结构动力学有限元模型修正的发展--模型确认

结构动力学有限元建模精度问题是力学分支中受到广泛关注的研究课题之一. 以提高建模精度为目标的有限元模型修正技术的发展日臻完善, 并已逐步在工业界得到应用. 然而模型修正技术未能全面解决建模精度中存在的问题. 近几年以美国三大国家实验室为代表的科技人员提出了模型确认技术, 以希望全面解决结构动力学建模精度问题. 本文以模型修正为基础, 讨论模型确认的相关问题以及与模型修正的关系.      

结构动力学模型中阻尼特性参数的修正

将结构分析计算的稳态位移响应和相应实测数据的差异映射为具有能量意义的误差范数,通过最小化该误差范数来修正与结构系统有关的阻尼特性参数．通过计算的或实测的频响函数获得稳态响应数据,使用的幅值在理论上完全包含了所有的复模态信息,参数值正过程采用迭代的方式．给出仿真算例,并对实验数据有噪声和无噪声两种情况进行了研究,结果表明方法合理且可行．     

结构动力学有限元模型修正的目标函数及算法

结构动力学有限元模型修正是结构动力学领域的一个热点问题,回顾了结构动力学有限元模型修正研究的发展历史和现状,简要评述了结构动力学有限元模型修正所使用的设计变量,着重阐述了各种结构动力学有限元模型修正方法中所使用的目标函数及修正算法,讨论了工程结构动力学有限元模型修正的一些策略,最后对结构动力学有限元模型修正技术的发展进行了总结和展望.     

动力模型总体修正的近似解析解

本文针对土木工程中理论计算的要求和特点，基于逆特征值理论给出了一种适合有限元动力模型总体修正的广义逆特征值方法，该方法在给出修正解的表达式基础上，要求修正解满足动力模型的力学特征，且仅需要少量试验数据，是一种简单、实用的有限元模型修正方法．     

结构动力模型修正方法研究进展

叙述了结构动力模型修正方法的一般原理及与其密切相关的模型缩聚和模态扩展方法,并且挑选其中具有代表性的文献, 介绍和比较了3种主要的修正方法, 即传统的动力模型修正方法, 包括矩阵型修正方法和参数型修正方法, 和最近兴起的基于神经网络的模型修正方法, 重点分析了这些方法的优点和不足之处, 力图能使读者对于这一研究领域的发展有一个脉络清晰的了解. 最后, 就目前研究中尚未解决的问题作了一些探讨.     

点式压电智能结构的模型修正与振动主动控制

提出了在点式压电智能结构中应用摄动有限元方法对结构的有限元模型进行修正,从而达到提高建模精度,改善实际结构振动主动控制效果的目的.通过对一悬臂梁在模型修正前后进行振动主动控制的不同的控制效果验证了该方法的有效性.     

结构动力模型修正方法的比较研究及评估

在实际工程中,由结构动力模型得到的计算值与通过试验获得的测量值间往往存在偏差,为了能够精确预测结构的动力响应,依据测量信息修正存在的动力模型是非常必要的.对现有几种有效的用于结构动力模型修正的理论方法(包括基于敏感性分析的矩阵型法、基于神经网络算法的参数型法和基于遗传优化算法的方法)做了详细的综述;介绍了这些方法的步骤和研究进展;并分析了这些动力模型修正方法在工程运用中存在的一些实际问题,如不完整的模态测量值、模型修正的鲁棒性、模型修正的计算效率和收敛性等.最后,通过对一实际的五层钢框架的动力模型修正,比较了这几种方法的优缺点,提出了今后需要解决的问题.      

有限元模型修正研究进展:从线性到非线性

有限元分析在实际工程中得到了广泛应用.然而有限元模型由于受到网格划分、边界条件和材料物理参数不确定性等的影响,与真实结构有差异. 因此须通过试验数据加以修正,使其尽可能接近实际结构,以保证之后的结构动力模拟分析和监测等具有实际意义. 经过多年发展,有限元模型修正技术已经能够成功应用于一些实际工程,但现代工程技术的进步对有限元模型修正提出了更高要求,修正后的有限元模型不仅要有较高的精确度,还需要为后续应用给出具有指导意义的置信度.而现有的有限元模型修正、确认方法多基于结构线性的假设,而未能考虑实际结构中广泛存在的非线性.因此本文以土木工程结构模型修正的一些研究成果为例,通过对传统有限元模型修正的发展历程进行全面回顾;总结评述传统有限元修正技术的主要方法,以及包括有限元模型确认在内的最新研究进展;重点探讨有限元模型修正技术向非线性发展的技术路线和目前主要研究成果,展望其未来发展方向, 并提出值得研究的问题.      

基于静动力分析的海洋井架钢结构有限元模型修正方法

为了得到能够更加真实地反映海洋井架静动态力学性能的有限元模型,本文提出联合运用静动力目标函数的井架结构有限元模型修正方法,相对于单独运用静力、动力目标函数的模型修正方法,本文方法能更好地适应海洋井架的静动态力学特性.为验证该修正理论的正确性,以某海洋井架为原型建立缩尺比为1:14的模型井架.在对该井架进行静动力测试和有限元仿真分析的基础上,根据对结构静动态性能的具体要求提出目标函数与约束条件,通过灵敏度分析选取合适的设计参数,采用一阶搜索优化算法对待修正的设计参数进行优化,得出有限元模型的修正结果.结果表明:与模型修正前相比,修正后井架一阶模态频率的误差减小到了-5.282%,二阶模态频率的误差减小到了-6.320%,而各个测点的应力误差控制在4%以内.这说明该方法可以较好的修正初始有限元模型,使井架有限元模型更加接近真实模型,可进一步用于分析预测井架结构的承载能力和使用寿命.     

动力模型修正中逆特征值问题的数值解法

本文提出了一种参数型模型修正的方法，因为这种方法与经典的逆特征值问题的提供是一致的，所以先建立起与逆问题等价的关于设计参数的非线性方程组，然后构造出可以用Ｎｅｗｔｏｗ法求解的格式。数值仿真结果表明本文方法具有较好的收敛性和较高的计算精度。     

Analysis of Laminated Rubber Bearings with a Numerical Reduction Model Method

In this paper, we present a reduction method for modeling slender laminated elastomeric structures, which is developed in the context of nearly incompressible hyperelasticity. This method, based on a finite element formulation, consists in projecting the unknown fields onto a polynomial basis in order to reduce the dimension of the problem and the model size. Two types of finite elements are used, one for plane-strain and the other for 3D structures. Comparisons with classical finite element models on single layers show the reliability of the present method. The method proposed successfully predicts the global and local behavior and since it reduces both the model size and the computing time. It can be used to model slender bearing consisting of several layers.     

薄壁杆系结构的梁元分析模型

本文导出了用于薄壁杆系结构弹性分析的薄壁梁元分析模型.在空间梁元分析模型[3]的基础上,采用了一种改进的位移模式,考虑了薄壁杆件可能发生的拉压、剪切、弯曲、扭转和翘曲等各变形形式以及它们的耦合效应,得出了相应的单元形函数;同时从工程应变的定义出发,采用Taylor级数展开的方法,建立了单元的五阶近似正应变表达式;并建立了相应的薄壁单元刚度方程,从而得出了局部坐标系下单元刚度矩阵的显式.根据本文所导出的薄壁梁元分析模型,编制了相应的结构计算程序.通过算例验证了本文所推导的单元刚度矩阵,同时通过与传统空间梁元计算模型计算结果的比较,阐述了截面翘曲对薄壁杆系结构的影响.     

A transient finite element analysis of natural convection around a horizontal hot cylinder

This paper presents an advanced method for a 2-dimensional analysis of transient natural convection by finite element method. The present method, based on stream function—vorticity formulation, could get rid of numerical errors and constraint of perpendicular mesh subdivision, since we excluded a finite difference approximation of vorticity on no-slip boundaries. A considerable effect of upwind weighting function was examined. The method was successfully applied to a problem of natural convection around a horizontal hot cylinder.     

An Unstructured Mesh Generation Algorithm for Shallow Water Modeling

The successful implementation of a finite element model for computing shallow water flow requires: (1) continuity and momentum equations to describe the physics of the flow, (2) boundary conditions, (3) a discrete surface water region, and (4) an algebraic form of the shallow water equations and boundary conditions. Although steps (1), (2), and (4) may be documented and can be duplicated by multiple scientific investigators, the actual spatial discretization of the domain, i.e. unstructured mesh generation, is not a reproducible process at present. This inability to automatically produce variably-graded meshes that are reliable and efficient hinders fast application of the finite element method to surface water regions. In this paper we present a reproducible approach for generating unstructured, triangular meshes, which combines a hierarchical technique with a localized truncation error analysis as a means to incorporate flow variables and their derivatives. The result is a process that lays the groundwork for the automatic production of finite element meshes that can be used to model shallow water flow accurately and efficiently. The methodology described herein can also be transferred to other modeling applications.     

On the finite-element calculation of turbulent flow using the k-ϵ model

Although the finite-element (FE) method has been successful in analysing complex laminar flows, a number of difficulties can arise when two-equation turbulence models (e.g. the k-? model) are incorporated. This work describes a particular FE discretization of the k-? model and reports its performance in recirculating flow. Severe problems encountered in attempts to obtain convergence of the numerical scheme are isolated and analysed, and methods by which the problems can be overcome are suggested. Insight gained in this work has enabled a practical turbulent flow FE code to be constructed which is robust and efficient. This code is the subject of a further paper.     

Proper Generalized Decomposition (PGD) for the numerical simulation of polycrystalline aggregates under cyclic loading

The numerical modelling of the behaviour of materials at the microstructural scale has been greatly developed over the last two decades. Unfortunately, conventional resolution methods cannot simulate polycrystalline aggregates beyond tens of loading cycles, and they do not remain quantitative due to the plasticity behaviour. This work presents the development of a numerical solver for the resolution of the Finite Element modelling of polycrystalline aggregates subjected to cyclic mechanical loading. The method is based on two concepts. The first one consists in maintaining a constant stiffness matrix. The second uses a time/space model reduction method. In order to analyse the applicability and the performance of the use of a space–time separated representation, the simulations are carried out on a three-dimensional polycrystalline aggregate under cyclic loading. Different numbers of elements per grain and two time increments per cycle are investigated. The results show a significant CPU time saving while maintaining good precision. Moreover, increasing the number of elements and the number of time increments per cycle, the model reduction method is faster than the standard solver.     

A compatible mixed design and analysis finite element method for the design of turbomachinery blades

In this paper the development of a compatible mixed design and analysis method is presented for the quasi-three-dimensional finite element blade-to-blade program FINSUP. The method consists of two parts. The first is concerned with a method of modelling changes to a blade shape using a surface transpiration model. The second is concerned with determining the relationship between the displaced blade surface and the surface velocity distribution. It is shown that with the Newton-Raphson procedure adopted in the method a very efficient manner of introducing the design option is possible. As a consequence the resulting program is fast and completely interactive. A number of examples are given to illustrate how the mixed design and analysis mode can be used in practical blade design.     

Development and application of an adaptive finite element method to reaction-diffusion equations

An adaptive finite element method is developed and applied to study the ozone decomposition laminar flame. The method uses a semidiscrete, linear Galerkin approximation in which the size of the elements is controlled by an integral which minimizes the changes in mesh spacing. The sizes and locations of the elements are controlled by the location and magnitude of the largest temperature gradient. The numerical results obtained with this adaptive finite element method are compared with those obtained using fixed-node finite-difference schemes and an adaptive finite-difference method. It is shown that the adaptive finite element method developed here using 36 elements can yield as accurate flame speeds as fourth-order accurate, fixed-node, finite-difference methods when 272 collocation points are employed in the calculations.     

结构分析中的刚体有限元法

本文给出了KAWAI教授的RBSM(刚体-弹簧模型)的数学解释。传统的以位移法为基础的有限元数值解中,其应力精度低于位移精度,而这里的刚体有限元法(RBFEM)给出的应力精度不会低于甚至高于位移精度,此外,RBFEM大大地减小了总刚的半带宽及体积,因而大幅度地降低了计算量。本文用刚体有限元法进行了静力分析、热应力分析、极限分析和安定分析,得到了相当满意的结果。刚体有限元法以其缩减的计算量及提高的应力精度,可以有利于结构分析,特别是非线性问题的数值解。