建立基于力的变截面梁单元质量矩阵的新方法

基于位移的有限梁单元中三次Hermite插值函数不能有效地描述变截面梁单元内部位移变化,只能通过加密网格增加单元数解决,会造成计算量增大。基于力的有限梁单元由于使用的力插值函数不受截面形状变化的影响,在处理变截面梁时有很大优势,可以得到精确的位移插值函数,利用较少的单元可以达到很高的精度,解决了基于位移的有限梁单元在处理变截面梁时的不足。本文得到了考虑剪切变形的位移插值函数和考虑转动惯量的一致质量矩阵。利用算例验证了本文理论的正确性和高效性。     

A NEW SPATIAL THIN-WALLED BEAM ELEMENT INCLUDING TRANSVERSE AND TORSIONAL SHEAR DEFORMATION

基于Timoshenko梁及Benscoter薄壁杆件理论,建立了考虑剪切变形、弯扭耦合以及翘曲剪应力影响的空间任意开闭口薄壁截面梁单元. 通过引入单元内部结点,对弯曲转角和翘曲角采用三节点Lagrange独立插值的方法,考虑了剪切变形和翘曲剪应力的影响并避免了横向剪切锁死问题;借助载荷作用下薄壁梁的截面运动分析,在位移和应变方程中考虑了弯扭耦合的影响. 通过数值算例将该单元的计算结果与理论解以及商用有限元软件和其他文献中的数值解进行对比和验证,结果对比表明该薄壁梁单元具有良好的精度和收敛性.     

考虑剪切效应的旋转FGM楔形梁刚柔耦合动力学建模与仿真

本文对一类中心刚体-柔性梁系统在大范围转动下的刚柔耦合动力学问题进行了研究. 柔性梁为功能梯度材料(functionally graded materials, FGM)楔形变截面梁,材料体积分数在梁轴向呈幂律分布变化. 以弧长坐标来描述柔性FGM梁的几何位移关系,分别使用倾角和拉伸应变变量描述柔性梁的横向弯曲和纵向拉伸变形,并计及剪切效应. 采用假设模态法离散变形场,运用第二类拉格朗日方程进行方程推导,得到系统考虑剪切效应的刚柔耦合动力学模型. 基于全新的刚柔耦合动力学建模理论,研究不同轴向材料梯度分布的FGM楔形梁,通过数值仿真计算,分析讨论不同的转速、梯度分布规律以及变截面参数对系统动力学特性的影响. 结果表明,剪切效应对大高跨比的FGM楔形梁的变形影响较为明显,不容忽略;材料梯度分布规律和截面参数的选取均会对旋转FGM楔形梁的动力学响应和频率产生较大影响. 本文提出的考虑剪切效应的倾角刚柔耦合动力学模型是对以往非剪切模型的进一步完善,可应用于工程中的 Timoshenko梁结构的动力学问题求解.      

考虑剪切效应的旋转FGM楔形梁刚柔耦合动力学建模与仿真

本文对一类中心刚体-柔性梁系统在大范围转动下的刚柔耦合动力学问题进行了研究.柔性梁为功能梯度材料(functionally graded materials,FGM)楔形变截面梁,材料体积分数在梁轴向呈幂律分布变化.以弧长坐标来描述柔性FGM梁的几何位移关系,分别使用倾角和拉伸应变变量描述柔性梁的横向弯曲和纵向拉伸变形,并计及剪切效应.采用假设模态法离散变形场,运用第二类拉格朗日方程进行方程推导,得到系统考虑剪切效应的刚柔耦合动力学模型.基于全新的刚柔耦合动力学建模理论,研究不同轴向材料梯度分布的FGM楔形梁,通过数值仿真计算,分析讨论不同的转速、梯度分布规律以及变截面参数对系统动力学特性的影响.结果表明,剪切效应对大高跨比的FGM楔形梁的变形影响较为明显,不容忽略;材料梯度分布规律和截面参数的选取均会对旋转FGM楔形梁的动力学响应和频率产生较大影响.本文提出的考虑剪切效应的倾角刚柔耦合动力学模型是对以往非剪切模型的进一步完善,可应用于工程中的Timoshenko梁结构的动力学问题求解.     

作大范围空间运动柔性梁的刚-柔耦合动力学

研究带中心刚体的作大范围空间运动梁的刚-柔耦合动力学问题．从精确的应变-位移关系式出发，在动力学变分方程中，考虑了横截面转动的惯性力偶和与扭转变形有关的弹性力的虚功率，用速度变分原理建立了考虑几何非线性的空间梁的刚-柔耦合动力学方程，用有限元法进行离散．通过对空间梁系统的数值仿真研究扭转变形和截面转动惯量对系统动力学性态的影响．     

中心刚体-变截面梁系统的动力学特性研究

对在平面内做大范围转动的中心刚体-变截面梁系统的动力学进行了研究.考虑柔性梁横向弯曲变形和纵向伸长变形, 且在纵向位移中计及由于横向变形而引起的纵向缩短项, 即非线性耦合变形项. 采用假设模态法描述变形, 运用第二类Lagrange方程推导得到系统刚柔耦合动力学方程. 在此基础上对做大范围旋转运动的中心刚体-楔形梁以及中心刚体-梯形梁模型的动力学进行了详细研究. 研究表明: 梁宽比、梁高比以及梯形梁变截面位置都对系统的动力学特性有很大影响.      

中性线修正型变截面梁类构件压电控制

传统绝对节点坐标法(absolute nodal coordinate formulation,ANCF)在变截面梁类构件建模过程中常以几何中位线等效构造单元中性线,难以对变截面单元位移场状态进行精确描述.为解决此类问题,本文以中细型变截面梁类构件为研究对象,深入考虑变截面结构几何因素及复合材料属性对变截面梁类构件中性...     

中心刚体-柔性梁系统的耦合变形影响

本文对作大范围运动的中心刚体-柔性梁系统的耦合变形的影响进行研究.给出一种新的描述柔性梁耦合变形的有限元插值方法,该方法采用笛卡尔变形坐标对横向变形和纵向变形之间的耦合项进行描述,该耦合变形项只与本单元的节点变形坐标相关.分别讨论了耦合变形项对惯性力与弹性力的贡献,分析了它们对刚-柔耦合动力学行为的影响.通过研究指出当采用笛卡尔变形坐标描述时,如果在计算弹性力的时候考虑了耦合变形影响,无论在计算惯性力时是否考虑耦合变形影响,都可以得到稳定收敛的结果.反之,如果在计算弹性力时忽略了耦合变形影响,无论在计算惯性力时是否考虑耦合变形影响,当大范围运动的速度较高时,将会得到错误的发散的结果.因此,通过忽略耦合变形对质量分布的影响,只保留耦合变形对弹性力的影响,可实现对动力学方程的简化.     

旋转楔形-回形梁的高次动力学建模和末端变形分析

对四种不同结构中心刚体-柔性Euler Bernoulli梁系统进行刚柔耦合动力学分析．其中以等截面梁、变截面梁、等截面回形梁、变截面回形梁为对象，研究楔形梁及回形梁对系统的末端变形位移影响．变截面梁的宽高尺寸沿着轴向线性变化．梁的变形包含了轴向、横向、耦合变形项（横向弯曲引起的纵向缩短）．采用假设模态法和第二类Lagrange方程建立系统的动力学方程，并用C++编写软件进行动力学仿真．研究表明：在相同条件下，梁的截面尺寸及空心部分对梁末端变形位移影响十分明显，且当梁在较大变形情况下，该高次耦合模型依然能得到正确的结果，因此在针对实际结构建模时，建立符合实际截面的模型至关重要．     

基于绝对节点坐标法的平面梁有限变形下变形重构

现有的对有限变形条件下柔性结构变形重构的研究往往单纯基于曲率与应变间的几何关系, 同时忽略了被测体的纵向变形及其与弯曲变形的耦合效应. 为得到一种更加精确且能借助现有的力学工具进行应用方向扩展的变形重构方法, 以平面梁为对象, 借鉴变形重构逆有限元法的思想, 将平面梁的变形重构问题视作一类最优化问题. 首先, 通过引入绝对节点坐标法(absolute nodal coordinate formulation, ANCF)对柔性结构大变形下非线性的平面梁应变?位移关系进行精确描述, 构造了一种逆梯度缩减ANCF平面索梁单元. 然后, 对此逆ANCF单元进行改进, 在简化节点自由度的同时通过引入罚函数确保单元节点处的曲率连续性, 既保证了本问题的适定性, 也提升了最终解的精确性. 最后, 基于该单元利用Newton法构造了平面梁有限变形下变形重构问题的两种求解算法, 即逐单元算法和多单元整体算法, 以实现不同需求下的稳定求解. 数值仿真结果表明, 本方法在大变形条件下的变形重构误差小于1%, 而且在测点较少的情况下依然保持较高的精度, 同时验证了本方法的收敛性与计算效率.      

A New Flexible Multibody Beam Element Based on the Absolute Nodal Coordinate Formulation Using the Global Shape Function and the Analytical Mode Shape Function

Several techniques for the reduced dimensionality of finite elementformulations were considered as component mode reduction methods in themiddle sixties. These techniques are widely used in flexiblemultibody simulations for solving small deformation problems. Theabsolute nodal coordinate formulation for solving large rotation anddeformation problems has been established as a full finite elementmethod instead of using similar kinds of reduction techniques. In thispaper, a reduced order absolute nodal coordinate formulation is newlyestablished by introducing the global beam shape function and theanalytical deformation modes as a full finite element. This formulationleads to a constant and symmetric mass matrix as the conventionalabsolute nodal coordinate formulation, and makes it possible to reducethe number of elements and system coordinates of the beam structurewhich undergoes large rotations and large deformations. Numericalexamples show that the excellent agreements between thepresent formulation and the conventional absolute nodal coordinateformulation using a large number of elements are examined. These results demonstratethat the present formulation has high accuracy in the sense that thepresent solutions are similar to the conventional ones with fewersystem coordinates, and high efficiency in computation.     

带转动自由度的内参型非协调元研究

非协调元虽然破坏了单元间位移的连续性，却能很好地反映弯曲类变形，然而在不增加单元结点自由度的情况下，非协调元的计算精度总是滞留在某一水平，无法得到较大改变。基于修正后的位移型Reissner泛函中引入独立转动场的变分原理，采用连续介质力学中的转动自由度的定义，转动场采用结点真实转角来插值，结合平面四结点单元讨论了有效附加非协调位移的合理形式，引入了适用于任何四边形单元的非协调位移函数，从而建立了一种带转动自由度的平面四结点内参型非协调元模型。本文单元能通过分片检验，并易于与带转动自由度的梁单元相容．教值算例表明具有较高的计算精度。     

刚体单元及其在多体系统动力学中的应用

多体系统动力学分析软件要求人工输入形状复杂物体的质量、质心位置和转动惯量,而实际上这些参量并不容易获得。本文探索了一种以组成物体的刚体单元为基本要素的新方法,并结合实际需要具体构造了刚性四面体和刚性梁单元。以刚体单元为基础并内嵌网格剖分模块的分析软件能够自动获得这些参数,从而具备处理任何复杂系统的能力。仿真结果的对比分...     

ANCF/CRBF平面梁闭锁问题及闭锁缓解研究

本文系统地研究了基于一致旋转场列式的绝对节点坐标 (ANCF consistentrotation-based formulation, ANCF/CRBF)平面梁单元的泊松闭锁问题及闭锁缓解技术.为了全面理解该类型单元的闭锁特性及明确单元的应用范围,文中首先开发了两种新的ANCF/CRBF刚性截面梁单元, 新单元在ANCF全参数梁的基础上,对梯度向量施加正交矩阵约束, 得到梯度与转角对时间导数之间的速度转换矩阵,从而引入转角参数. 新单元节点处完全消除了泊松闭锁和剪切效应,这是与传统ANCF/CRBF刚性截面梁单元的不同之处. 然后,对比分析了这三种ANCF/CRBF刚性截面梁单元泊松闭锁的特点.发现该类型单元对节点的横向梯度施加了运动学约束, 导致节点处截面不能变形,无法捕捉泊松效应, 但是单元内部能完全捕捉,这种不连续情况会加重单元整体的泊松闭锁问题. 并且发现对单元梯度约束的越多,闭锁问题越严重. 随后, 分别采用两种闭锁缓解技术, 弹性线方法和应变分解方法,进一步研究了单元的收敛性. 最终,通过多种静力学和动力学测试研究了泊松闭锁对ANCF/CRBF平面梁单元计算精度的影响及闭锁缓解技术在该类型单元上的缓解效果.      

Mechanics and fracture of crack tip deformable bi-material interface

Novel interface deformable bi-layer beam theory is developed to account for local effects at crack tip of bi-material interface by modeling a bi-layer composite beam as two separate shear deformable sub-layers with consideration of crack tip deformation. Unlike the sub-layer model in the literature in which the crack tip deformations under the interface peel and shear stresses are ignored and thus a “rigid” joint is used, the present study introduces two interface compliances to account for the effect of interface stresses on the crack tip deformation which is referred to as the elastic foundation effect; thus a flexible condition along the interface is considered. Closed-form solutions of resultant forces, deformations, and interface stresses are obtained for each sub-layer in the bi-layer beam, of which the local effects at the crack tip are demonstrated. In this study, an elastic deformable crack tip model is presented for the first time which can improve the split beam solution. The present model is in excellent agreements with analytical 2-D continuum solutions and finite element analyses. The resulting crack tip rotation is then used to calculate the energy release rate (ERR) and stress intensity factor (SIF) of interface fracture in bi-layer materials. Explicit closed-form solutions for ERR and SIF are obtained for which both the transverse shear and crack tip deformation effects are accounted. Compared to the full continuum elasticity analysis, such as finite element analysis, the present solutions are much explicit, more applicable, while comparable in accuracy. Further, the concept of deformable crack tip model can be applied to other bi-layer beam analyses (e.g., delamination buckling and vibration, etc.).     

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考虑共面载荷作用时薄壁蜂窝铝孔壁的弯曲、伸缩和剪切变形,基于Timoshenko粱理论精 确推导出了其共面弹性模量的计算公式,并利用壳单元设计了利用蜂窝铝特征单元来求共异 面弹性模量的有限元方法. 对厂家提供的两种蜂窝样品分别利用理论和有限元法进行了计算, 计算结果和实验数据相吻合,证明理论公式和有限元法的正确性. 最后就结构参数对蜂窝铝 各弹性模量相关材料效率的影响规律进行了分析.     

基于开放式结构有限元系统 SiPESC.FEMS平板壳单元研发

基于开放式结构有限元系统SiPESC.FEMS的单元计算模块的设计模式,研发设计一种通用的平板壳单元计算框架。考虑板壳单元的组合关系和程序编制过程中的重用性及灵活性等特点,采用了软件设计中的构造器(Builder)模式实现不同的组合单元。本框架具有很好的通用性和可扩展性,为有限元程序研发提供了一个新的方式;同时,系统能够处理复杂荷载和边界条件,并可灵活实现不同类型单元的组合分析。本文利用此方法构造五种平板壳单元,通过数值算例分析对比讨论其性能,为选取合适的平板壳单元类型进行结构数值分析提供参考。     

An efficient procedure to find shape functions and stiffness matrices of nonprismatic Euler–Bernoulli and Timoshenko beam elements

Nonprismatic beam modeling is an important issue in structural engineering, not only for versatile applicability the tapered beams do have in engineering structures, but also for their unique potential to simulate different kinds of material or geometrical variations such as crack appearing or spreading of plasticity along the beam. In this paper, a new procedure is proposed to find the exact shape functions and stiffness matrices of nonprismatic beam elements for the Euler–Bernoulli and Timoshenko formulations. The variations dealt with here include both tapering and abrupt jumps in section parameters along the beam element. The proposed procedure has found a simple structure, due to two special approaches: The separation of rigid body motions, which do not store strain energy, from other strain states, which store strain energy, and finding strain interpolating functions rather than the shape functions which suffer complex representation. Strain interpolating functions involve low-order polynomials and can suitably track the variations along the beam element. The proposed procedure is implemented to model nonprismatic Euler–Bernoulli and Timoshenko beam elements, and is verified by different numerical examples.     

Advancements in subsea riser analysis using quasi-rotations and the Newton–Raphson method

Beam structures undergoing finite deflections and rotations in space have extensive application in the subsea industry particularly for the analysis of holistic systems with larger numbers of mooring and riser components. In using the finite element analysis approach, there is an increasing requirement for large element sizes which preserve accuracy with regard to the coupling of axial, bending and torsion response.The authors outline a method for improving the current state of practice for the analysis of riser systems. The approach draws on the convected coordinates method, Euler–Bernoulli beam theory, the principle of virtual work and the finite element method. Two quasi-rotation measures are developed including a quasi-material rotation definition for rotational deformation relative to the convected axis of a beam and a quasi-space rotation definition to deal with the path dependent nature of rotations in three dimensions.The novel aspect of this work is to relate the rate of change of the quasi-material rotation vector along the beam axis to a linear transformation of the beam axis rate-of-rotation vector through utilising the convected coordinates axes system. In this way, incremental values of quasi-material rotation are directly linked to incremental values of nodal quasi-space rotation and a global Newton–Raphson solution technique for interconnecting beam elements is straightforward to assemble.Furthermore, this leads to accurate definitions of coupled axial, bending and torque response for beams with significant deflection. The approach has particular advantages in the analysis of subsea riser sections. Also, the accuracy of the solution is preserved for a fewer number of elements compared to alternative solutions for computationally sensitive load cases with highly non-linear loading regimes.     

Geometrically exact beam theory without Euler angles

In modeling highly flexible beams undergoing arbitrary rigid–elastic deformations, difficulties exist in describing large rotations using rotational variables, including three Euler angles, two Euler angles, one principal rotation angle plus three direction cosines of the principal rotation axis, four Euler parameters, three Rodrigues parameters, and three modified Rodrigues parameters. The main problem is that such rotational variables are either sequence-dependent and/or spatially discontinuous because they are not mechanics-based variables. Hence, they are not appropriate for use as nodal degrees of freedom in total-Lagrangian finite-element modeling. Moreover, it is difficult to apply boundary conditions on such discontinuous and/or sequence-dependent rotational variables. This paper presents a new geometrically exact beam theory that uses no rotation variables and has no singular points in the spatial domain. The theory fully accounts for geometric nonlinearities and initial curvatures by using Jaumann strains, exact coordinate transformations, and orthogonal virtual rotations. The derivations are presented in detail, fully nonlinear governing equations and boundary conditions are presented, a finite element formulation is included, and the corresponding governing equations for numerically exact analysis using a multiple shooting method is also derived. Numerical examples are used to illustrate the problems of using rotational variables and to demonstrate the accuracy of the proposed geometrically exact displacement-based beam theory.