优化设计的拟满应力方法;这种方法能直接求解具有应力约束和几何约束的离散变量结构优化设计问题。通过在遗传算法中定义拟满应力算子,建立了一种离散变量结构优化设计的混合遗传算法拟满应力遗传算法。算例表明:这种混合遗传算法对于离散变量结构优化设计问题具有较高的计算效率。     

钢筋混凝土结构的应力拓扑优化方法研究

基于预测混凝土失效行为的Drucker-Prager(D-P)屈服准则,研究了进行钢筋混凝土结构配筋设计的应力拓扑优化方法。结合扩展的双材料密度惩罚模型,优化问题构造为以单元人工密度为设计变量、混凝土材料Drucker-Prager屈服函数为约束条件的钢筋用量最小化问题。为合理定义混凝土应力并防止应力奇异解现象,采用局部应力插值模型和ε-松弛方法对混凝土应力约束条件进行处理。推导约束函数的伴随法灵敏度计算公式,运用基于梯度的连续性优化算法求解优化问题。数值算例验证了所提优化模型的正确性及数值算法的有效性,并通过与传统最小柔顺性拓扑优化结果的比较,说明了该文方法能够充分利用混凝土的抗压能力和钢筋的抗拉能力,设计结果更为实用。     

基于UG平台的截面特征曲线全局约束优化研究

截面曲线是曲面建模过程中的重要特征,将截面特征曲线重建技术与正向设计技术相结合是实现复杂特征曲面模型重建的重要方法。针对这一问题提出了一种基于UG草图的截面特征曲线全局约束优化技术,并对实现该方法的约束表达、全局约束优化模型的建立及求解、基于UG平台的算法实现等关键技术进行了深入研究。应用实例表明,基于UG的截面特征曲线全局约束优化方法可以得到满足约束条件下的与数据点逼近的最优曲线,基于该曲线可以快速、准确地重建出具有复杂特征的曲面模型。