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面板堆石坝的三维非线性有限元分析,对并行计算提出了较高的要求. 在建模阶段挖掘出模 型内在的并行性,由相邻坝段构成子结构,既方便灵活又能满足区域分解法的要求. 编制了 适用于机群的并行多波前法计算程序,并应用于西龙池下库沥青混凝土面板堆石坝的有限元 数值分析,其计算结果和串行完全相同,通过对加速比和并行效率进行分析,结果表明采用 并行多波前法求解面板堆石坝的三维非线性有限元问题有效且算法简单,易于实现,无需辅 助的任务分配程序.     

基于区域分解的并行有限元程序及其在水下爆炸中的应用

基于MPI标准定义的消息传递接口实现了显式动力学有限元程序的并行计算.通过基于Hilbert空间填充曲线的区域分解算法,实现各区域的独立运算和区域之间共享数据的相互通信.利用程序对水下爆炸自由场中的冲击波传播规律进行了数值模拟,并通过对不同进程数下的并行加速比进行测试,验证了程序的并行效率.     

大变形问题分析的局部Petrov-Galerkin法

在微机电系统(MEMS)的建模和模拟研究中,大变形或大移动要充分予以考虑.用有限元法分析这类问题,由于难以避免的网格畸变,使模拟效率精度降低甚至失效,无网格方法(Meshless Method)则能在分析这类问题时显示出明显的优势,无网格局部Petrov-Galerkin(MLPG)法被誉为是一种有发展前景的真正无网格法.本文进一步发展了MLPG法,通过对任意的离散分布节点采用局部径向基函数构造插值形函数和Heaviside权函数,分析方程采用局部加权弱形式离散,建立了变量仅依赖于初始构型的完全Lagrange分析格式,最后用Newton-Raphson法迭代求解.文中分析了悬臂梁典型算例和微机电开关非线性大变形问题,通过与有限元结果的比较,表明本文提出的大变形问题无网格局部Petrov-Galerkin法具有稳定性好及收敛性快等优点.     

圆柱壳的非线性有限元分析及其并行求解

采取16节点曲线边等参元对圆柱壳的几何非线性进行有限元分析. 分析考 虑了完全非线性运动关系以便预测在非线性区域的稳定平衡路径. 建立了基于广义非线性位 移的有限元公式. 提出了基于全Lagrangian格式的非线性有限元分析的并行计算策略. 在集 群环境下, 对圆柱壳的几何非线性分析进行了并行计算. 计算结果表明: 在集群环境下, 所提并行算法具有良好的加速比和效率.     

基于集群的并行有限元分析研究

利用面向对象的方法实现了基于集群的并行有限元分析.首先介绍构建高性能计算集群的系统分析新方法,并针对建成集群系统的特点,对并行消息传递库MPI进行了并行语义分析,进而对其主要的实现函数进行面向对象的重构而建立起OO消息传递库,以此为基础分别利用两种不同的策略实现了面向对象的并行有限元分析(OOParaFEA: Object-Oriented Parallel FEA),一种是通过对传统的基于域分解方法的并行PCG算法进行改造而在集群平台实现,另一种是对已有的基于子结构方法的串行有限元分析程序加以扩展,加入系统方程组并行求解器而达到有限元分析并行化的目的.多个分析算例表明,基于集群进行面向对象的并行有限元分析可以有效提高计算效率,为进一步的网络化CAD/CAE研究奠定良好基础.     

火灾下圆钢管混凝土柱非线性有限元分析

首先提出合理的火灾下钢管混凝土拉、压材料数值热-力耦合本构模型及相应的计算方法;然后基于连续介质力学,推导火灾下U.L.列式虚功增量方程,采用非线性梁单元理论,给出火灾下钢管混凝土柱非线性有限元方程组的求解方法,编制非线性有限元程序NACFSTLF;最后对已有火灾下钢管混凝土柱的试验资料进行双重非线性有限元分析并考察钢管混凝土柱初始缺陷对其抗火性能的影响。分析结果表明:火灾下钢管混凝土柱的轴向变形-火灾时间曲线的计算结果基本上反映钢管混凝土柱的变形特性,而计算的耐火极限基本上是试验结果的上限;同时随着火灾下柱初始缺陷的增大,相同火灾时间下柱的跨中侧向挠度变形逐渐增大,耐火极限逐渐降低,而对柱的轴向变形影响相对较小。     

基于欧拉描述的两节点索单元非线性有限元法

本文针对柔性悬索结构几何非线性分析的特点,提出了一种用欧拉描述来表示的两节点索单元非线性有限元模型,在索元变形后的位置上由虚功能建立了非线有限元基本方程及切线刚度矩阵。这样建立的非线性有限元分析方法可充分考虑拉索的几何非线性特性的影响并给悬索结构的初始平衡分析带来方便,算例结果表明,本文方法是精确有效的。     

考虑支承的大跨度索膜结构整体分析与设计

基于修正的拉格朗日法,建立非线性有限元平衡方程,介绍了空间梁单元非线性刚度矩阵。针对此类结构在形态分析及设计中的难点问题,提出利用定力单元、定形单元和微调单元建立数值模型。采用AutoCAD二次开发工具ObjectARX编制有限元软件,能够进行考虑支承的大跨度索膜结构整体分析与设计。以芜湖体育场为工程背景,进行了形态分析和长期荷载组合下的反应。计算结果表明,本文所提方法和有限元软件显著地提高了设计工作的效率,并能准确地获得满足设计要求的结构初始形态及受力分析数据,便于实际工程的设计应用。     

受压油管屈曲变形与内外层杆管接触分析

针对机械采油工程中杆管偏磨问题, 考虑直井内受压油管屈曲变形与套管、 抽油杆的双层接触, 以及油管和抽油杆的变截面结构和环空间隙, 采用有限元结构稳定性分 析方法对受压油管进行失稳计算, 将求得的多阶失稳波形叠加值作为油管柱的初始位移, 再 采用大位移和接触非线性分析方法模拟受压油管屈曲变形, 以及与套管和抽油杆间的接触摩 擦, 为套管内受压油管屈曲变形分析提供了一种计算方法.     

横向载荷作用下轴向运动梁的屈曲失稳以及非线性振动特性

梁的轴向运动会诱发其产生横向振动并可能导致屈曲失稳，对结构的安全性和可靠性产生重大的影响。本文重点研究了横向载荷作用下轴向运动梁的屈曲失稳及横向非线性振动特性。基于Hamilton变分原理，建立了横向载荷作用下轴向运动梁的动力学方程，获得了梁的后屈曲构型。使用截断Galerkin法，将控制方程改写成Duffing方程的形式。用同伦分析方法确定载荷作用下轴向运动梁的非线性受迫振动的封闭形式的表达式。结果表明，后屈曲构型对轴向速度和初始轴向应力有明显的依赖性。通过同伦分析法得出非线性基频的显式表达式，获得了初始轴向力会影响非线性频率随初始振幅和轴向速度的线性关系。另外，轴向外激励的方向也会改变系统固有频率。     

Finite element formulation of slender structures with shear deformation based on the Cosserat theory

This paper addresses the derivation of finite element modelling for nonlinear dynamics of Cosserat rods with general deformation of flexure, extension, torsion, and shear. A deformed configuration of the Cosserat rod is described by the displacement vector of the deformed centroid curve and an orthogonal moving frame, rigidly attached to the cross-section of the rod. The position of the moving frame relative to the inertial frame is specified by the rotation matrix, parameterised by a rotational vector. The shape functions with up to third order nonlinear terms of generic nodal displacements are obtained by solving the nonlinear partial differential equations of motion in a quasi-static sense. Based on the Lagrangian constructed by the Cosserat kinetic energy and strain energy expressions, the principle of virtual work is employed to derive the ordinary differential equations of motion with third order nonlinear generic nodal displacements. A cantilever is presented as a simple example to illustrate the use of the formulation developed here to obtain the lower order nonlinear ordinary differential equations of motion of a given structure. The corresponding nonlinear dynamical responses of the structures are presented through numerical simulations using the MATLAB software. In addition, a MicroElectroMechanical System (MEMS) device is presented. The developed equations of motion have furthermore been implemented in a VHDL-AMS beam model. Together with available models of the other components, a netlist of the device is formed and simulated within an electrical circuit simulator. Simulation results are verified against Finite Element Analysis (FEA) results for this device.     

基于Kriging代理模型的迭代更新高效反演方法

为提高混凝土坝等大体积结构参数反演效率和精度,减少由于应用有限元进行大量正分析而产生的计算机时,建立了一种结合Kriging代理模型和粒子群优化(PSO)算法的迭代更新反演方法。通过拉丁超立方抽样(LHS)方法确定初始样本点的空间分布,并使用有限元正分析获取对应的响应值,构建粗糙的初始代理模型,结合具有全局寻优能力的PSO算法,反演大体积结构的分区弹性模量,随之再代入有限元模型中,计算获取新的位移响应,并将其作为新样本加入到样本集中,通过迭代更新获得局部更高精度的代理模型。工程实际算例表明,该方法对混凝土坝等大体积结构参数反演精度较高和适用性好,且能大幅减少传统有限元模型反演方法所需消耗的正分析机时,提高反演效率。     

Geometrically exact curved beam element using internal force field defined in deformed configuration

This paper presents a study on the development of high-performance finite elements for geometrically nonlinear analysis of frame structures with curved members. Based on the geometrically exact beam theory, a highly efficient and accurate mixed finite element is developed. A new approach is proposed for constructing the independent internal force field by including major terms satisfying equilibrium conditions in the deformed configuration. An element-level equilibrium iteration procedure is employed for the condensation of element internal degrees of freedom during the nonlinear solution. Numerical results are presented to demonstrate the excellent performance of the element developed, and it is shown that even when each structural member is modelled with just one element, accurate solutions can still be achieved.     

Large deformation analysis of a cantilever beam made of axially functionally graded material by homotopy analysis method

Large deformation of a cantilever axially functionally graded(AFG) beam subject to a tip load is analytically studied using the homotopy analysis method(HAM).It is assumed that its Young's modulus varies along the longitudinal direction according to a power law. Taking the solution of the corresponding homogeneous beam as the initial guess and obtaining a convergence region by adjusting an auxiliary parameter,the analytical expressions for large deformation of the AFG beam are provided. Results obtained by the HAM are compared with those obtained by the finite element method and those in the previous works to verify its validity. Good agreement is observed. A detailed parametric study is carried out. The results show that the axial material variation can greatly change the deformed configuration, which provides an approach to control and manage the deformation of beams. By tailoring the axial material distribution, a desired deformed configuration can be obtained for a specific load. The analytical solution presented herein can be a helpful tool for this procedure.     

Initial stresses in elastic solids: Constitutive laws and acoustoelasticity

On the basis of the nonlinear theory of elasticity, the general constitutive equation for an isotropic hyperelastic solid in the presence of initial stress is derived. This derivation involves invariants that couple the deformation with the initial stress and in general, for a compressible material, it requires 10 invariants, reducing to 9 for an incompressible material. Expressions for the Cauchy and nominal stress tensors in a finitely deformed configuration are given along with the elasticity tensor and its specialization to the initially stressed undeformed configuration. The equations governing infinitesimal motions superimposed on a finite deformation are then used to study the combined effects of initial stress and finite deformation on the propagation of homogeneous plane waves in a homogeneously deformed and initially stressed solid of infinite extent. This general framework allows for various different specializations, which make contact with earlier works. In particular, connections with results derived within Biot's classical theory are highlighted. The general results are also specialized to the case of a small initial stress and a small pre-deformation, i.e. to the evaluation of the acoustoelastic effect. Here the formulas derived for the wave speeds cover the case of a second-order elastic solid without initial stress and subject to a uniaxial tension [Hughes and Kelly, Phys. Rev. 92 (1953) 1145] and are consistent with results for an undeformed solid subject to a residual stress [Man and Lu, J. Elasticity 17 (1987) 159]. These formulas provide a basis for acoustic evaluation of the second- and third-order elasticity constants and of the residual stresses. The results are further illustrated in respect of a prototype model of nonlinear elasticity with initial stress, allowing for both finite deformation and nonlinear dependence on the initial stress.     

基于POD-RBF代理模型的迭代更新反演方法

针对常规的水工大坝等大型工程结构参数反演需要耗费大量有限元正分析机时的问题,建立了具有较好反演精度和泛化性能的POD-RBF代理模型和快速迭代更新反演算法。基于有限元分析获得足量数据样本,利用POD提取本征向量,并使用RBF方法进行插值得到有限元模型的代理模型;同时结合粒子群算法的全局寻优能力和高斯-牛顿法的快速局部收敛优势,建立了一种新的高效率迭代反演方法,并应用于混凝土大坝分区弹性模量反演。结果表明,该方法适用于大坝等大体积混凝土结构的力学参数反演。同时,相较于传统的单一反演方法,该方法在反演效率和反演精度两方面均显示出优势。     

Exact statement of the instability problem for frames and its direct numerical solution

A general approach for the systematic evaluation of the critical buckling load and the determination of the buckling mode is presented. The Navier-Bernoulli beam model is considered, having the possibility of variable cross-section under any type of load (including pressures and thermal loading). With this purpose, the equilibrium equations of each beam element in its deformed configuration under the hypothesis of infinitesimal strains and displacements is considered, resulting in a system of differential equations with variable coefficients for each element. To obtain the nonlinear response of the frame, one should impose the compatibility of displacements and the equilibrium of forces and moments in each beam-end, also in the deformed configuration. The solution is obtained by requiring that the total variation of potential energy is zero at the instant of buckling. The objective of this work is to develop a systematic method to determine the critical buckling load and the bucklingmode of any frame without using the common simplifications usually assumed in matrix analysis or finite element approaches. This way, precise results can be obtained regardless of the discretization done.     

Nonlinear vibrations in beams and frames: The effect of the deformed equilibrium state

In the study of nonlinear vibrations of planar frames and beams with infinitesimal displacements and strains, the influence of the static displacements resulting from gravity effect and other conservative loads is usually disregarded. This paper discusses the effect of the deformed equilibrium configuration on the nonlinear vibrations through the analysis of two planar structures. Both structures present a two-to-one internal resonance and a primary response of the second mode. The equations of motion are reduced to two degrees of freedom and contain all geometrical and inertial nonlinear terms. These equations are derived by modal superposition with additional subsidiary conditions. In the two cases analyzed, the deformed equilibrium configuration virtually coincides with the undeformed configuration. Also, 2% is the maximum difference presented by the first two lower frequencies. The modes are practically coincident for the deformed and undeformed configurations. Nevertheless, the analysis of the frequency response curves clearly shows that the effect of the deformed equilibrium configuration produces a significant translation along the detuning factor axis. Such effect is even more important in the amplitude response curves. The phenomena represented by these curves may be distinct for the same excitation amplitude.     

Self-actuated snap back of viscoelastic pulsing structures

The effect of material viscoelasticity on the stability of structures is investigated. It is demonstrated that viscoelastic effects can cause structures to exhibit temporary bistability in a deformed configuration. When this bistability is lost, the structure may suddenly jump back to its initial configuration in a phenomenon described as self-actuated snap back. It is shown for both a single degree of freedom system and a hemispherical cap that the viscoelastic behaviour may be inferred by consideration of the purely elastic response. These inferences are confirmed by means of finite element analysis.