钢管混凝土结构材料非线性的一种有限元分析方法

为了更简单地考虑梁单元的材料非线性受力性能,把断面广义力和广义应变的概念运用于单元分析中,将单元的弹塑性刚度矩阵分离为弹性刚度矩阵和塑性刚度矩阵。这样,梁单元的变形可以由弹性变形和塑性变形简单地迭加,结构内力可通过弹性应变能的斜率(弹性刚度矩阵)与位移的乘积求得,从而在增量-迭代计算时可较准确且较快地计算出结构变形后的不平衡力。应用这一计算方法,推导了基于纤维模型的三维梁单元的钢管混凝土结构的有限元基本公式,并将其植入能考虑几何非线性的三维梁单元非线性计算程序NL_Beam3D中以计算结构的双重非线性问题。算例分析表明该方法和程序能较准确地反映钢管混凝土结构的双重非线性特性。     

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。     

基于场一致性的可带铰空间梁元几何非线性分析

虽然关于几何非线性分析的空间梁单元研究成果较多,但这些单元均是基于几何一致性得到的单元刚度矩阵,而基于场一致性的单元研究则较少,该文基于局部坐标系(随转坐标系)下扣除结构位移中的刚体位移得到的结构变形与结构坐标系下的总位移的关系,直接利用微分方法导出两者增量位移之间的关系,再基于场一致性原则,最终获得空间梁单元在大转动、小应变条件下的几何非线性单元切线刚度矩阵,在此基础上根据带铰梁端受力特征,导出了能考虑梁端带铰的单元切线刚度矩阵表达式,利用该文的研究成果编制了程序,对多个梁端带铰和不带铰的算例进行了空间几何非线性分析,计算结果表明这种非线性单元列式的正确性,实用价值较强。     

混杂CFRP/GFRP筋HPC梁的非线性梁壳组合单元研究

对于混杂CFRP/GFRP筋高性能混凝土（HPC）梁, 研究一种新的三维非线性梁壳组合单元, 对HPC梁进行了全过程分析。引入实体退化壳单元理论, 利用空间梁单元模拟预应力CFRP筋, 并根据CFRP筋单元节点线位移和转角位移的协调性, 推导CFRP筋单元对梁壳组合单元刚度矩阵的贡献, 同时对GFRP筋和HPC梁采用分层壳单元模拟。并运用Jiang屈服准则、 Madrid强化准则等描述混凝土的材料非线性, 提出一种新的非线性梁壳组合单元, 研制相应的三维非线性计算程序。计算结果与试验数据吻合良好, 说明本文构造的非线性梁壳组合单元的正确性和研制程序的可靠性, 以及混凝土材料非线性描述的合理性; 采用组合单元能准确模拟CFRP筋的几何构形, 能综合考虑其拉压弯剪性能, 利于全面地反映配筋对结构的增强作用。      

考虑剪切效应三维纤维梁单元的几何非线性增量有限元分析

该文以三维连续介质力学和虚功原理为基础,推导了增量U.L.有限元列式,该列式保留了大位移刚度矩阵项,并对该刚度矩阵进行修正使其成为对称矩阵。根据增量U.L.列式,推导了三维纤维梁单元的刚度矩阵。该单元采用平截面假定,以轴向节点位移表示截面上任意一点的位移,并结合Timoshenko梁理论来考虑剪切效应。以上原理编制分析程序,通过几个算例分析,证明了该方法的精确性、通用性。     

组合构件双重非线性分析模型研究与应用

以超高层建筑中当前广泛应用的杆系组合构件为研究对象,采用三维空间梁单元对其进行复杂受力状态下的双重非线性分析。为贴近实际工程同时简化计算,首先根据有限元方法和最小势能原理建立单元考虑几何非线性的弹性切线刚度矩阵;然后通过划分截面广义应变将单元截面刚度矩阵分离为弹性刚度矩阵与塑性刚度矩阵,在假定广义应变增量分布状态基础上,基于纤维模型法推导出单元塑性刚度矩阵;最后将考虑几何非线性的弹性刚度矩阵与塑性刚度矩阵集合成整体刚度矩阵,根据构件自身特性选取合理材料本构关系及数值计算方法进行构件非线性受力分析。数值分析结果表明,该文模型与方法概念清晰、计算精度高,还可应用于钢筋混凝土构件的受力性能非线性分析。     

空间钢框架结构的改进双重非线性分析

为了探讨三维结构的高等分析方法,给出基于UL法的严格三维单元虚功增量方程,详细推导了考虑剪切变形影响的三维梁柱单元的几何非线性切线刚度矩阵和基于三维单元简化塑性区模型的双重非线性刚度方程,并编制空间钢框架结构的双重非线性分析程序。使用包括几何与材料双重非线性的数值算例来验证方法和计算机程序的可行性、精确度与有效性。利用该程序,只需一个单元/构件即可准确预测空间钢框架结构的极限承载力与失稳模态,提高了结构的非线性分析效率。     

基于共旋法与稳定函数的几何非线性平面梁单元

建立一个准确、高效的几何非线性梁单元对于描述杆系结构的非线性行为至关重要。该文基于共旋坐标法和稳定函数提出了一种几何非线性平面梁单元。该单元在形成中把变形和刚体位移分开,局部坐标系内采用稳定函数以考虑单元P-δ效应的影响,从局部坐标系到结构坐标系的转换则采用共旋坐标法以及微分以考虑几何非线性,给出了几何非线性平面梁单元在结构坐标系下的全量平衡方程和切线刚度矩阵;在此基础上根据带铰梁端弯矩为零的受力特征,导出了能考虑梁端带铰的单元切线刚度矩阵表达式。通过多个典型算例验证了算法与程序的正确性、计算精度和效率。     

改进共旋坐标法的Timoshenko梁单元非线性分析

为提高空间Timoshenko梁单元非线性问题的计算精度,在共旋坐标法的基础上,提出了一种改进的Timoshenko梁单元几何非线性分析方法。利用虚功原理得到改进空间梁单元的刚度矩阵;使用有限质点法中的逆向运动思路计算单元局部坐标系下的刚体旋转矩阵;根据整体坐标系与局部坐标系之间旋转角度的转化以及微分关系,求得空间梁单元的切线刚度矩阵;编制了相应的有限元程序,对多个经典的大变形结构进行几何非线性分析。计算结果印证了该文所提出改进方法的正确性,同时与传统共旋坐标法相比,具有更高的精度。     

基于混合单元法的预应力混凝土梁非线性分析

利用共旋坐标法提出了一种预应力钢筋混凝土梁非线性分析的混合单元模型,在随转坐标系内,采用分层梁单元来模拟混凝土结构,带初应变的杆单元来模拟预应力钢筋,预应力钢筋杆元和混凝土梁元的变形协调则通过非线性刚臂来实现,通过刚臂单元两端节点位移和力的关系形成预应力钢筋对混合单元刚度矩阵的贡献,从而导出随转坐标系下预应力混凝土梁考虑材料非线性的切线刚度矩阵,几何非线性则由单元随转坐标系到结构坐标系的转换矩阵及其微分来体现,从而获得结构坐标系下混合单元模型的几何与材料双非线性切线刚度矩阵。数个钢筋混凝土及预应力钢筋混凝土梁非线性分析算例表明:所提出的混合单元模型能较好地分析预应力钢筋混凝土梁非线性性能,具有一定的实用价值。     

Effect of on-axis tensile loading on shear properties of an orthogonal 3D woven SiC/SiC composite

The present study examines in-plane and out-of-plane shear properties of an orthogonal 3D woven SiC fiber/SiC matrix composite. A composite beam with rectangular cross-section was subjected to a small torsional moment, and the torsional rigidities were measured using an optical lever. Based on the Lekhnitskii’s equation (Saint–Venant torsion theory) for a orthotropic material, the in-plane and out-of-plane shear moduli were simultaneously calculated. The estimated in-plane shear modulus agreed with the modulus measured from ±45° off-axis tensile testing. The effect of on-axis (0°/90°) tensile stress on the shear stiffness properties was also investigated by the repeated torsional tests after step-wise tensile loading. Both in-plane and out-of-plane shear moduli decreased by about 50% with increasing the on-axis tensile stress, and it is mainly due to the transverse crack propagation in 90° fiber bundles and matrix cracking in 0° fiber bundles. It was demonstrated that the torsional test is an effective method to estimate out-of-plane shear modulus of ceramic matrix composites, because a thick specimen is not required.     

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。     

Free vibration analysis of arches using curved beam elements

The natural frequencies and mode shapes for the radial (in‐plane) bending vibrations of the uniform circular arches were investigated by means of the finite arch (curved beam) elements. Instead of the complicated explicit shape functions of the arch element given by the existing literature, the simple implicit shape functions associated with the tangential, radial (or normal) and rotational displacements of the arch element were derived and presented in matrix form. Based on the relationship between the nodal forces and the nodal displacements of a two‐node six‐degree‐of‐freedom arch element, the elemental stiffness matrix was derived, and based on the equation of kinetic energy and the implicit shape functions of an arch element the elemental consistent mass matrix with rotary inertia effect considered was obtained. Assembly of the foregoing elemental property matrices yields the overall stiffness and mass matrices of the complete curved beam. The standard techniques were used to determine the natural frequencies and mode shapes for the curved beam with various boundary conditions and subtended angles. In addition to the typical circular arches with constant curvatures, a hybrid beam constructed by using an arch segment connected with a straight beam segment at each of its two ends was also studied. For simplicity, a lumped mass model for the arch element was also presented. All numerical results were compared with the existing literature or those obtained from the finite element method based on the conventional straight beam element and good agreements were achieved. Copyright © 2003 John Wiley & Sons, Ltd.     

采油井架钢结构非线性力学行为分析

本文对采油井架钢结构进行了非线性有限元分析。采用空间梁单元,通过包含单元几何刚度阵和变形刚度阵的增量切线刚度法考虑大变形问题;用杆端集中塑性法来简化材料非线性;采用弧长法迭代计算,最终可得到考虑几何和材料双重非线性情况下,井架钢结构的极限承载力。文中最后给出了A型采油井架的算例。     

分裂导线舞动非线性有限元分析方法

采用具有三个平动自由度和一个扭转自由度的三节点等参单元离散覆冰导线,用欧拉梁单元离散间隔棒,考虑覆冰导线所受空气动力的非线性和导线大幅运动的几何非线性,利用虚功原理建立覆冰分裂导线非线性有限元方程。用Newmark时间积分和Newton-Raphson非线性迭代法求解有限元方程。编制了相应的计算程序,通过算例验证了方法和程序的正确性。进一步利用由风洞实验获得的覆冰四分裂导线的空气动力系数,模拟研究具有不同档距的覆冰四分裂线路的舞动,为舞动防止技术的研究提供参考。所给出的方法适用于任意多分裂导线的舞动研究。     

Effects of approximations in analyses of beams of open thin‐walled cross‐section—part I: Flexural–torsional stability

In formulating a finite element model for the flexural–torsional stability and 3‐D non‐linear analyses of thin‐walled beams, a rotation matrix is usually used to obtain the non‐linear strain–displacement relationships. Because of the coupling between displacements, twist rotations and their derivatives, the components of the rotation matrix are both lengthy and complicated. To facilitate the formulation, approximations have been used to simplify the rotation matrix. A simplified small rotation matrix is often used in the formulation of finite element models for the flexural–torsional stability analysis of thin‐walled beams of open cross‐section. However, the approximations in the small rotation matrix may lead to the loss of some significant terms in the stability stiffness matrix. Without these terms, a finite element line model may predict the incorrect flexural–torsional buckling load of a beam. This paper investigates the effects of approximations in the elastic flexural–torsional stability analysis of thin‐walled beams, while a companion paper investigates the effects of approximations in the 3‐D non‐linear analysis. It is found that a finite element line model based on a small rotation matrix may predict incorrect elastic flexural–torsional buckling loads of beams. To perform a correct flexural–torsional stability analysis of thin‐walled beams, modification of the model is needed, or a finite element model based on a second‐order rotation matrix can be used. Copyright © 2001 John Wiley & Sons, Ltd.     

薄壁高墩大跨度连续刚构桥的非线性稳定分析

结合龙潭河特大桥的工程实例,采用有限元程序ANSYS,分别选取两种单元建立了梁单元模型和壳单元模型,对比分析了该大跨度连续刚构桥高墩的稳定性。在对刚构桥的稳定分析时采用几何非线性和材料非线性耦合的方法。采用U.L.列式法求解切线刚度矩阵来考虑几何非线性。为了模拟桥墩材料非线性性能,在壳模型中用COMBIN39多线性单元多弹簧模型(MS模型)来模拟墩底塑性铰区,在梁模型中用COMBIN40双线性弹簧单元模拟墩底塑性铰。通过分析可知,考虑非线性影响的稳定分析对于指导工程实践具有更好的实际意义。