基于等几何分析的结构优化设计研究进展

结构等几何分析是计算固体力学领域一种新兴的数值方法,致力于将CAD（计算机辅助设计）和CAE（计算机辅助工程）纳入到统一的数学表达框架。等几何分析紧密联系几何信息,采用相同的数学表达将几何精确建模、结构分析和设计过程结合,为结构优化设计提供了新的选择和机会。相比基于有限元的结构优化方法,等几何优化设计方法可在一定程度上提高结构优化的精度、效率和便利性。本文针对具有代表性的结构等几何优化设计,包括形状优化、尺寸优化和拓扑优化等问题,系统梳理和综述了主要的等几何优化方法及其在结构优化设计中的应用。比较分析和评述了结构等几何优化设计方法的算法特点及计算优势与劣势,探讨了基于等几何分析的结构优化研究的前沿问题,并展望了未来的发展方向,包括：基于复杂剪裁CAD几何的高效等几何分析与优化设计、基于实体几何构造的结构等几何分析和优化设计、等几何分析与其他力学分析方法结合的结构优化、基于等几何分析的壳体优化设计、基于等几何分析的材料和结构一体化优化设计以及考虑不确定性的结构等几何优化设计等。     

Postbuckling analysis of axially-loaded laminated cylindrical shells with piezoelectric actuators

A compressive postbuckling analysis is presented for a laminated cylindrical shell with piezoelectric actuators subjected to the combined action of mechanical, electric and thermal loads. The temperature field considered is assumed to be a uniform distribution over the shell surface and through the shell thickness, and the electric field is assumed to be the transverse component E_Z only. The material properties are assumed to be independent of the temperature and the electric field. The governing equations are based on the classical shell theory with von Kármán–Donnell-type kinematic nonlinearity. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A boundary layer theory of shell buckling, which includes the effects of nonlinear prebuckling deformations, large deflections in the postbuckling range, and initial geometric imperfections of the shell, is extended to the case of hybrid laminated cylindrical shells. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the compressive postbuckling behavior of perfect and imperfect, cross-ply laminated cylindrical thin shells with fully covered or embedded piezoelectric actuators under different sets of thermal and electric loading conditions. The effects played by temperature rise, applied voltage, shell geometric parameter, stacking sequence, as well as initial geometric imperfections are studied.     

Some problems of optimizing shell shape and thickness distribution on the basis of a genetic algorithm

We consider problems related to designing axisymmetric shells of minimal weight (mass) and the development of efficient nonlocal optimization methods. The optimization problems under study consist in simultaneous search for the optimal geometry and the shell thickness optimal distribution from the minimal weight condition under strength constraints and additional geometric constraints imposed on the thickness function, the transverse cross-section radii distribution, and the volume enclosed by the shell. Using the method of penalty functions, we reduce the above optimal design problem to a nonconvex minimization problem for the extended Lagrange functional. To find the global optimum, we apply an efficient genetic algorithm. We present the results of numerical solution of the optimal design problem for dome-like shells of revolution under the action of gravity forces. We present some data characterizing the convergence of the method developed here.     

Optimum design of hierarchical stiffened shells for low imperfection sensitivity

A concept of hierarchical stiffened shell is proposed in this study, aiming at reducing the imperfection sen- sitivity without adding additional weight. Hierarchical stiffened shell is composed of major stiffeners and minor stiff- eners, and the minor stiffeners are generally distributed between adjacent major stiffeners. For various types of geo- metric imperfections, e.g., eigenmode-shape imperfections, hierarchical stiffened shell shows significantly low imper- fection sensitivity compared to traditional stiffened shell. Furthermore, a surrogate-based optimization framework is proposed to search for the hierarchical optimum design. Then, two optimum designs based on two different opti- mization objectives （including the critical buckling load and the weighted sum of collapse loads of geometrically imperfect shells with small- and large-amplitude imperfections） are compared and discussed in detail. The illustrative example demonstrates the inherent superiority of hierarchical stiffened shells in resisting imperfections and the effectiveness of the proposed framework. Moreover, the decrease of imperfection sensitivity can finally be converted into a decrease of structural weight, which is particularly important in the development of large-diameter launch vehicles.     

Postbuckling analysis of axially loaded functionally graded cylindrical panels in thermal environments

A postbuckling analysis is presented for a functionally graded cylindrical panel of finite length subjected to axial compression in thermal environments. Material properties are assumed to be temperature dependent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The governing equations of a functionally graded cylindrical panel are based on Reddy’s higher order shear deformation shell theory with a von Kármán–Donnell-type of kinematic nonlinearity and including thermal effects. Two cases of the in-plane boundary conditions are considered. The nonlinear prebuckling deformations and initial geometric imperfections of the panel are both taken into account. A boundary layer theory of shell buckling, which includes the effects of nonlinear prebuckling deformations, large deflections in the postbuckling range, and initial geometric imperfections of the shell, is extended to the case of functionally graded cylindrical panels under axial compression. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behavior of axially loaded, perfect and imperfect, functional graded cylindrical panels with two constituent materials and under different sets of thermal environments. The influences played by temperature rise, volume fraction distributions, the character of in-plane boundary conditions, transverse shear deformation, panel geometric parameters, as well as initial geometric imperfections are studied.     

初始几何缺陷对网壳截面优化结果影响研究

单层网壳结构是缺陷敏感结构,初始几何缺陷不同对"网壳截面优化结果"有显著影响,该文研究了网壳杆件截面取值与缺陷分布、结构极限承载力之间的关系.结果表明:经截面优化设计的网壳结构最不利应力最早并且一直出现在初始几何缺陷较大处;优化寻优结果与初始几何缺陷分布有直接关系,增大缺陷较大处杆件截面能显著提高结构承载力;由于缺陷随机分布,经截面优化设计的网壳结构须校核其在不同缺陷下的稳定承载力以确保结构安全.     

基于可靠性的桁架结构拓扑优化设计

建立了以杆截面为设计变量、结构重量极小化为目标、具有位移、应力等性态可靠性约束的桁架结构拓扑优化设计数学模型．通过引入可靠性安全系数，并利用结构力学的三个基本方程，将结构的位移和杆件应力可靠性约束等价显示化为设计变量的线性函数，使原基于可靠性的优化模型转化为常规的序列线性规划问题，利用修正的单纯形法求解．算例表明文中提出的方法既简单又有效．     

Torsional buckling and postbuckling of FGM cylindrical shells in thermal environments

A postbuckling analysis is presented for a functionally graded cylindrical shell subjected to torsion in thermal environments. Heat conduction and temperature-dependent material properties are both taken into account. The temperature field considered is assumed to be a uniform distribution over the shell surface and varied in the thickness direction. The material properties of functionally graded materials (FGMs) are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents, and are assumed to be temperature-dependent. The governing equations are based on a higher order shear deformation theory with a von Kármán–Donnell-type of kinematic non-linearity. The non-linear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A singular perturbation technique is employed to determine the buckling load and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behavior of twist, perfect and imperfect, FGM cylindrical shells under different sets of thermal fields. The results reveal that the volume fraction distribution of FGMs has a significant effect on the buckling load and postbuckling behavior of FGM cylindrical shells subjected to torsion. They also confirm that the torsional postbuckling equilibrium path is weakly unstable and the shell structure is virtually imperfection–insensitive.     

Thermo-piezoelectric effects on the postbuckling of axially-loaded hybrid laminated cylindrical panels

IntroductionCompositelaminatedcylindricalpanelhasbeenusedextensivelyasastructuralconfiguration,mainlyintheaerospaceindustry .Oneoftherecentadvancesinmaterialandstructuralengineeringisinthefieldofsmartstructureswhichincorporatesadaptivematerials.Bytakingadvantageofthedirectandconversepiezoelectriceffects,piezoelectriccompositestructurescancombinethetraditionalperformanceadvantagesofcompositelaminatesalongwiththeinherentcapabilityofpiezoelectricmaterialstoadapttotheircurrentenvironment.Therefore…     

Postbuckling of pressure-loaded shear deformable laminated cylindrical panels

IntroductionInrecentyears,fiber_reinforcedcompositelaminatedpanelshavebeenwidelyusedintheaerospace,marine ,automobileandotherengineeringindustries .Theproblemofbucklingandpostbucklingofcylindricalpanelsunderaxialcompressionortorsionhasbeenextensivelystudied .Incontrast,theliteratureoncylindricalpanelsunderpressureloadingisrelativelyspares.Thesestudiesincludealinearbucklinganalysis (Singeretal.[1]) ,anonlinearbucklinganalysi(YamadaandCroll[2 ]) ,anelastoplasticbucklinganalysisusingreducedstif…     

Design Optimization of Connection Section for Concentrated Force Diffusion

In many load carrying thin shell structures, a connection section is arranged to transfer concentrated external forces to its main section. It is very important for the concentrated external forces to diffuse as uniformly as possible. Nevertheless the traditional design of uniform radial rib is not optimized. The present paper studies an integrated optimization procedure for design optimization of connection section. Variance constraint of node forces at the interface between the main section and connection section is firstly proposed as the evaluation criterion of concentrated force diffusion efficiency and introduced into the topology optimization formulation. Afterwards, for improving the manufacturability of the final design the topology optimization results are interpreted and further optimized by size or shape optimization. Two strategies of interpretation are examined. The first strategy is called strategy of making holes, which inserts a number of internal holes of regular geometric features and smooth boundary with B-spline curves in the continuum based on the topology optimization result. In the second strategy, an initial truss-like design is extracted from the characteristic of topology optimization result. Then a further shape and sizing optimization is followed to obtain the final optimal design. An example of design optimization of plane connection section is presented. The effectiveness of the present approach is demonstrated. The respective advantages and disadvantages of the two strategies are discussed.     

Global optimum design of externally pressurized isogrid stiffened cylindrical shells with added T-rings

PANDA2 is a code for the minimum-weight design of perfect and imperfect elastic stiffened panels and shells made of composite laminates and subjected to multiple sets of in-plane loads, edge moments, normal pressure, and temperature. The scope of PANDA2 is increased to include global optimization and the capability to handle isogrid stiffening. The enhanced program is used to find global optimum designs of internally T-isogrid and internally T-ring stiffened perfect and imperfect isotropic cylindrical shells under uniform external pressure. For the cases studied, it is found that for the perfect optimized shells the isogrid stiffening is important but the rings are not, whereas the opposite holds for the optimized shells with an initial general buckling modal imperfection of amplitude equal to one per cent of the shell radius     

考虑最小尺寸精确控制的SIMP和MMC混合拓扑优化方法

拓扑优化作为一种先进设计方法, 已被成功用于多个学科领域优化问题求解, 但从拓扑优化结果到其工程应用之间仍存在诸多阻碍, 如在结构设计中存在难以制造的小孔或边界裂缝和单铰链连接等. 在拓扑优化设计阶段考虑结构最小尺寸控制是解决上述问题的一种有效手段. 在最小尺寸控制的结构拓扑优化方法中, 通用性较强的固体各向同性材料惩罚法SIMP优化结果边界模糊不光滑, 包含精确几何信息的移动变形组件法MMC对初始布局具有较强依赖性. 本文提出一种考虑最小尺寸精确控制的SIMP和MMC混合拓扑优化方法. 所提方法继承了二者优势, 避免了各自缺点. 在该方法中, 首先采用活跃轮廓算法ACWE获取SIMP输出的拓扑结构边界轮廓数据, 提出了SIMP优化结果到MMC组件初始布局的映射方法. 其次, 通过引入组件的3个长度变量, 建立了半圆形末端的多变形组件拓扑描述函数模型. 最后, 以组件厚度变量为约束, 构建了考虑结构最小尺寸控制的拓扑优化模型. 采用最小柔度问题和柔性机构问题验证了所提方法的有效性. 数值结果表明, 所提方法在无需额外约束的条件下, 仅通过组件厚度变量下限设置, 可实现整体结构的最小尺寸精确控制, 并获得了具有全局光滑的拓扑结构边界.      

压电曲壳结构形状控制和优化设计

板壳结构作为航空、航天工程以及控制系统中的重要工作元件，在工作状态 中，要承受机械载荷、温度载荷、冲击载荷等各种负面影响， 而航空航天部件对结构形状变化非常敏感，如飞行器机翼、信息接收天线等结构, 微小的结构变形就会引起很大的性能改变，想要在设计初始阶段充分考虑所有不 利因素的影响显然是比较困难的. 利用压电材料控制结构变形往往是现代空间结 构开关控制中一个很好的选择. 基于一般壳体有限单元法, 推导了空间任意曲壳 压电单元, 利用约束方程连接主体壳元和压电壳元, 模型中约束方程的使用大大 减少了结构自由度, 使得计算速度有了明显的提升. 在此基础上, 重点研究了压 电曲壳结构的形状控制方法, 首先利用最小二乘法优化结构的电压分布, 控制结 构形状接近最优工作状态; 其次构建了以压电壳元厚度和电压联合作为设计变量 的优化控制模型, 采用非线性优化求解方法, 取得了更好的控制效果. 数值算例 表明了该文计算模型、 优化设计和控制方法的有效性.     

Postbuckling of FGM cylindrical shells under combined axial and radial mechanical loads in thermal environments

A postbuckling analysis is presented for a shear deformable functionally graded cylindrical shell of finite length subjected to combined axial and radial loads in thermal environments. Heat conduction and temperature-dependent material properties are both taken into account. The temperature field considered is assumed to be a uniform distribution over the shell surface and varied in the thickness direction only. Material properties are assumed to be temperature-dependent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The formulations are based on a higher order shear deformation shell theory with von Kármán–Donnell-type of kinematic nonlinearity. A boundary layer theory of shell buckling, which includes the effects of nonlinear prebuckling deformations, large deflections in the postbuckling range, and initial geometric imperfections of the shell, is extended to the case of functionally graded cylindrical shells. A singular perturbation technique is employed to determine the interactive buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling response of perfect and imperfect cylindrical shells with two constituent materials subjected to combined axial and radial mechanical loads and under different sets of thermal environments. The results reveal that the temperature field and volume fraction distribution have a significant effect on the postbuckling behavior, but they have a small effect on the imperfection sensitivity of the functionally graded shell.     

桁架结构概率-非概率混合可靠性拓扑优化

研究了桁架结构概率-非概率混合可靠性拓扑优化问题。建立了以结构重量为目标函数、混合可靠性指标为约束条件的拓扑优化数学模型,针对强度为随机变量和应力为区间变量、强度为区间变量和应力为随机变量两种情况推导了可靠性指标对设计变量的灵敏度计算公式。实例结果表明：混合可靠性拓扑优化的截面尺寸和结构重量相对于非概率可靠性优化都更大,使得结构除了能够容许载荷存在一定变异程度外,也允许位移和强度存在一定变异程度。     

Three-dimensional structure optimal design for extending fatigue life by using biological algorithm

This paper presents some applications of a new structural shape optimization procedure for maximizing fatigue life or inspection intervals for damage tolerant structures. In this approach, a new and simple method, which we termed FAST (Failure Analysis of Structures), for estimating the stress intensity factor for cracks at a notch, as well as an extension of the biological algorithm was employed to study the problem of optimization with fatigue life as the design objective. Research by the authors has demonstrated that the optimum shape for minimizing stress is not necessarily the optimum shape for static strength or fatigue life of a damage tolerant structure. The examples are presented that highlight this difference. The optimal shapes for stress are compared with optimized shapes found for static strength with different crack lengths. These are also compared with optimized shapes found for maximum fatigue life. The choice of initial crack size was found to have a significant effect on the optimal shapes for the structures presented.     

Sampling-Based RBDO of Ship Hull Structures Considering Thermo-Elasto-Plastic Residual Deformation

We present a shape optimization method using a sampling-based RBDO method linked with a commercial finite element analysis (FEA) code ANSYS, which is applicable to residual deformation problems of the ship hull structure in welding process. The programming language ANSYS Parametric Design Language (APDL) and shell elements are used for the thermo-elasto-plastic analysis. The shape of the ship hull structure is modeled using the bicubic Ferguson patch and coordinate components of vertices, tangential vectors of boundary curves are selected as design variables. The sensitivity of probabilistic constraint is calculated from the probabilistic sensitivity analysis using the score function and Monte Carlo Simulation (MCS) on the surrogate model constructed by using the Dynamic Kriging (DKG) method. The sequential quadratic programming (SQP) algorithm is used for the optimization. In two numerical examples, the suggested optimization method is applied to practical residual deformation problems in welding ship hull structures, which proves the sampling-based RBDO can be successfully utilized for obtaining a reliable optimum design in highly nonlinear multi-physics problem of thermo-elasto-plasticity.