复合材料对称层合板特征值问题的灵敏度分析

由于复合材料层合板的横向剪切模量较低,因此基于克希霍夫理论而计算的层合板特征值及其灵敏度与实际情况相差较大。本文采用层合板的一阶剪切变形理论,将纤维铺设角、材料参数和从层合板的中面到第K层板上表面的距离Z_K视为设计变量,研究了对称层合板特征值的灵敏度计算问题。     

复合材料层合板屈曲稳定性优化设计及其灵敏度计算方法

笔者在有限元分析基础上研究了以屈曲稳定性作为约束条件或优化目标的复合材料层合板结构优化设计及其灵敏度分析方法,重点讨论了屈曲临界荷载灵敏度对内力场和载荷的依赖关系及其在铺层优化、尺寸优化和形状优化问题中的不同计算方法,并在JIFEX软件中实现了复杂结构复合材料层合板优化设计方法。数值算例验证了本文算法和程序的有效性。     

复合材料层合板声功率及灵敏度研究

采用分层理论结合有限元模型分析复合材料层合板结构的振动特性,并用声辐射模态理论进行结构声辐射分析。在此基础上,分析声功率关于设计参数的灵敏度,推导声功率灵敏度的表达公式。以四层复合材料层合板为例,着重对声功率关于层合板结构铺层角度和铺层厚度的灵敏度进行了分析研究。数值计算结果显示在层合板基频处,辐射声功率达到最大值,同时在该处灵敏度有明显的升降过程。另外,对于低噪声层合板应以±45°对称的铺设将是最为恰当的设计方案。     

复合材料层合板结构振动声辐射优化

通过有限元法计算复合材料层合板结构的振动特性,然后采用瑞利积分进行结构的声辐射分析.在此基础上,给出考虑振动声辐射特性的复合材料层合板的优化设计模型,研究简谐激励力下的结构灵敏度计算,重点推导了声学灵敏度分析公式,并采用序列线性规划方法进行了优化求解.数值算例表明通过层合板铺层厚度和角度的优化可以有效降低结构的振动声辐射,同时验证了灵敏度算法的精度和优化方法的有效性.     

基于灵敏度分析的复合材料层合板优化设计

工程结构中的复合材料层合板的几何参数往往具有随机性质.如何研究随机参数层合板的灵敏度,并对参数进行优化分析,这对正确估计结构设计的可靠性有着非常重要的意义.根据层合板的一阶剪切理论,采用样条有限元法,推导并建立了层合板的振动方程,刚度矩阵,质量矩阵,比例阻尼矩阵以及求解反对称层合板响应灵敏度的计算公式,在基于灵敏度分析的基础上,进行了复合材料层合板的基频分析和优化设计,并用网格法计算最佳铺层角.数值算例验证了算法的有效性.     

基于分层设计变量的复合材料层合板优化设计及灵敏度分析

在复合材料层合板的结构优化设计中,提出分层设计变量的优化方法以满足实际工程需要。在结构位移、自振频率和屈曲临界荷载灵敏度分析中,给出了刚度矩阵对分层厚度和分层角度设计变量的灵敏度计算公式,考虑了分层厚度变化引起层合板对称中心的改变,保证了计算准确性。数值算例验证了灵敏度算法的精度,应用实例显示了分层设计变量方法的实用性。     

层合板振动特征值对铺层角的灵敏度

研究了层合板特征值对铺层角的灵敏度, 从经典层合板理论出发, 结合有限元方法, 通过虚功原理, 推导了层合板的刚度矩阵和质量矩阵, 并且导出了质量、刚度矩阵和铺层角、铺层厚度之间的显式关系; 利用摄动方法, 推导了层合板各阶特征值对各个铺层角灵敏度的显式表达式。通过数值算例, 对比了本文方法与有限差分法得到的结果, 表明差分法只有当增量步很小时才能够达到本文方法的精度。      

铺设角度与铺层顺序对层合板稳定性的影响

以层合板结构的临界屈曲载荷系数最大化为优化目标,基于改进型模拟退火算法对层合板结构铺设角度和铺层顺序进行优化。由于层合板结构的铺层角度是离散变量,模拟退火算法适合求解离散变量的优化问题。利用模拟退火算法优化层合板铺层,在算法内采用并行计算、引入记忆功能同时设置双阈值终止准则,有效地提高了优化过程的收敛速度,同时避免优化过程中出现局部最优解。以临界屈曲载荷系数作为目标函数,选取复合材料层合板的铺设角度顺序为设计变量,采用改进的模拟退火算法得出复合材料层合板的最优铺设角度以及铺层顺序。     

基于Layerwise理论的共固化粘弹阻尼复合材料动特性分析

共固化粘弹性复合材料兼具结构承载和阻尼减振功能。针对传统的混合单元法在应用于粘弹性夹层复合材料结构阻尼性能分析时存在着前处理困难、计算规模大、精度低以及难以考虑正交各向异性铺层自身损耗能力的缺点,推导了一种基于Layerwise离散层理论的四节点四边形复合材料层合板单元,并利用直接复特征值解法建立了共固化粘弹性复合材料结构的阻尼性能分析方法。将该方法应用于不同的阻尼结构,分析结果与文献中已公开结果和混合单元法的计算结果进行了对比验证。结果表明,基于离散层理论的层合板单元具有计算精度高、前处理建模简单和计算规模小的优点,可有效应用于复杂共固化粘弹性复合材料结构的阻尼性能分析和设计。     

天然纤维增强复合材料吸声性能研究

采用热压成型法制备天然纤维增强复合材料层合板和蜂窝夹芯结构,利用双传声器阻抗管进行吸声性能测试,并与合成纤维增强复合材料层合板和蜂窝夹芯结构进行对比。结果表明:与合成纤维增强复合材料层合板相比,天然纤维增强复合材料层合板虽然具有更优异的吸声性能,但是仍不能满足吸声材料的要求,需通过材料设计进一步提高这种材料的吸声性能。而天然纤维增强蜂窝夹芯结构具有优异的吸声性能,吸声系数峰值高达0.4,可以被用作吸声材料。     

大跨度空间结构抗风分析的数值风洞方法

数值风洞方法可为复杂形体结构的风压分布确定和结构风振系数选取等提供非试验性的依据。基于计算流体动力学理论,以空间结构为对象,研究数值风洞技术。数值模拟了不同空间结构形体表面及其周围的风场,计算了结构风载体型系数,并与风洞模型实验成果比较,验证数值风洞计算结果的正确性。研究了因其他结构物存在引起的结构风场和结构体型系数变化,探讨了用数值风洞模拟技术鉴别风洞模型试验可能存在的误差及其原因。基于结构表面等压线划分结构受风区域,并以面积加权平均计算得到区域体型系数。还分析了结构多风向角下的结构风载体型系数。     

A continuum approach for second-order shape design sensitivity of elastic solids with loaded boundaries

A second-order shape design sensitivity analysis (DSA) method applicable to the shape change on the loaded boundaries is derived for three-dimensional linear elastic solids using a continuum method with the material derivative. The continuum method is also used to derive mixed second-order variations of stress and displacement performance measures with respect to shape design variables and distribution of non-conservative traction loads, and also with respect to shape design variables and material properties. A shape design acceleration field is defined for the second-order shape design sensitivity. Both direct differentiation and hybrid methods are presented in this paper. A numerical method, which can be implemented using established finite element analysis (FEA) codes, is developed. The feasibility and accuracy of the proposed second-order shape DSA method has been demonstrated by solving a structural example-doubly curved arch dam.     

Implementation of regularized isogeometric boundary element methods for gradient‐based shape optimization in two‐dimensional linear elasticity

The present work addresses shape sensitivity analysis and optimization in two‐dimensional elasticity with a regularized isogeometric boundary element method (IGABEM). Non‐uniform rational B‐splines are used both for the geometry and the basis functions to discretize the regularized boundary integral equations. With the advantage of tight integration of design and analysis, the application of IGABEM in shape optimization reduces the mesh generation/regeneration burden greatly. The work is distinct from the previous literatures in IGABEM shape optimization mainly in two aspects: (1) the structural and sensitivity analysis takes advantage of the regularized form of the boundary integral equations, eliminating completely the need of evaluating strongly singular integrals and jump terms and their shape derivatives, which were the main implementation difficulty in IGABEM, and (2) although based on the same Computer Aided Design (CAD) model, the mesh for structural and shape sensitivity analysis is separated from the geometrical design mesh, thus achieving a balance between less design variables for efficiency and refined mesh for accuracy. This technique was initially used in isogeometric finite element method and was incorporated into the present IGABEM implementation. Copyright © 2016 John Wiley & Sons, Ltd.     

基于EMD和VARMA模型的结构损伤识别

提出了基于EMD和VARMA模型的结构损伤识别方法。该方法首先将结构反应信号用EMD方法分解成一系列固有模态函数,然后将固有模态函数表示为时变VARMA模型并用Kalman滤波方法估计时变VARMA参数,最后根据时变VARMA参数定义一个新的损伤指标用于结构损伤识别。为检验该指标的实际性能,算例中选用ImperialCounty Services Building和Van Nuys Hotel作为基准结构。通过其实测地震反应记录的分析表明:该指标在实际的量测环境和噪声条件下具有较好的敏感性和抗噪能力,可有效地识别结构多处损伤的发生过程和严重程度;由于该指标定义在反应信号特征提取的基础上,无需其他额外的信息,它可同时用于结构整体和局部两个层次损伤的识别;同时,该指标还适于实时(在线)的结构损伤识别或健康监测,因其直接由时变VARMA参数推导得出。最后,对后续研究工作进行了展望。     

Inverse problem of simultaneously estimating the thermal conductivity and boundary shape

An inverse analysis is used to simultaneously estimate the thermal conductivity and the boundary shape in steady-state heat conduction problems. The numerical scheme consists of a body-fitted grid generation technique to mesh the heat conducting body and solve the heat conduction equation – a novel, efficient, and easy to implement sensitivity analysis scheme to compute the sensitivity coefficients, and the conjugate gradient method as an optimization method to minimize the mismatch between the computed temperature distribution on some part of the body boundary and the measured temperatures. Using the proposed scheme, all sensitivity coefficients can be obtained in one solution of the direct heat conduction problem, irrespective of the large number of unknown parameters for the boundary shape. The obtained results reveal the accuracy, efficiency, and robustness of the proposed algorithm.     

Parametric design sensitivity analysis of high‐frequency structural–acoustic problems using energy finite element method

A design sensitivity analysis of high‐frequency structural–acoustic problems is formulated and presented. The energy finite element method (EFEM) is used to predict structural–acoustic responses in the high frequency range, where the coupling between structural junctions and the structural–acoustic interface are modelled using power transfer coefficients. The continuum design sensitivity formulation is derived from the governing equation of EFEM and the discrete method is applied in the variation of the structural–structural and structural–acoustic coupling matrices. The direct differentiation and adjoint variable method are both developed for the sensitivity analysis, where the difficulty of the adjoint variable method is overcome by solving a transposed system equation. Parametric design variables such as panel thickness and material damping are considered for sensitivity analysis, and numerical sensitivity results show excellent agreement as compared to analytical finite difference results. Copyright © 2004 John Wiley & Sons, Ltd.     

Configuration design sensitivity analysis of built-up structures part I: Theory

A continuum based configuration design sensitivity analysis method is developed for built-up structures that include truss, beam, plane elastic solid and plate design components. The configuration design variation of a structural component can be characterized by changes in the domain shape and in the orientation of the component. A variational approach is then used to incorporate both shape and orientation effects in the same energy equation. A continuum shape design sensitivity analysis method that utilizes the material derivative idea of continuum mechanics is employed to account for effects of shape variation. An approach that is similar to the continuum shape design sensitivity analysis method is developed in this paper to account for the effect of orientation variation. Variations of energy bilinear and load linear forms, with respect to both shape and orientation design variables, are derived for each structural component. Using the adjoint variable or direct differentiation method, configuration design sensitivity results for built-up structures are obtained in terms of the design velocity fields. Configuration design sensitivity analyses of both static and eigenvalue responses are considered.     

Inclusion boundary reconstruction and sensitivity analysis in electrical impedance tomography

Reconstruction of conductive inclusions in a homogeneous background medium is commonly seen in electrical impedance tomography (EIT). One of the methods to deal with the inclusion reconstruction problems is the shape-based method. With prior knowledge of conductivity of target inclusions, the boundary of inclusions is parameterized by several shape coefficients and recovered from EIT measurements. This paper presents a shape-based inclusion reconstruction method and its numerical implementation with boundary element method (BEM). A shape perturbation method (SPM) is proposed to calculate the shape sensitivity in EIT. To evaluate the accuracy of the presented method, a series of numerical tests are conducted. The characteristics of EIT shape sensitivity are analysed. Some factors influencing the reconstruction performance are discussed.     

基于遗传算法的高耸结构环形TLD满意优化设计

针对高耸结构环形TLD的多目标优化设计开展研究。首先,建立了高耸结构环形TLD控制的动力学模型,并编制了其求解程序。随后,提出了采用Sigmoid函数作为独立满意度函数,并通过线性加权建立了复合满意度函数。进而,基于遗传算法(Genetic Algorithm, GA),选取环形TLD的几何参数作为设计变量,结构响应和阻尼器行程的复合满意度作为优化目标,建立了高耸结构环形TLD控制的满意优化设计方法。最后,针对某自立式钢烟囱,编制程序开展了其在风荷载作用下环形TLD减振的优化设计。研究表明,该方法能够快速有效地得到一组满足工程需要且较为经济的设计参数,同时该方法对权重系数的敏感度较低,降低了多目标优化设计时权重系数选择的难度。     

斜拉桥跨中竖向位移的温度灵敏度系数研究

环境温度变化下桥梁跨中竖向位移的变化规律是结构健康监测关注的重要问题。前期研究表明,拉索温度和主梁平均温度是引起斜拉桥主跨跨中竖向位移变化的关键温度变量。该文通过平面几何分析和级数展开得到了对称双塔斜拉桥主跨跨中竖向位移关于拉索温度、主梁平均温度的灵敏度系数的实用计算公式。该公式反映温度变形的物理机理,揭示温度灵敏度系数与材料特性（线膨胀系数）和结构尺寸参数（主跨长度L₀、边中跨比γ₀和塔高跨比ζ）之间的关系,为斜拉桥温度变形的研究提供了新思路。