两种波浪理论下铰接塔平台的非线性运动特性分析

将铰接塔平台简化为底端具有线扭转弹簧支撑,顶端附有集中质量块的水中柔性梁.采用连续介质力学方法,在小变形假设下,应用大挠度理论建立了梁的非线性耦合运动控制方程和边界条件.基于Airy线性波理论和二阶Stokes波理论,应用Morison方程计算梁在水中所受的水动力.运用有限差分法和Runge-Kutta法得到了方程数值...     

基于当前构形的虚场方法识别正交各向异性材料力学参数

正交各向异性材料刚度矩阵随坐标系转动而变化,虚场方法中虚位移场的定义与数据点坐标有关,常用的基于参考构形全局坐标系的虚场方法直接忽略了变形过程中数据点的移动和材料坐标系转动,这样即使在弹性变形这样的小变形条件下也将导致材料力学参数识别结果不准确。针对上述问题该文提出用基于当前构形的虚场方法识别正交各向异性材料弹性力学参数,并用模拟试验验证了该方法的可靠性;定量地分析了数据点移动和转动对力学性能参数识别结果的影响,结果表明基于当前构形虚场方法,能够提高参数Q₁₂、Q₂₂识别的准确性。     

深基坑开挖的大变形有限元分析

本文建立了基于初始构形的大变形增量有际元方程，讨论了非线性方程的求解过程，在此基础上，首次运用大变形理论对深基坑开挖过程中的大变形问题进行了研究，作为对比，也进行了相同材料模型下的小变形理论分析，通过了对比分析，从数值结果上分析了用小变形理论研究基坑变形问题时，可能会产生的误差，并以此定量地确定了大，小变形理论适用范围。     

桩基贯入过程中土体大变形分析与流动机理研究

土体大变形问题是海洋岩土工程界研究的难点,由于其变形梯度较大、流动机理复杂等特点,常规的岩土工程分析方法在求解该问题时表现出明显的局限性。因此,该文研究了求解土体大变形问题的解析方法,即Strain Path Method （SPM）和Shallow Strain Path Method （SSPM）,详细介绍了这两种方法的计算原理;并基于大、小应变理论,采用SSPM分析了理想土性条件下桩基础贯入过程中周围土体的流动机理和位移场变化规律;最后,将SPM和SSPM计算结果进行比较分析,阐明了两者之间的内在关系。基于大应变理论,采用SSPM计算得到的土体位移场与Sagaseta给出的结果具有较好的一致性,验证了计算结果的准确性。研究结果显示桩端上部土体会发生隆起现象,而桩端附近及底部土体具有下沉的位移,且在贯入深度位置处,土体下沉位移达到最大值。在径向位置r/R=3（距桩壁1倍直径）处,基于大、小应变理论计算结果具有较好的一致性。研究成果有助于了解土体的大变形特性,也可为数值计算结果的校验提供基本数据。     

有限变形下闭孔泡沫铝的非线性压缩行为

基于Huang（北京大学）和Wang（北京大学）的理论和热力学第二定律,研究了有限变形下闭孔泡沫铝的非线性压缩行为。通过引入内变量及内变量的演化方程,给出了有限变形下同时考虑细观结构参数和黏性效应的有效幂律势函数及相应的应力表达式。基于所提出的理论模型,通过算例讨论了细观力学方法、孔隙度和黏性效应对泡沫铝应力-应变曲线的影响规律。结果表明:模型预测与实验结果基本一致,且随着黏性系数的增大,考虑黏性效应的模型预测趋向于未考虑黏性效应时的模型预测。      

考虑损伤的蠕变问题的变形场与损伤场

本文研究了考虑损伤的蠕变介质的变形场与损伤场的解。求得了下列三个问题的新解:(1)考虑损伤的指数律蠕变材料在小损伤条件下的变形场与损伤场;(2)幂律蠕变材料在大损伤条件下的裂纹尖端场;(3)全耦合蠕变损伤的圆柱扭转问题的变形场与损伤场,这三个新解均可用解析的形式表达。     

开式冷挤压成形深小锥孔件时极限变形程度的理论研究

给出了深小锥孔件开式冷挤压成形时极限变形程度的定义,建立了变形区非稳态连续速度场;利用上限原理得到了极限变形程度的理论判据.分析了各主要参数对极限变形程度的影响规律,对指导制定深小锥孔件开式冷挤压成形工艺具有重要意义.     

Levinson 矩形微板谐振器热弹性阻尼解析解

基于 Levinson 高阶剪切板理论,给出了四边简支微板谐振器热弹性耦合自由振动的复频率以及板内变温场的精确解析解;由复频率法给出了表征微板热弹性阻尼的逆品质因子;通过数值结果分析了 Levinson 微板的热弹性阻尼随几何尺寸和振动模态变化的规律,并与一阶剪切变形理论和经典板理论的预测结果进行了比较,分析了剪切变形对热弹性阻尼的影响程度。数值结果表明,对于中厚板和厚板谐振器,经典板理论预测的热弹性阻尼值明显大于剪切变形板理论的预测值。这是由于经典板理论忽略了横向剪切变形,从而过高地估计了微板的抗弯刚度。另外,在四边简支条件下,还给出了 Mindlin 微板和 Levinson 微板热弹性阻尼预测值之间的比较。结果表明,Levinson高阶剪切变形理论能够更好地预测厚板谐振器的热弹性阻尼。这是因为 Levinson 理论下的位移场能够精确满足上下表面应力为零的条件,温度场包含了厚度方向坐标的高阶项。     

有限变形下的后继屈服面演化规律研究

有限变形下的后继屈服面会出现膨胀或收缩,移动和畸变等变形特征。基于塑性变形的滑移机制,建立了适用于有限变形条件下的多晶塑性本构模型。提出了一种混合硬化假设,可以一致描述后继屈服面演化中的等向、运动和畸变硬化以及正或负交叉效应、包氏效应等。预测了2种加工硬化铝合金（A16061-T6511和annexed1100A1）分...     

两相介质大变形动力问题的数值模拟

基于Biot理论和u-p列式,推导了两相介质动力问题的控制方程。固相的位移和液相孔隙压力是两个基本的未知量。采用更新的Lagrangian方法和Jaumann应力对这一耦合问题进行了大变形分析。用建议的方法,对一饱和土柱在静力和动力荷载作用下的反应进行了数值模拟,并对大、小变形理论下的计算结果进行了对比。     

Theoretical modeling framework for an unsaturated freezing soil

Based on the authors' theoretical modeling framework of the saturated freezing soil, this paper further discusses the air phase in the unsaturated freezing soil in two ideal situations: air in the soil is linked to the atmosphere (the open porous medium) and air in the soil is isolated from the atmosphere (the sealed porous medium). The corresponding theoretical modeling framework for a multi-phase porous medium with interaction of water, heat and deformation is established in this paper. The proposed theoretical model is then extended to the general case (unsaturated half-open and half-sealed porous medium). Also, a finite element numerical solution to the heat-moisture-deformation coupling behavior of the unsaturated freezing soil is obtained. The computer software for solving this problem is also developed. The in-situ measurements for Hua Shixia highway roadbed located in Qinghai–Tibetan Plateau are introduced to compare with the numerical results obtained by the proposed model. The measurement results indicate that the numerical results for the temperature field variations with time are found to be in good correlation with the roadbed depth, just as the relative freezing deformations are correlated with road surface. Numerical modeling results, when compared to field measurements of temperature and deformation, are within 10 to 20%. The comparative analysis shows that proposed theoretical modeling framework and its numerical solution for the temperature–moisture-deformation coupling behavior is suitable and acceptable.     

Application of the finite element–difference method to vibration problems

The so-called finite element–difference method introduced in References 1 and 2 yields a continuous stress field by finite difference operations and finite element interpolations. In the present paper, applications of the method to vibration problems are discussed. The inverse iteration procedure is modified for this method. Numerical results show that the accuracy of solutions depends strongly on the type of finite difference operator chosen: for reliable and accurate solutions in modal analysis problems, element internal strains must be included in the strain field used to compute nodal forces associated with element deformations.     

无网格法在中心刚体-旋转柔性梁系统动力学分析中的应用EI北大核心CSCD

将无网格点插值法、径向基点插值法、光滑节点插值法用于中心刚体-旋转柔性梁的动力学分析。基于浮动坐标系方法,考虑梁的纵向拉伸变形和横向弯曲变形,并计入横向弯曲变形引起的纵向缩短,即非线性耦合项,运用第二类Lagrange方程推导得到作大范围运动的中心刚体-旋转柔性梁系统的动力学方程。将无网格法的仿真结果与有限元法和假设模态法进行比较分析,表明其作为一种柔性体离散方法在中心刚体-旋转柔性梁的刚柔耦合多体系统动力学的研究中具有可推广性。     

基于结点6自由度的分裂导线有限元模型

大跨越输电线路分裂导线较单导线更容易发生舞动现象,基于空间曲梁理论,建立了结点6自由度的导线有限元模型。假定间隔棒为刚性体,根据位移协调条件,建立了4分裂导线的有限元模型。通过虚功原理建立静力有限元方程,采用Newton-Raphson迭代法进行静力非线性求解。算例表明:采用曲梁模型研究输电线的平动位移是准确的。由于考虑了平动与扭转的耦合作用,扭转角的计算更加精确。输电线抗弯刚度对扭转角也有较大影响。分裂导线的参数分析表明,弧垂、分裂间距、边界条件等对抗扭刚度均有较大的影响,间隔棒的数量不能显著提高导线的抗扭刚度。     

一种基于应变插值大变形梁单元的刚-柔耦合动力学分析

柔性多体系统动力学中的“动力刚化”现象起因于变形间的耦合。一次近似模型成功地解决了小变形情况下的刚柔耦合建模问题,但在大变形情况下则需要考虑更多的耦合效应。本文选取表征梁弯曲应变的曲率和轴向应变作为单元参数进行离散;在大变形大转动基础上得到了单元两端节点运动学参数的递推关系,构造出了能够自动计及“动力刚化项”且适用于大变形刚柔耦合动力学分析的平面梁单元。最后采用本文所提应变插值单元求解了包含大变形和刚柔耦合动力学柔性梁的数值算例,验证了文中算法的正确性和有效性。     

Total Lagrangian formulation for the large displacement analysis of rectangular plates

In this paper, a method for the non-linear dynamic analysis of rectangular plates that undergo large rigid body motions and small elastic deformations is presented. The large rigid body displacement of the plate is defined by the translation and rotation of a selected plate reference. The small elastic deformation of the midplane is defined in the plate co-ordinate system using the assumptions of the classical theories of plates. Non-linear terms that represent the dynamic coupling between the rigid body displacement and the elastic deformation are presented in a closed form in terms of a set of time-invariant scalars and matrices that depend on the assumed displacement field of the plate. In this paper, the case of simple two-parameter screw displacement, where the rigid body translation and rotation of the plate reference are, respectively, along and about an axis fixed in space, is first considered. The non-linear dynamic equations that govern the most general and arbitrary motion of the plate are also presented and both lumped and consistent mass formulations are discussed. The non-linear dynamic formulation presented in this paper can be used to develop a total Lagrangian finite element formulation for plates in multibody systems consisting of interconnected structural elements.     

多层多道焊温度和热应力场对角变形影响分析

为探究Q235中厚板多层多道焊温度与热应力耦合场作用下对工件角变形的影响,利用有限元软件COMSOL对中厚板多层多道焊温度和热应力耦合场进行分析.通过建立中厚板多层多道焊温度与热应力耦合场模型,对工件不同方向温度场、热应力场的变化以及工件最终角变形情况进行模拟,并将模拟结果与相同工艺条件下焊接试验结果进行比较验证.结果表明：仿真分析结果与焊接实验结果具有较好的重合度;温度和热应力耦合场主要作用于工件的横向和纵向,对厚度方向的角变形影响较小.这为后续多层多道焊接角变形问题的进一步研究奠定了基础.     

A coupling extended multiscale finite element method for dynamic analysis of heterogeneous saturated porous media

A coupling extended multiscale finite element method (CEMsFEM) is developed for the dynamic analysis of heterogeneous saturated porous media. The coupling numerical base functions are constructed by a unified method with an equivalent stiffness matrix. To improve the computational accuracy, an additional coupling term that could reflect the interaction of the deformations among different directions is introduced into the numerical base functions. In addition, a kind of multi‐node coarse element is adopted to describe the complex high‐order deformation on the boundary of the coarse element for the two‐dimensional dynamic problem. The coarse element tests show that the coupling numerical base functions could not only take account of the interaction of the solid skeleton and the pore fluid but also consider the effect of the inertial force in the dynamic problems. On the other hand, based on the static balance condition of the coarse element, an improved downscaling technique is proposed to directly obtain the satisfying microscopic solutions in the CEMsFEM. Both one‐dimensional and two‐dimensional numerical examples of the heterogeneous saturated porous media are carried out, and the results verify the validity and the efficiency of the CEMsFEM by comparing with the conventional finite element method. Copyright © 2015 John Wiley & Sons, Ltd.     

A three-dimensional least-squares finite element technique for deformation analysis

The development of a three-dimensional least-squares finite element technique suitable for deformation analysis was presented. By adopting a spatial viewpoint, a consistent rate formulation that treats deformation as a process was established. The technique utilized the least-squares variational principle that minimizes the squares of errors encountered in any attempt to meet the field equations exactly. Both velocity and Cauchy stress rate fields were discretized by the same linear interpolation function. The discretization always yields a sparse, symmetric, and positive-definite coefficient matrix. A conjugate gradient iterative solver with incomplete-Choleski preconditioner was used to solve the resulting linear system of equations. Issues such as finite element formulation, mesh design, code efficiency, and time integration were addressed. A set of linear elastic problems was used for patch-test; both homogeneous and non-homogeneous deformations were considered. Additionally, two finite elastic deformation problems were analysed to gauge the overall performance of the technique. The results demonstrated the computational feasibility of a three-dimensional least-squares finite element technique for deformation analysis. © 1997 John Wiley & Sons, Ltd.     

The coupled radial–axial deformations analysis of flexible pipes conveying fluid

This paper presents large deformation analysis of pipes conveying fluid in which two complicated behaviours are taken into consideration. The first is the coupling between radial and axial deformations of pipe wall, and the other is the interaction between a deformed pipe and transported fluid having the variable internal flow velocity. The coupled radial–axial deformation theory of the pipes and the continuity theory of flow inside the moving deformed pipes are developed to undertake these coupling behaviours. All strong and weak forms of governing equations are obtained by carrying out the virtual work formulation. The hybrid‐finite element method is used to solve the highly non‐linear static problems, which configure the initial large deflection and large strain conditions of the pipes. The state‐space finite element model for use in analyses of non‐linear vibration and system stability is established as well as the suggested numerical solution procedures. The numerical studies of the pipes under circumstances of intense radial loads such as deep‐water risers demonstrate that even a slight change of the radial deformation has a significant effect in increasing non‐linear responses, and reducing stabilities of the pipes. Copyright © 2004 John Wiley & Sons, Ltd.