基于有限质点法的多尺度精细化分析

多尺度作为一种精细化分析的建模手段,能有效平衡结构分析中的计算效率和精度。有限质点法是一种能准确分析结构非线性行为的方法,在多种复杂行为分析中得到应用。该文利用有限质点法以质点为基本元素和显式积分的特点,基于梁、壳等低维单元的平截面假定,将多尺度连接处的质点分为主质点和从质点,集成从质点的质量、质量惯性矩阵、力、力矩等物理量至主质点,求解主质点运动方程后,由位移约束条件求得从质点位移,从而实现不同维度单元的多尺度连接。算例表明该多尺度方法对梁-壳、梁-固体及壳-固体的连接是有效的,在几何非线性及动力问题中具有良好的精度及稳定性,适合于结构复杂行为分析。     

考虑扭转作用的钢管混凝土纤维梁模型

通过引入纤维梁截面的正应变平截面假定和剪应变线性分布假定, 根据美国学者Hsu 提出的转角软化桁架模型中的混凝土材料二维本构关系, 从基本的材料力学原理出发, 推导了可考虑扭转作用的钢管混凝土纤维梁单元的本构关系求解流程。基于大型通用有限元程序ABAQUS 提供的用户自定义子程序UEL, 采用FORTRAN语言开发了可考虑扭转作用的钢管混凝土纤维梁模型, 能够模拟钢管混凝土柱在轴力-弯矩-扭矩复合受力下的全过程力学行为, 并可考虑任意加载路径。该文所开发的纤维梁模型具有较高的精度和求解效率。     

矩形钢管混凝土柱在扭矩作用下的截面剪应变场研究

对矩形截面钢管混凝土柱在纯扭和压扭荷载作用下的滞回性能进行了试验研究,得到了矩形截面钢管混凝土柱的扭矩-扭转角滞回曲线。基于材料力学基本原理建立了纤维梁截面扭率和纤维剪应变间的关系,进而对矩形截面钢管混凝土柱在扭矩作用下的截面剪应变场分布规律进行了分析,并建立了三维精细有限元模型进行精度验证,最后给出了钢管混凝土柱截面扭率和截面纤维剪应变间关系的矩阵表达,引入了考虑扭转效应的纤维梁模型,使该模型能够用于分析矩形截面钢管混凝土柱在扭矩作用下的非线性反应。与试验结果的对比表明,考虑扭转效应的纤维梁模型在分析矩形截面往复扭矩荷载作用下的受力行为时具有较高的求解精度和求解效率,可为分析不同类型结构体系在地震复杂受力状态下的动力反应提供依据。     

空间薄壁截面梁非线性有限单元模型

基于Timoshenko梁理论和Vlasov薄壁杆件理论,通过设置单元内部节点并对弯曲转角和翘曲角采取独立插值的方法,建立了可考虑横向剪切变形和扭转剪切变形及其耦合作用、弯扭耦合、以及二次剪应力影响的空间薄壁梁非线性有限元模型。以更新的拉格朗日格式描述的几何非线性应变推得几何刚度矩阵。同时考虑了材料非线性,假定材料为理想塑性体,服从Von Mises屈服准则和Prandtle-Reuss增量关系,采用有限分割法,由数值积分得到空间薄壁梁的弹塑性刚度矩阵。算例表明该文所建梁单元模型具有良好的精度,适用于空间薄壁结构的有限元分析。     

复合材料加筋板的大变形有限元分析

本文将考虑横向剪切变形的Mindlin's理论应用于复合材料加筋板的大变形分析,在Total-Lagrange坐标系下推导了八结点等参弯曲板单元和三结点等参梁单元的增量平衡方程和切线刚度矩阵,非线性问题采用增量法和Newton-Raphson迭代法相结合的方法求解.本文通过一些算例,证明了所采用单元具有良好的收敛性和足够的精度,并讨论了边界条件、纤维铺设角和加筋疏密等因素对复合材加料筋板非线性解的影响.     

Reddy高阶组合梁的非线性有限元分析

该文基于Reddy高阶梁理论,提出了小变形双层组合梁的隐式运动学假定;应用拉格朗日乘子法,将该隐式关系引入到组合梁的最小势能原理,得到了考虑各子梁和粘结滑移层非线性材料特性的高阶组合梁非线性位移法有限单元,且该单元可以容易地转化为非线性Timoshenko和Euler-Bernoulli组合梁有限单元。随后,该研究分别应用提出的Reddy、Timoshenko和Euler-Bernoulli组合梁有限单元对双跨连续钢-混凝土组合梁进行了准静力分析,考察剪切效应对组合梁构件的挠度、粘结层滑移和截面应力的影响,且参数分析了组合梁的跨高比对剪切效应的影响。参数分析表明:短粗组合梁结构往往表现出显著的剪切效应,Newmark假定不再适用。     

腹板开孔的钢-混凝土组合梁的挠度计算

描述了一种腹板开孔组合梁挠度的计算方法。提出了楼板参与开孔段上部截面抗弯的有效宽度的概念,并进行了拟合。将剪切变形和空腹桁架弦杆的弯曲变形合并为等效剪切变形,得到开孔段的等效剪切刚度。利用开孔段与未开孔段截面刚度不同的现象,建立分段梁单元模型,采用传统梁理论求解挠度计算公式。与采用实体单元和板壳单元的有限元分析结果的对比表明,该文公式具有很好的精度。     

基于静力凝聚的高精度变截面梁单元及其几何非线性分析研究

基于Euler-Bernoulli梁单元基本假定,通过静力凝聚获得截面特性沿单元轴向连续变化的变截面梁单元高精度刚度矩阵,并提出一种基于随动坐标法求解变截面梁杆结构大位移、大转动、小应变问题的新思路。首先依据插值理论和非线性有限元理论推导出三节点变截面梁单元的切线刚度矩阵,然后使用静力凝聚方法消除中间节点自由度,从而得到一种新型非线性两节点变截面梁单元。结合随动坐标法,在变形后位形上建立随动坐标系,得到变截面梁单元的大位移全量平衡方程。实例计算表明,该新型变截面梁单元具有较高的计算精度,可应用于变截面梁杆系统大位移几何非线性分析。     

空间钢框架精细塑性铰法高等分析

几何非线性单元的精度主要决定于单元恢复力的计算方法,刚度矩阵对单元精度的影响很小。建立了考虑剪切变形影响的精细塑性铰法空间梁柱单元。单元二阶效应由稳定函数考虑,采用精细塑性铰模型考虑材料非线性,可考虑截面的逐渐屈服以及由残余应力引起的分布塑性对单元刚度的削弱。单元刚度矩阵包含了轴向、弯曲和扭转位移之间的耦合效应。利用ANSYS软件的用户可编程特性(UPFs)编写了单元程序,通过连接将用户单元添加到ANSYS软件单元库中。算例分析结果表明,采用作者提出的单元时,每根杆件用一个单元模拟分析可达到很高精度,而采用ANSYS中BEAM189单元时,每根柱需3~4单元模拟才能达到合适的精度。分析结果还表明,多高层框架结构中构件剪切变形的影响不可忽略。     

剪力墙非线性分析单元MFBFE的理论及开发

纤维单元以其单元自身的优点被广泛使用于梁柱构件的非线性分析中,对于剪力墙构件,由于纤维单元采用平截面假定,忽略单元的截面剪切变形,会造成很大的误差。该文对基于力插值的纤维单元进行修正,将其引入到剪力墙构件的分析中,介绍了考虑截面剪切变形的修正基于力插值纤维单元(MFBFE)和材料单轴本构的形成,给出单元在OpenSees平台上的开发过程,特别是迭代过程中的非线性分析算法和OpenSees框架下单元和材料本构的实现方式。通过实例分析对MFBFE的应用效果进行检验,得到了两组6片剪力墙的水平低周往复模拟数据,与试验结果对比,可以认为试件模拟结果中各项抗震性能指标均与试验值相接近,单元分析精度较高。     

《薄壁Timoshenko梁弯扭耦合振动的动态有限元法》

通过直接求解单对称均匀薄壁Timoshenko梁单元弯扭耦合振动的运动微分方程,推导了其精确的动态刚度矩阵。在本文研究中考虑了弯扭耦合、翘曲刚度、转动惯量和剪切变形的影响。针对某弯扭耦合的薄壁梁算例,应用本文推导的动态刚度矩阵,采用自动Muller法和结合频率扫描法的二分法求解频率特征方程,计算了该薄壁梁的固有特性,并讨论了翘曲刚度、剪切变形和转动惯量对该弯扭耦合薄壁梁的固有频率和模态形状的影响。数值结果验证了本文方法的精确性和有效性,并指出随着模态阶次的增加,剪切变形、转动惯量和翘曲刚度对薄壁梁的固有特性的影响更加显著。     

Theory and numerics of three‐dimensional beams with elastoplastic material behaviour

A theory of space curved beams with arbitrary cross‐sections and an associated finite element formulation is presented. Within the present beam theory the reference point, the centroid, the centre of shear and the loading point are arbitrary points of the cross‐section. The beam strains are based on a kinematic assumption where torsion‐warping deformation is included. Each node of the derived finite element possesses seven degrees of freedom. The update of the rotational parameters at the finite element nodes is achieved in an additive way. Applying the isoparametric concept the kinematic quantities are approximated using Lagrangian interpolation functions. Since the reference curve lies arbitrarily with respect to the centroid the developed element can be used to discretize eccentric stiffener of shells. Due to the implemented constitutive equations for elastoplastic material behaviour the element can be used to evaluate the load‐carrying capacity of beam structures. Copyright © 2000 John Wiley & Sons, Ltd.     

Shear deformation effect in second-order analysis of frames subjected to variable axial loading

In this paper a boundary element method is developed for the second-order analysis of frames consisting of beams of arbitrary simply or multiply connected constant cross section, taking into account shear deformation effect. Each beam is subjected to an arbitrarily concentrated or distributed variable axial loading, while the shear loading is applied at the shear center of the cross section, avoiding in this way the induction of a twisting moment. To account for shear deformations, the concept of shear deformation coefficients is used. Three boundary value problems are formulated with respect to the beam deflection, the axial displacement and to a stress function and solved employing a BEM approach. The evaluation of the shear deformation coefficients is accomplished from the aforementioned stress function using only boundary integration. Numerical examples with great practical interest are worked out to illustrate the efficiency, the accuracy and the range of applications of the developed method. The influence of both the shear deformation effect and the variableness of the axial loading are remarkable.     

A 3D fibre beam-column element with shear modelling for the inelastic analysis of steel structures

A force-based fiber beam-column element is proposed for the capacity assessment of frame structures under high shear. The proposed element is suitable for the performance assessment of large scale steel structures, which are not flexure-dominated. The element formulation follows the assumptions of the Timoshenko beam theory, while its kinematics are obtained through the natural-mode method. The element state-determination phase, instead of uniaxial material laws, typically associated with fiber elements, is based on a three-dimensional law taking into consideration the interaction between axial, bending, shear and torsion. Numerical examples are presented confirming the accuracy and the computational efficiency of the proposed formulation under monotonic, cyclic and dynamic/seismic loading. Compared to experimental results and the results of detailed finite element models, excellent agreement is achieved.     

Timoshenko薄壁梁弯扭耦合振动的动态传递矩阵法

通过直接求解单对称均匀Timoshenko薄壁梁单元弯扭耦合振动的运动偏微分方程,导出了其自由振动时的动态传递矩阵,同时采用结合频率扫描法的二分法求解频率特征方程,并讨论了剪切变形和转动惯量对弯扭耦合Timoshenko薄壁梁的固有频率的影响.数值结果验证了本文方法在其适用范围内的精确性和有效性.     

Spectral element model for axially loaded bending–shear–torsion coupled composite Timoshenko beams

The use of frequency-dependent spectral element matrix (or exact dynamic stiffness matrix) in structural dynamics is known to provide extremely accurate solutions, while reducing the total number of degrees-of-freedom to resolve the computational and cost problems. Thus, in this paper, the spectral element model is developed for an axially loaded bending–shear–torsion coupled composite laminated beam which is represented by the Timoshenko beam model based on the first-order shear deformation theory. The high accuracy of the spectral element model is then numerically verified by comparing with exact theoretical solutions or the solutions obtained by conventional finite element method. For the numerical verification, the finite element model is also provided for the composite laminated beam.     

单拱面预应力混凝土系杆拱桥极限承载力分析

本文将系杆拱桥的拱肋离散为空间圆弧梁单元,基于拖带圆柱坐标推导格林应变张量,用平截面假定及三次插值函数描述圆弧梁单元位移模式,采用加权残值配点法消除剪力和薄膜力闭锁;现吊杆为二力杆单元。对于多室箱形梁系杆离散为梁段单元,考虑箱形梁翘曲、畸变、横向弯曲等。基于连续介质力学U．L．列式法建立系杆拱桥的平衡方程并考虑材料的非线性。根据分析模型编制了相应的计算程序,计算结果与实验结果一致,同时分析了单拱面系杆拱桥极限承载力的影响因素,并计算了一座实桥的极限承载力。     

基于协调翘曲场的开闭口混合薄壁截面杆件约束扭转一维有限元分析

开口及闭口薄壁杆件约束扭转问题已由经典Timoshenko和Benscoter理论解决。然而,开闭口混合薄壁截面杆件约束扭转分析必须考虑开、闭口部分翘曲能力的差异,翘曲剪流形成机理有待进一步研究。该文假定开、闭口截面翘曲分别满足Vlasov和Umanskii假定,考虑开、闭口截面公共节点翘曲连续性要求,建立含有待定翘曲参数的协调翘曲模型。由截面受力平衡,确定翘曲参数显式列式,提出开闭口混合薄壁截面杆件约束扭转分析的一维有限元模型。算例及参数分析结果表明,基于Umanskii第二理论的I类方法在悬臂板及闭口周边引入附加剪流,影响翘曲剪应力精度。基于Umanskii第二理论的II类方法只能计算截面板件平均剪应力,无法反映真实翘曲剪流分布。基于Vlasov约束扭转假定的Beam-189单元忽略闭口周边约束效应产生的附加翘曲及剪流,影响翘曲正应力和剪应力精度。该文方法与Shell-63单元能得到基本吻合的变形与应力结果,说明一维梁元能正确反映开闭口混合薄壁截面杆件约束扭转及翘曲刚度。     

A BEM solution to transverse shear loading of beams

In this paper a boundary element method is developed for the solution of the general transverse shear loading problem of beams of arbitrary simply or multiply connected constant cross section. The analysis of the beam is accomplished with respect to a coordinate system that has its origin at the centroid of the cross section, while its axes are not necessarily the principal ones. The transverse shear loading is applied at the shear center of the cross section, avoiding in this way the induction of a twisting moment. Two boundary value problems that take into account the effect of Poisson’s ratio are formulated with respect to stress functions and solved employing a pure BEM approach, that is only boundary discretization is used. The evaluation of the transverse shear stresses at any interior point is accomplished by direct differentiation of these stress functions, while both the coordinates of the shear center and the shear deformation coefficients are obtained from these functions using only boundary integration. Numerical examples with great practical interest are worked out to illustrate the efficiency, the accuracy and the range of applications of the developed method. The accuracy of the proposed shear deformation coefficients compared with those obtained from a 3-D FEM solution of the ‘exact’ elastic beam theory is remarkable.