振动体声学灵敏度分析的边界元法

振动结构关于设计变量的声学灵敏度分析可以为机械系统的低噪声设计提供量化依据,为结构的优化设计提供方向。采用边界元法,推导了辐射声压关于频率、表面振速等设计变量的声学灵敏度公式。在对系数矩阵求导时,没有采用传统的有限差分法,而是直接求导,并利用不连续单元替换点法处理边界元法中的奇异积分问题。将数值解与理论值比较,证明了计算公式的准确性和有效性。该灵敏度计算方法为机械系统的低噪声设计打下了基础。     

基于分布源边界点法和伴随变量法的声学灵敏度分析

针对实际中存在的设计变量多于目标函数的情况,提出了基于分布源边界点法和伴随变量法的声学灵敏度分析方法,并建立了其理论模型,推导了其计算公式。该方法能够避免声学灵敏度分析的直接求导法中边界条件的重复计算,减少了计算量,数值仿真的结果证明了基于分布源边界点法和伴随变量法的声学灵敏度分析方法的正确性。以箱体为对象,以其上盖板厚度为设计变量进行了实验研究,场点声压灵敏度实验值与计算值的对比证明了该方法的正确性。     

基于正交球面波源边界点法的声学灵敏度分析

提出采用正交球面波源边界点法作为声学灵敏度算法,计算空间任意点的声学量关于设计变量的灵敏度,克服基于边界元的声灵敏度分析中所固有的各阶奇异积分和非唯一性问题,降低数值处理难度和工作量.提出近场声全息与声学灵敏度的组合分析方法,利用声全息重建出表面法向振速及其导数,然后再进行灵敏度分析,解决表面声学量获取困难的问题.数值仿真的结果充分证明该声学灵敏度分析方法的正确性和可行性.     

求解声学问题的伽辽金多极边界元法

针对传统边界元法在数值求解大规模声学问题时的超大计算量问题,将快速多极算法与伽辽金边界元法相结合,提出了基于Burton-Miller方程的伽辽金多极边界元法。在已有二维快速多极算法的基础上,引入核函数的对角展开形式及自适应树结构算法,同时使用经过近似求逆预处理的广义极小残差法求解系统线性方程组,最后将该方法应用于二维矩形管道与刚性圆柱面声散射问题的求解。数值计算结果表明:在求解无限域声学问题时,Burton-Miller方程保证了全频率段解的唯一性,特别是在特征频率处解的稳定性。与传统边界元方法相比,伽辽金多极边界元法的计算量由原来的I(n~2)降到了O(nlog~2n)量级,该方法非常适合用于求解大规模声学问题。     

封闭空腔内声场分析的等效声传递向量法

提出了一种用于封闭空腔内声场的计算方法--等效声传递向量法。采用位于腔体表面附近的若干虚构声源的叠加声场来等效由结构振动形成的封闭空腔声场,通过匹配振动结构表面上的法向振速获得虚构声源的源强,建立起结构表面的法向振速与腔体内场点声压的联系,并推导了结构面板声学贡献度的计算公式。计算过程避免了边界元法中复杂的数值计算和奇异积分的处理,提高了计算效率。仿真结果证明了该方法的正确性和有效性。     

注射模冷却系统三维优化设计

针对注射模三维冷却系统,以修正的三维边界元法为基础给出型腔表面温度的计算方法。在此基础上,以冷却管道线单元节点和冷管半径为设计变量,通过构造边界积分灵敏度方程得到型腔温度对设计变量的灵敏度。在优化设计中,以型腔表面各点温度与某一设定目标温度的均方差为目标函数,在一定的约束条件下,通过寻求目标函数的最小值求出冷却管道的优化位置和尺寸,并在实例进行验算。     

超声系统辐射声场的研究

研究了用于声场分布的直接边界元法.采用ANSYS对超声系统进行模态分析和谐响应分析,利用SYSNOISE实现边界元法计算了超声系统辐射声场,得到了矩形变幅杆的表面声压和辐射声场,并与理论值比较,验证了边界元的正确性.结果表明,利用边界元方法能为用于近场悬浮现象的超声系统设计提供理论依据和参考.     

基于管口噪声灵敏度分析的进气系统结构改进

发动机进气系统噪声是车辆最主要的噪声源之一,为了满足车辆舒适性越来越高的要求,控制和匹配进气系统的声学性能至关重要.依据三维几何模型建立进气系统的声学模型,其中四分之一波长管的声学模型为参数化模型.基于管道声学理论,研究发动机进气系统噪声仿真方法--无源法,并应用"无源法",进行进气系统管口噪声的模拟仿真.以试验设计分析为基础,研究基于管口噪声的四分之一波长管灵敏度分析方法,并应用该方法,进行四分之一波长管的各个参数灵敏度分析.在不具备发动机仿真模型的情况下,仍然能进行进气系统管口噪声的模拟仿真,并通过灵敏度分析确定四分之一波长管的设计参数.基于管口噪声的四分之一波长管灵敏度分析方法具有很高的工程应用价值,并为进气系统四分之一波长管的参数化设计提供了理论依据.     

结构特征值灵敏度的半解析伴随变量法

灵敏度分析在结构优化设计和可靠性分析中起着至关重要的作用。针对特征值敏度的解析法在有限元分析中不足,本文提出了一种基于半解析的伴随变量特征值敏度分析方法,用有限差分法代替了常规的解析求导。另外,针对导数矩阵稀疏性的特点提出了一种新颖的存储方法,并将这种方法应用于伴随变量法涉及到的导数矩阵存储,节省了存储空间。最后将本文提出的伴随变量方法与常见的解析法敏度分析方法进行对比,证实本文方法在精确性和计算效率上得到了较大的提高,且非常适合于大型结构的敏度分析。     

微机电系统中基于模态展开和边界元法的静电-结构耦合高效分析方法

为了提高微机电系统中静电-结构耦合数值计算速度,提出了一种新的针对微结构小变形的静电-结构耦合高效率数值计算方法。该方法将用于结构分析的微梁线性方程与用于静电场分析的边界积分方程相结合,微梁方程部分用标准的模态分析法处理,静电边界元方程则采用边界元法处理,并且将边界元方程用Taylor级数在微梁未变形的位置展开,以使静电计算能在微梁未变形的位置进行。同以往的常规算法相比,当微结构变形微小时,使用该方法,微结构变形后的面电荷密度可以在微结构未变形中计算,从而大大提高了静电-结构耦合数值计算效率。将该方法的计算结果与已有的文献计算结果和ANSYS的计算结果做了对比,验证了本方法的正确性,并且计算效率有显著提高。     

An adjoint variable method for structural design sensitivity analysis of a distinct eigenvalue problem

New adjoint variable method for design sensitivity analysis of distinct eigenvlaues and eigenvectors is presented. In the viewpoint of efficiency for the design sensitivity analysis of eigenvectors especially, the developed adjoint variable method is required to compute adjoint variables from simultaneous linear equations, the so-called adjoint equations, instead of linear combination of eigenvectors. Once we obtain the adjoint variables, design sensitivity analysis of response function that is given in terms of eigenvalues, eigenvectors and design variables can be computed directly. In this way, design sensitivity analysis of eigenvectors can be obtained by using eigenvalues and their corresponding eigenvectors of the mode being differentiated only. To verify the proposed method, numerical examples are demonstrated. This can have considerable impact on computer implementation of the developed method in the design sensitivity analysis of eigenproblem needed for practical applications.     

An adjoint variable method for design sensitivity analysis of elastoplastic structures

Design sensitivity analysis of structural problems obeying an elastoplastic material behavior is developed using adjoint variable method. An elastoplastic constitutive equation with yield surface and kinematic hardening is considered to describe the material behavior. The traditional incremental procedure and its design variation need special treatments in order to predict the discontinuity of the structural response sensitivity because the contribution from the design sensitivity at the material transition point is lost during the calculation. In this study, discontinuities of the design variations at the material transition points are alleviated in the adjoint variable method. Analytical and numerical examples are used not only to demonstrate the developed sensitivity procedure but also to gain insights of numerical implementation for the design sensitivity analysis of the elastoplastic structure based on the adjoint variable method. The comparisons between adjoint variable and direct variation methods are also discussed.     

基于能量变分形式的频响系统的设计灵敏度分析

复杂结构系统的设计灵敏度分析及其优化是工程结构设计中的重要问题之一。利用连续介质动力学理论，得到基于能量变分法的设计灵敏度方程。以浮筏隔振系统为对象，计算动态频率响应对筏体厚度的灵敏度系数。首先采用有限元分析程序计算得到初始结构和伴随结构的动态响应，然后在后处理过程中，通过数值积分得到对结构位移的设计灵敏度。计算结果表明相对于中心差分法，用伴随变量法计算精度高，且克服了传统方法中需要计算质量矩阵、刚度矩阵和阻尼矩阵偏导的缺点。     

板中Lamb波激励响应计算方法

采用基于半解析有限元的激励响应计算方法来求解薄板中Lamb波的激励响应结果,替代常规的实验方法,实现对薄板中Lamb波传播特性的仿真分析。与三维有限元仿真方法相比,采用激励响应计算方法仿真导波在波导介质中的传播过程可以节省计算量,提高效率。通过求解薄板中Lamb波的一般均质方程,基于频谱叠加原理,可以计算薄板中Lamb波激励响应结果。分别提取激励响应计算结果和实验测量数据,通过小波分析计算两种数据的Lamb波群速度。经验证,激励响应仿真计算结果与实验数据有很好的一致性,通过群速度频散曲线对比两种方法获取的数据,模态分析结论一致。激励响应计算方法还可以仿真计算任意截面波导介质中导波的传播过程,具有较好的通用性。     

基于柔性并联机构的变刚度夹持器设计分析

提出一种新型双夹爪变刚度夹持器,每个夹爪是一个由四根对称旋转柔性支链组成的变刚度柔性并联机构（VSFPM）。夹持器由两个电动机驱动,其中一个宏动电动机用于控制夹爪的开合运动,适应被抓取物体的几何尺寸;另一个微动电动机用于控制柔性支链的旋转角度,以调整夹爪在开合方向的刚度,实现变刚度柔顺抓取,提高对被抓取物体几何形状、材料属性的适应能力。基于刚度投影方法,分析了基于旋转支链柔性并联机构在夹持方向上的变刚度原理;应用基于伴随变换的刚度分析方法,求得了夹爪在任意旋转角度下的刚度模型;通过有限元仿真分析,验证了刚度模型的准确性。此外,有限元分析结果表明,提出的VSFPM机构具有较大的刚度调整范围（0.178~9.663 N/mm）,为变刚度柔性夹持器设计提供了新的思路和方法。     

Shape design sensitivity analysis based on boundary integral equation method considering general shape variations

A procedure for shape design sensitivity analysis is developed using a standard boundary integral equation (BIE) formulation for elliptic problems with static response. The performance functional to be considered involves both the domain and boundary integrals, and a complete consideration is given in describing the shape variation by including the tangential as well as the normal component of the velocity field. The material derivative concept and the adjoint variable method as applied to the BIE formulation are basic tools for the derivation. This has opened a new unfied approach using the BIE to the shape design sensitivity problems.     

Topological design sensitivity on the air bearing surface of head slider

In this study, a topological design sensitivity of the air bearing surface (ABS) is suggested by using an adjoint variable method. The discrete form of the generalized lubrication equation based on a control volume formulation is used as a compatible condition. A residual function of the slider is considered as an equality constraint function, which represents the slider in equilibrium. The slider thickness parameters at all grid cells are chosen as design variables since they are the topological parameters determining the ABS shape. Then, a complicated adjoint variable equation is formulated to directly handle the highly nonlinear and asymmetric coefficient matrix and vector in the discrete system equation of air-lubricated slider bearings. An alternating direction implicit (ADI) scheme is utilized for the numerical calculation. This is an efficient iterative solver to solve large-scale problem in special band storage. Then, a computer program is developed and applied to a slider model of a sophisticated shape. The simulation results of design sensitivity analysis (DSA) are directly compared with those of FDM at the randomly selected grid cells to show the effectiveness of the proposed approach. The overall distribution of DSA results are reported, clearly showing the region on the ABS where special attention should be given during the manufacturing process.     

Constrained and non-constrained aerodynamic optimization using the adjoint equations approach

In this research, the continuous adjoint method is applied to optimize an airfoil in subsonic and transonic flows. An inverse design problem is solved to evaluate the ability of the optimization algorithm and then, two types of optimizations, constrained and non-constrained, are investigated in a drag minimization problem. In the non-constrained drag minimization problem, the optimization is performed in a fixed angle of attack with neither geometric nor aerodynamic constraint, but in the constrained drag minimization problem, the optimization is performed in a fixed lift coefficient. Comparison of the results of these two optimizations shows the effects of the constraint on the optimization trend and the optimized geometry. Moreover, imposing the aerodynamic constraint increased the computational costs of the adjoint method. In constrained and non-constrained drag minimization problems, the surface points are adopted as design variables to show the performance of the adjoint equations approach in problems with numerous design variables.     

基于均匀化理论的微小型柔性结构拓扑优化的敏度分析

介绍微小型柔性结构在ＭＥＭＳ中的应用前景及连续体结构拓扑优化的一般方法。在此基础上探讨利用均匀化理论,有限元及伴随变量法计算连续体结构拓扑优化敏度应的方法,并取得较为理想的数值计算结果。