具有动应力和动位移约束的离散变量结构拓扑优化设计方法

讨论了动应力、动位移约束下离散变量结构拓扑优化设计问题.首先给出问题的数学模型,然后用拟静力算法,将结构惯性力极值作为静载荷施加到结构上,求得结构的动位移和动内力,将考虑动应力约束和动位移约束的离散变量结构拓扑设计问题化为静应力和静位移约束的优化问题,然后利用两类变量统一考虑的离散变量结构拓扑优化设计的综合算法进行求解.     

具有动应力、位移和稳定性约束的离散变量桁架结构布局优化设计算法

给出了在动应力、动位移和动稳定约束下离散变量结构布局优化设计问题的数学模型,用“拟静力”算法,将具有动应力约束、动位移约束和动稳定约束的离散变量结构布局优化设计问题化为静应力、静位移和静稳定约束的优化问题,然后利用两级优化算法求解该模型．优化过程由两级组成,拓扑级优化和形状级优化．在每一级,都使用了综合算法,并且在搜索过程中都根据两类设计变量的相对差商值进行搜索．对包含稳定约束和不包含稳定约束的优化结果做了比较,结果显示稳定性约束对优化结果产生较大的影响．     

基于对偶二次规划的大型框架结构优化方法

将准则法和数学规划相结合,对于不同的约束采用不同的处理方法:应力约束作为局部性约束,用0阶近似进行处理,借助满应力准则将其转化为动态尺寸下限;位移约束作为全局性约束,根据单位虚载荷法将其显式化,从而建立了满足应力和位移约束的框架结构截面优化的显式模型．为了提高模型的求解效率,根据对偶理论将大规模的框架结构优化问题转化为仅仅几个对偶变量的对偶问题,采用二次规划方法求解,算例证明该方法能极大的提高模型的求解效率．采用近似射线步既能减小计算量又能使迭代过程更加平稳,采用删除无效约束技术能减小优化模型的规模. 以MSC/Nastran软件为结构分析的求解器,以MSC/Patran软件为开发平台,完成了满足刚度和强度的多工况、多变量的框架截面优化软件．算例结果表明上述程序算法的高效性．     

基于磨光反演映射的拓扑优化ICM方法

对结构拓扑优化ICM(independent continuous mapping)方法中的磨光映射和过滤映射加以拓广,利用反演映射极限形式的磨光特性构造其与过滤映射相协调的复合映射.由于该复合映射的叠加离散效应,首先引入幂函数和正弦函数的复合形式过滤函数,用ICM方法建立位移约束下重量最小为目标的连续体结构拓扑优化模型,并采用二次规划精确对偶算法进行求解.再将求得的离散解为主的连续最优解依照动态反演策略,用最佳阈值和理性反演函数求出最严格的0-1离散解,给出了拓扑优化"离散→连续"和"连续→离散"先后相反的二阶段解法.基于MATLAB软件平台开发了相应的拓扑优化计算程序,给出的数值算例对该文提出的方法进行验证,结果表明:该方法计算效率高,最优解灰度单元少,反演后结构重量更小,并且能够计算出更合理的结构拓扑.     

基于参数化水平集法的材料非线性子结构拓扑优化

针对利用传统水平集法进行非线性结构拓扑优化计算过程复杂及计算效率低等问题,将参数化水平集方法引入材料非线性结构拓扑优化中。通过全局径向基函数插值初始水平集函数,建立了以插值系数为设计变量、结构的应变能最小为目标函数、材料用量为约束条件的材料非线性结构拓扑优化模型,利用有限元分析对材料非线性结构建立平衡方程,并用迭代法求解。同时,采用子结构法划分设计区域为若干个子区域,将全自由度平衡方程的求解分解为缩减的平衡方程和多个子结构内部位移的求解,减小了计算成本。算例表明,这种处理非线性关系的方法可以在保证数值稳定的同时提高计算效率,得到边界清晰、结构合理的拓扑优化构形。     

基于可靠性的工程结构动力响应优化设计

在考虑结构物理参数和作用荷栽同时具有随机性的情况下,建立了具有动应力、动位移可靠性约束和设计变量上下限约束的工程结构优化设计数学模型;分别对结构动力响应的数字特征和基于可靠性的结构动力响应的灵敏度进行了推导.利用内罚函数法求解.算例表明文中构建的优化模型和提出的求解方法是合理与可行的.     

基于辛对偶体系的层合板自由边缘效应的分析解

在原变量——位移和其对偶变量——应力组成的辛几何空间,建立了Pipes-Pagano模型的复合材料层合板问题的辛对偶求解体系．与传统的单类变量不同,辛对偶变量有利于同时描述层间位移连续性条件和应力平衡条件．进入辛对偶体系以后,就可以应用辛对偶体系的统一解析求解方法,如分离变量和辛本征展开的方法对层合板问题进行解析分析和求解．对层合板自由边缘效应的分析求解,验证了辛对偶体系的方法对层合板问题的分析求解是十分有效的．     

基于变体积约束的阻尼材料微结构拓扑优化研究北大核心CSCD

阻尼复合结构的抑振性能取决于材料布局和阻尼材料特性.该文提出了一种变体积约束的阻尼材料微结构拓扑优化方法,旨在以最小的材料用量获得具有期望性能的阻尼材料微结构.基于均匀化方法,建立阻尼材料三维微结构有限元模型,得到阻尼材料的等效弹性矩阵.逆用Hashin-Shtrikman界限理论,估计对应于期望等效模量的阻尼材料体积分数限,并构建阻尼材料体积约束限的移动准则.将获得阻尼材料微结构期望性能的优化问题转化为体积约束下最大化等效模量的优化问题,建立阻尼材料微结构的拓扑优化模型.利用优化准则法更新设计变量,实现最小材料用量下的阻尼材料微结构最优拓扑设计.通过典型数值算例验证了该方法的可行性和有效性,并讨论了初始微构型、网格依赖性和弹性模量等对阻尼材料微结构的影响.     

多层次结构优化方法

本文提出了—种包含虚节点和虚单元的力学模型。称为广义结构;导出了分析广义结构的公式;利用Kuhn-Tucker,条件和满应力准则分别建立了虚单元转为实单元的条件;利用这一条件,可以把结构拓扑优化的非线性规划由混合型转化为连续型,使问题的困难度大为降低。这是一种以单一的尺寸变量为变量的,适用于尺寸优化、几何优化和拓扑、布局优化等各个层次结构优化问题的方法,文内还讨论了用本方法得到的解与总极值的关系,并有几个算例说明方法的有效性。     

数据驱动下的声学器件音质优化

音质是声学器件声音表现的重要衡量标准.但音质的优化过程需要对大量频点的响应进行协同优化,造成优化问题的可求解性较差.该文提出了一种数据驱动下的声学通道拓扑优化设计方法,可实现声-结构系统中的声频响快速预测,进而借助显式拓扑优化技术实现声学器件的音质优化.通过人工神经网络对结构几何参数、激励频率与声频响之间的非线性关系进行建模,以可移动变形组件(moving morphable components, MMC)法中的结构几何参数、激励频率为输入变量,以声压频响作为输出变量,通过训练多层前馈网络建立了声频响的人工神经网络模型.所得结果可以有效地将目标频带内的声压级范围差从44.89 dB缩小至6.49 dB,相较于传统优化方法,求解速度约为之前的16.3倍,表明了当前方法对音质优化问题的快速求解具有明显效果.     

Bi-directional evolutionary topology optimization of geometrically nonlinear continuum structures with stress constraints

This paper proposes a design method to maximize the stiffness of geometrically nonlinear continuum structures subject to volume fraction and maximum von Mises stress constraints. An extended bi-directional evolutionary structural optimization (BESO) method is adopted in this paper. BESO method based on discrete variables can effectively avoid the well-known singularity problem in density-based methods with low density elements. The maximum von Mises stress is approximated by the p-norm global stress. By introducing one Lagrange multiplier, the objective of the traditional stiffness design is augmented with p-norm stress. The stiffness and p-norm stress are considered simultaneously by the Lagrange multiplier method. A heuristic method for determining the Lagrange multiplier is proposed in order to effectively constrain the structural maximum von Mises stress. The sensitivity information for designing variable updates is derived in detail by adjoint method. As for the highly nonlinear stress behavior, the updated scheme takes advantages from two filters respectively of the sensitivity and topology variables to improve convergence. Moreover, the filtered sensitivity numbers are combined with their historical sensitivity information to further stabilize the optimization process. The effectiveness of the proposed method is demonstrated by several benchmark design problems.     

Improvements in the treatment of stress constraints in structural topology optimization problems

Topology optimization of continuum structures is a relatively new branch of the structural optimization field. Since the basic principles were first proposed by Bendsøe and Kikuchi in 1988, most of the work has been dedicated to the so-called maximum stiffness (or minimum compliance) formulations. However, since a few years different approaches have been proposed in terms of minimum weight with stress (and/or displacement) constraints.These formulations give rise to more complex mathematical programming problems, since a large number of highly non-linear (local) constraints must be taken into account. In an attempt to reduce the computational requirements, in this paper, we propose different alternatives to consider stress constraints and some ideas about the numerical implementation of these algorithms. Finally, we present some application examples.     

Multiple-Load Truss Topology and Sizing Optimization: Some Properties of Minimax Compliance

This paper considers the mathematical properties of discrete or discretized mechanical structures under multiple loadings which are optimal w.r.t. maximal stiffness. We state a topology and/or sizing problem of maximum stiffness design in terms of element volumes and displacements. Multiple loads are handled by minimizing the maximum of compliance of all load cases, i.e., minimizing the maximal sum of displacements along an applied force. Generally, the problem considered may contain constraints on the design variables. This optimization problem is first reformulated in terms of only design variables. Elastic equilibrium is hidden in potential energy terms. It is shown that this transformed objective function is convex and continuous, including infinite values. We deduce that maximum stiffness structures are dependent continuously on the bounds of the element volumes as parameters. Consequently, solutions to sizing problems with small positive lower bounds on the design variables can be considered as good approximations of solutions to topology problems with zero lower bounds. This justifies heuristic approaches such as the well-known stress-rationing method for solving truss topology problems.     

Two basic problems in reliability-based structural optimization

Optimization of structures with respect to performance, weight or cost is a well-known application of mathematical optimization theory. However optimization of structures with respect to weight or cost under probabilistic reliability constraints or optimization with respect to reliability under cost/weight constraints has been subject of only very few studies. The difficulty in using probabilistic constraints or reliability targets lies in the fact that modern reliability methods themselves are formulated as a problem of optimization. In this paper two special formulations based on the so-called first-order reliability method (FORM) are presented. It is demonstrated that both problems can be solved by a one-level optimization problem, at least for problems in which structural failure is characterized by a single failure criterion. Three examples demonstrate the algorithm indicating that the proposed formulations are comparable in numerical effort with an approach based on semi-infinite programming but are definitely superior to a two-level formulation.     

Optimización mixta de estructuras de transporte de energía: aplicación del algoritmo de recocido simulado

A general methodology to optimize the weight of power transmission structures is presented in this article. This methodology is based on the simulated annealing algorithm defined by Kirkpatrick in the early ‘80s. This algorithm consists of a stochastic approach that allows to explore and analyze solutions that do not improve the objective function in order to develop a better exploration of the design region and to obtain the global optimum. The proposed algorithm allows to consider the discrete behavior of the sectional variables for each element and the continuous behavior of the general geometry variables. Thus, an optimization methodology that can deal with a mixed optimization problem and includes both continuum and discrete design variables is developed. In addition, it does not require to study all the possible design combinations defined by discrete design variables. The algorithm proposed usually requires to develop a large number of simulations (structural analysis in this case) in practical applications. Thus, the authors have developed first order Taylor expansions and the first order sensitivity analysis involved in order to reduce the CPU time required. Exterior penalty functions have been also included to deal with the design constraints. Thus, the general methodology proposed allows to optimize real power transmission structures in acceptable CPU time.     

Using artificial reaction force to design compliant mechanism with multiple equality displacement constraints

Monolithic compliant mechanisms are elastic workpieces which transmit force and displacement from an input position to an output position. Continuum topology optimization is suitable to generate the optimized topology, shape and size of such compliant mechanisms. The optimization strategy for a single input single output compliant mechanism under volume constraint is known to be best implemented using an optimality criteria or similar mathematical programming method. In this standard form, the method appears unsuitable for the design of compliant mechanisms which are subject to multiple outputs and multiple constraints. Therefore an optimization model that is subject to multiple design constraints is required. With regard to the design problem of compliant mechanisms subject to multiple equality displacement constraints and an area constraint, we here present a unified sensitivity analysis procedure based on artificial reaction forces, in which the key idea is built upon the Lagrange multiplier method. Because the resultant sensitivity expression obtained by this procedure already compromises the effects of all the equality displacement constraints, a simple optimization method, such as the optimality criteria method, can then be used to implement an area constraint. Mesh adaptation and anisotropic filtering method are used to obtain clearly defined monolithic compliant mechanisms without obvious hinges. Numerical examples in 2D and 3D based on linear small deformation analysis are presented to illustrate the success of the method.