基于应力及其灵敏度的结构拓扑渐进优化方法

在导出应力灵敏度的基础上，建立了一种改进的基于应力及其灵敏度的结构拓扑双方向渐进优化算法．该方法是对传统ESO和BESO方法的改进和完善．算例表明该方法能较大程度减少解的振荡状态数，获得更佳的拓扑结构．具有概念上的简洁性和应用上的有效性。     

基于变密度法的平模台振加强筋布局优化

针对混凝土预制构件水平成型振动台(简称平模台振)振动效果改进的问题,提出了通过优化振动台面加强筋布局来提高其振动效果的方法.基于变密度拓扑优化法,建立以加强筋单元相对密度为设计变量,振动台面柔度最小为目标的优化模型,并进行灵敏度分析,采用最优准则法求解优化模型;根据拓扑优化结果,对振动台面加强筋进行布局优化,获得了合理...     

基于拓扑与形状优化的小型化金属天线设计方法

天线小型化设计需要基于先进的设计方法,基于拓扑优化的设计往往存在灰度单元,因此设计结果无法直接应用,需要进一步规整设计。而对于电磁金属结构,粗糙的规整方法会引起结构性能的很大变化以致偏离最优结果。提出一种拓扑优化和形状优化相结合的方法,用于金属天线结构的小型化设计。该方法通过拓扑优化获得金属天线结构的概念构型,进而利用形状优化对概念构型进行边界规整和精细化设计。形状优化方法采用多控制点贝塞尔曲线描述拓扑概念构型,通过贝塞尔曲线控制点的移动实现天线构型的调控。给出了贝塞尔曲线控制点的设置原则,基于拓扑优化得到场量分布结果,利用较少的贝塞尔曲线控制点实现天线拓扑构型结构特征的有效调控。该方法可以获得无灰度单元残留的拓扑结果,同时可有效避免密度阈值规整方法中天线性能改变的问题,并且获得的拓扑构型边界光滑。数值算例表明拓扑优化和形状优化相结合方法的有效性。此外,该方法可拓展到其他类型电磁器件的优化设计中。     

热结构瞬态响应的耦合灵敏度分析方法与优化设计

研究结构瞬态热变形和热应力的灵敏度分析方法及其优化设计,灵敏度计算给出了直接法和伴随法两种算法.考虑了温度场的耦合作用,在直接法中需要计算温度场对设计变量的导数,在伴随法中需要计算热载荷对温度场的导数.数值算例验证了该方法的精度.伴随法在应用程序中的实现,为大型结构优化提供了高效率的灵敏度计算方法.     

一种新的形状灵敏度分析方法——具有两类变量的伴随方程法

本文将所考虑的问题视为具有两类独立变量的力学系统,通过建立具有两类变量的伴随系统方程,得到了定义在变化边界上的目标或约束泛函的敏度分析公式,由此建立了完全边界型的形状优化方法。     

基于应变能与频率灵敏度的静动力双目标ESO

当前在运用渐进结构优化(ESO)时,大多仅设定了单一的静力或动力目标,难以满足工程结构设计的需求。为此,将单目标优化常用的应变能灵敏度和频率灵敏度进行无量纲处理,再与多目标优化理论结合,开发出静动力双目标ESO。通过多个不同边界条件的深受弯构件数值算例,证实了新方法的运行稳定性和普遍适用性,同时还得到了静力优化与动力优化间的权重系数比取值建议。有限元对比分析结果表明,该新方法相较于传统的单目标优化,能够兼顾结构的静动力性能,使结构耗材减少但静力刚度基本维持,同时材料利用率和一阶固有频率还能不断提升。     

基于目标函数的渐进结构频率优化二次灵敏度及其应用

渐进结构频率优化中的二次灵敏度反映了结构变化后单元灵敏度的变化情况,利用二次灵敏度的二次删除法能够在一定程度上解决标准渐进结构频率优化方法中效率和精度的矛盾,是一种可行的折衷算法.本文将二次灵敏度的表达式进行了进一步推广,给出了基于目标函数的二次灵敏度的表达式,然后结合算例分析了利用基于目标函数二次灵敏度的二次删除法的性能,可以看出,推广的二次灵敏度以及利用该二次灵敏度的二次删除法能够应用于复杂条件下的结构频率优化问题.     

形状设计灵敏度分析的改进的再生核质点法

基于物质导数概念和直接微分法,将再生核质点法应用于形状设计灵敏度分析（DSA）中。导出了基于无网格近似的灵敏度方程,特别强调了在考虑形状函数关于设计变量的物质导数时无网格方法与有限元法的不同。通过对RKPM形状函数及其物质导数进行矩式显式表述,提高了无网格方法的计算效率。对两个二维线弹性问题进行了位移灵敏度和应力灵敏度分析,计算结果与解析解吻合的很好;同时通过对通常的RKPM和改进的RKPM计算耗时的比较,显示了该方法不仅有效,而且可以显著地提高计算效率。     

基于虚荷载变量的形状优化和灵敏度分析

基于选择施加在结构“控制点”上的虚荷载作为优化设计变量,针对一种新的承受约束的形状优化数值方法进行了研究。借助于节点位移与虚荷载之间的线性关系,提出了一种新的计算灵敏度系数的解析方法。利用节点移动速度域概念构造了优化新形状产生的计算公式,以结构中节点的最大应力最小化作为优化目标,通过控制网格结点的最大位移量,较好地解决了单元网格在形状优化中的扭曲问题。对三个不同的实例成功地完成了形状优化。     

A sensitivity equation method for fast evaluation of nearby flows and uncertainty analysis for shape parameters

This paper presents the application of the continuous sensitivity equation method (CSEM) to fast evaluation of nearby flows and to uncertainty analysis for shape parameters. The flow and sensitivity fields are solved using an adaptive finite-element method. A new approach is presented to extract accurate flow derivatives at the boundary, which are needed in the shape sensitivity boundary conditions. Boundary derivatives are evaluated via high order Taylor series expansions used in a constrained least-squares procedure. The proposed method is first applied to fast evaluation of nearby flows: the baseline flow and sensitivity fields around a NACA 0012 airfoil are used to predict the flow around airfoils with nearby shapes obtained by modifications of the thickness (NACA 0015), the angle of attack and the camber (NACA 4512). The method is then applied to evaluate the influence of geometrical uncertainties on the flow around a NACA 0012 airfoil.     

Robust design in aerodynamics using third‐order sensitivity analysis based on discrete adjoint. Application to quasi‐1D flows

In this paper, the second‐order second moment approach, coupled with an adjoint‐based steepest descent algorithm, for the solution of the so‐called robust design problem in aerodynamics is proposed. Because the objective function for the robust design problem comprises first‐order and second‐order sensitivity derivatives with respect to the environmental parameters, the application of a gradient‐based method , which requires the sensitivities of this function with respect to the design variables, calls for the computation of third‐order mixed derivatives. To compute these derivatives with the minimum CPU cost, a combination of the direct differentiation and the discrete adjoint variable method is proposed. This is presented for the first time in the relevant literature and is the most efficient among other possible schemes on condition that the design variables are much more than the environmental ones; this is definitely true in most engineering design problems. The proposed approach was used for the robust design of a duct, assuming a quasi‐1D flow model; the coordinates of the Bézier control points parameterizing the duct shape are used as design variables, whereas the outlet Mach number and the Darcy–Weisbach friction coefficient are used as environmental ones. The extension to 2D and 3D flow problems, after developing the corresponding direct differentiation and adjoint variable methods and software, is straightforward. Copyright © 2011 John Wiley & Sons, Ltd.     

基于随机响应面法的可靠性灵敏度分析及可靠性优化设计

基于随机响应面法建立了可靠性灵敏度分析方法,并将其用于结构可靠性优化设计。建立的方法利用随机响应面法将隐式的结构响应函数转换成显式函数,在显式的响应函数基础之上求解失效概率和进行可靠性灵敏度分析,得到的可靠性灵敏度能为基于函数梯度的优化算法提供梯度信息。算例表明,本文提出的可靠性灵敏度分析方法具有较高的效率和精度,提高了结构可靠性优化设计的效率。     

线性常微分方程灵敏度分析的精细积分法

利用指数矩阵的导数计算来求解一类一阶线性常系数微分方程组对某一设计变量的灵敏度计算问题。对于初值问题,利用指数矩阵的导数,递推得到状态向量的灵敏度;对于线性两点边值问题,通过两点之间的状态向量的导数关系,得到全部初始条件,进而转化为初值问题计算。指数矩阵及其导数阵的高精度计算基于2N类算法,在此基础上可实施灵敏度分析的计算。本文给出了初值和两点边值常微分方程的高精度灵敏度计算方法,计算结果可认为是计算机上的精确解,算例验证了算法的有效性。     

结构优化半解析灵敏度分析的改进算法

提出了结构半解析灵敏度分析的改进算法,该算法实现简便,对于设计变量摄动步长具有极佳的数值稳定特性。首先,从总体角度推导静力问题半解析法灵敏度分析新算法,提出了位移与应力灵敏度列式,并给出了算法实施途径;然后,将此思路推广于自振频率、屈曲临界荷载和瞬态响应等多种问题,提出了相应的计算步骤。以梁单元与壳单元等典型结构为例,开展了多个算例测试。测试表明,改进算法计算精度和效率均有提升,特别是设计变量步长有更大的数值稳定区域,为复杂工程结构形状优化的灵敏度分析提供了新途径。     

Shape sensitivity analysis for non-differentiable performance measures in multiscale crack propagation simulation using regression hybrid method

In this paper, we present a regression hybrid method that calculates shape sensitivity coe?cients for multiscale crack propagation problems with performance measures that are non-differentiable in numerical implementation. These measures are crack propagation speed (or crack speed) defined at atomistic level obtained by solving coupled atomistic/continuum structures using the bridging scale method (BSM). The major contributions of this paper are: first, by analyzing the characteristics of the performance measures of crack speed in design space, this paper verifies for the first time that these measures are theoretically continuous and differentiable with respect to design variables, and as a result, the sensitivity coe?cients exist in theory; second, to overcome the non-differentiability of the performance measures in numerical computation due to the finite size of integration time step, this paper proposes a regression hybrid method that calculates the shape sensitivity coe?cients of crack speed through polynomial regression analysis based on the sensitivity of atomic responses, which is calculated through analytical shape design sensitivity analysis (DSA). And finally, the proposed method supports for 3D crack propagation problems with periodic boundary condition in one direction. A nano-beam example is used to demonstrate numerically the feasibility, accuracy, and e?ciency of the proposed method.     

Direct sensitivity analysis for smooth unsteady compressible flows using complex differentiation

A method for the direct computation of the instantaneous sensitivities of unsteady compressible flows is proposed. It is based on the complex differentiation of the full compressible Navier–Stokes equations and does not require the storage of the unsteady flow solution to be differentiated. The method does not rely on any assumption on the basic Navier–Stokes solver, and can therefore be implemented in a straightforward way. The method is assessed on several cases, including a two‐dimensional subsonic mixing layer. It is observed that the sensitivity patterns can be interpreted thanks to Kovasznay's decomposition for perturbations in a compressible flow. Copyright © 2006 John Wiley & Sons, Ltd.     

基于Monte-Carlo方法的结构系统可靠度计算及敏度分析

基于可靠性分析理论,将结构失效概率对随机变量均值的敏度表示成失效概率与正则化随机变量在失效域上期望的乘积,并利用敏度分析的结果给出了结构线性等效安全余量的表达式.通过等概率转换,使得该方法可以应用于服从任意分布的随机变量.该方法在给出失效概率的同时,能够给出失效概率对随机变量均值的敏度,而无需重新对结构进行计算,提高了...