初始扭转欧拉梁有限元力学模型研究

基于传统欧拉直梁力学模型,对初始扭转欧拉梁有限元模型进行系统的分析与研究。采用2节点12个自由度模型,单元轴向位移插值函数采用2节点拉格朗日插值函数,梁截面横向弯曲位移u,v仍采用三次式位移模式。绕梁轴扭转角位移函数φz同轴向位移函数一样采用2节点拉格朗日插值函数。首先基于作者先前文献中初始扭转梁的弯曲正应变关系,导出初始扭转欧拉梁单元刚度矩阵。最后,通过矩形截面初始扭转悬臂梁算例,并与ANSYS三维实体有限元分析结果进行对比分析,表明建立的初始扭转欧拉梁单元刚度矩阵具有良好的精度。     

包含开口和闭口截面非均匀扭转的新型三维Timoshenko梁单元

提出一种考虑翘曲扭转(W型钢)的新型线弹性三维Timoshenko梁单元。它适用于分析由开口和中空截面(HCS)梁组成的空间结构。通过二阶梁理论(轴心受拉)与扭转(包括翘曲)的类比,建立非均匀扭转方程。局部梁单元刚度矩阵考虑二阶扭矩和剪力对变形的影响。将扭转角一阶导数的翘曲部分作为节点单元的附加自由度,该自由度代表双弯矩引起的扭转角。对数值分析结果进行讨论、比较和评价,对计算结果进行了试验验证,表明分析HCS梁应力-变形时考虑翘曲的重要性。     

国际期刊导读

1 钢框架节点翘曲传递模型 摘要：由于薄壁钢框架节点的作用,局部翘曲变形具有连续性,应用梁有限元分析,给出考虑局部翘曲连续性影响的简单方法。通过子结构分析方法,得到节点的压缩刚度矩阵,采用翘曲弹簧模拟交叉构件间的局部翘曲约束。通过数值算例对该模型进行了验证,所给节点模型的梁有限元分析结果与精确壳有限元分析结果相符。     

基于稳定函数的空间薄壁构件几何刚度矩阵

为真实描述结构二阶弹性分析中可能出现的侧扭屈曲变形和翘曲扭转变形,精确满足增量虚位移原理,结合梁柱法和有限单元法,基于更新拉格朗日构形的增量虚位移原理和三维空间薄壁构件理论,提出采用拉弯、压弯、纯弯及扭转状态下薄壁构件平衡微分方程的解作为插值函数,详细推导了考虑截面翘曲影响的空间薄壁梁柱单元的几何非线性切线刚度矩阵,推导过程中同时考虑了双向弯曲和扭转及其各耦合项对刚度矩阵的影响。并通过算例证实了文中方法的精确度和有效性。     

一种新型初始扭转Euler-Bernouli梁单元

采用有限元理论,借鉴平面Euler梁单元的位移模式,提出了一种2节点8自由度的初始扭转Euler梁单元,基于该单元的刚度矩阵和质量矩阵,自编有限元程序,求解初始扭转梁的自振频率,并通过算例,分析证明了初始扭转Euler梁单元的合理性和高效性。     

考虑弯扭耦合的解析型薄壁梁单元

为提高分析薄壁梁杆件弯扭问题的精度和效率,以Vlasov薄壁杆件理论为基础,考虑大位移和截面翘曲的影响,建立弯扭杆件位移控制方程,构造了薄壁梁杆单元的解析位移形函数,采用势能原理建立了薄壁梁杆势能泛函。利用势能驻值变分原理构造了用于内力分析的解析型薄壁梁杆单元列式,给出了解析型单元刚度矩阵,将其与理论解、插值多项式弯扭杆单元进行对比分析。结果表明,采用构造的解析型单元计算的薄壁梁扭转角及翘曲率的精度远高于插值多项式单元,且不需划分单元,即可保证计算结果与理论解的相对误差在0. 065%之内,可用于开口薄壁杆件结构的弯扭耦合受力分析及稳定计算。     

基于拉压与翘扭插值函数几何非线性刚度矩阵

提出了翘曲扭转稳定函数的概念和计算公式,首次推导了基于扭转翘曲稳定插值函数的双轴对称开口轻型薄壁梁柱单元的翘曲扭转切线刚度矩阵,同时提出了基于拉压与翘扭稳定插值函数的轻钢梁柱单元空间几何非线性切线刚度矩阵。     

初始扭转矩形梁力学性能研究

初始扭转梁在工程结构中的使用越来越广泛。对初始扭转梁力学性能进行系统的分析研究,提出可靠的力学分析模型和计算理论具有非常重要的实际意义。基于小变形线弹性基本假定,对初始扭转矩形梁进行力学性能分析,得出初始扭转矩形梁的位移解,举例并利用ANSYS进行验证分析。验证结果表明:初始扭转矩形梁小变形问题的求解方法是可行的;且由于初始扭转角的存在,初始扭转悬臂梁的位移较无初始扭转直梁增大,并且出现侧向位移,截面"等效抗弯刚度"变小。同时,小变形位移解为初始扭转梁有限元数值分析提供了精确的位移插值函数模式。     

钢筋混凝土槽形薄壁梁弯剪扭复合作用非线性分析

混凝土槽形薄壁梁近年来在城市轨道交通桥梁中得到了广泛应用,但其在弯剪扭复合作用下的力学性能研究相对滞后,已制约了其应用和发展。基于Vlasov开口薄壁构件弹性理论及本课题组所建立的钢筋混凝土槽形薄壁纯扭构件非线性分析模型,引入弯矩的影响,建立了钢筋混凝土槽形薄壁梁弯剪扭复合作用的非线性模型。该模型考虑了裂缝出现前后自由扭转刚度的变化;借助条带法、面积等效代换和修正坐标系等方法,得到翘曲扭转刚度与扭转角二阶导数的关系;最后采用四阶龙格-库塔法求解扭转平衡微分方程,得到扭矩-扭转角全过程曲线。根据求解过程编制了非线性分析程序,分析结果与本课题组已完成的两根梁的试验结果吻合良好,表明所建立的力学模型及分析程序可应用于弯剪扭复合作用下开口薄壁梁的受力分析和承载力预测。     

薄壁曲线杆系结构空间分析的刚度法

本文根据断面周线不变形的薄壁曲线梁翘曲扭转理论,用能量原理导出了当轴线在同一平面内的空间薄壁曲线梁进行刚度法分析的单元刚度矩阵以及各类荷载作用时的固端力计算方法.取一个节点为七个自由度,分别为空间三个方向的线位移、角位移以及梁端的翘曲位移.在分析中,考虑了断面的剪切中心与形心不重合的影响.本文最后给出了几个算例,证明计算公式是正确的.     

A model for warping transmission through joints of steel frames

A simple approach is developed in this paper which considers the effect of partial warping continuity through the joints of thin-walled steel frames when using beam finite element analysis. Using a condensed stiffness matrix for the joint generated by the substructuring technique, warping springs are introduced to represent the condition of partial warping restraint at intersections between members. The performance of the proposed model is demonstrated through a number of numerical examples. Excellent agreement is achieved between the results of beam finite element analysis using the suggested joint model and accurate shell finite element analysis.     

考虑翘曲变形的复合材料叠合梁几何非线性的有限元分析

提出了一个用于复合材料叠合梁结构分析的有限元模型,梁结构具有几何非线性性能,包括扭转翘曲变形。采用一个考虑了改进拉格朗日法和广义位移控制法的公式对结构的变形进行计算。采用二次等参有限单元对梁横截面进行离散化,以确定梁的弯扭特性。利用两结点的Hermitean三维有限梁元对结构进行离散化,其中每结点具有7个自由度。运用数个实例,分析了层的取向对结构性能的影响。     

薄壁梁元几何非线性分析模型的研究

本文在非线性空间梁元力学模型的基础上，考虑薄壁杆件扭转的影响，利用虚功原理导出了薄壁梁元几何非线性刚度矩阵。其中几何刚度矩阵由轴向力、双向弯曲和截面翘曲的影响组成。根据本文导出的分析模型编制了相应的结构分析程序。算例表明，本文导出的薄壁梁元几何非线性分析模型能较好地反映出薄壁构件的受力特点，可用于薄壁杆件组成的结构的非线性分析。     

Warping and bimoment transmission through diagonally stiffened beam-to-column joints

For beam-to-column rigid joints with a diagonal stiffener, the warping degrees of freedom at the beam-to-column joint have been taken to be continuous in some current literature. A new warping transmission model is presented for this type of joint in this paper, in which the bending deformation and twisting of the diagonal stiffener are considered and the restraining of the web in the joint panel zone to the twist of the diagonal stiffener is taken into account. Comparison with FEA using shell elements demonstrated the high accuracy of the proposed model, while the results with the continuous warping assumption have greater deviation with the finite element results. The suggested model can be implemented simply though modifying the traditional thin-walled beam element matrix at the joints. The proposed model is applicable for solving combined flexural and torsional problems of frames composed of thin-walled members.     

初始扭转梁力学性能参数分析

根据作者先前对初始扭转梁的变形规律和基本微分方程的讨论,进一步研究初始扭转角和抗弯刚度比两参数对初始扭转梁力学性能的影响。研究表明:由于初始扭转角的存在,梁单向弯曲时将产生侧向位移。且当初始扭转角ω∈[0,π/2],由于耦合效应产生的侧向位移随着初始扭转角ω的增加而增加;当初始扭转角ω∈[π/2,π],由于耦合效应产生的侧向位移随着初始扭转角ω的增加而减少。变化抗弯刚度比参数时,研究表明:截面为正方形,即两主轴方向的抗弯刚度相等时,梁的力学性能与普通直梁相同,无侧向位移产生;而当梁截面为非正方形,即梁截面抗弯刚度比μ≠1时,由于初始扭转角的存在,梁单向弯曲时将产生侧向位移,且μ越大,梁的两弯曲主轴位移耦合效应越来越大,产生的侧向位移也越来越大。     

薄壁曲线箱梁空间分析的梁段单元

广义符拉索夫薄壁梁理论耦合有限元技术 ,推导出一种能模拟拉压、弯曲、扭转、扭翘、剪切和剪力滞效应的薄壁曲线箱梁梁段单元。单元为两节点九自由度 ,除了常规梁单元的六个自由度外 ,还有三个分别考虑扭翘、剪切和剪力滞效应的自由度。利用变分原理在曲线坐标系下推导了单元刚度矩阵的显式及其等效结点荷载列阵。并在推导中考虑了曲线箱梁横截面剪心与形心不重合的影响。算例表明了本单元的有效性和准确性。     

Torsion analysis of thin-walled beams including shear deformation effects

The first part of the paper develops a theory for the torsional analysis for open thin-walled beams of general cross-sections which accounts for shear deformation effects. Statically admissible stress fields are postulated in agreement with those resulting from the Vlasov thin-walled beam theory. The principle of stationary complementary energy is then adopted to formulate the governing field compatibility condition under the stress fields postulated. The naturally arising boundary terms are found to relate the warping deformations to the internal force fields. A torsion beam example is solved using the new theory in order to illustrate its applicability to practical problems. The second part of the paper implements the solution numerically in a force-based finite element context. Two finite elements are developed by assuming linear and hyperbolic bimoment fields. The FEA solutions are shown to provide lower bound representations of the stiffness when compared to those based on conventional beam theories founded on postulated kinematic assumptions.     

Torsion warping transmission at thin-walled frame joints: Kinematics, modelling and structural response

This paper reports on the use of simple kinematic models to simulate the torsion warping restraint and transmission at thin-walled frame joints in the context of beam finite element structural analysis. After reviewing the main concepts involved in the torsional behaviour of thin-walled members, the paper addresses the development of kinematic models aimed at simulating the torsion warping transmission at frame joints connecting two or more non-aligned plain channel (U-section) or I-section members. Finally, numerical results are presented and discussed, in order to illustrate the application and show the capabilities of the above kinematic models, which make it possible to use beam finite element models accounting for the joint torsion warping behaviour. For validation purposes, the beam finite element results obtained are compared with values yielded by rigorous shell finite element analyses.     

Torsional analysis of thin-walled composite beams with single- and double-celled sections

The exact solutions for twist angle and fiber stresses of thin-walled composite box beams with single- and double-celled sections subjected to torsional moment are presented by introducing fourteen displacement parameters. For this, a general thin-walled composite box-beam theory including the effects of elastic couplings and restrained warping is developed based on the Vlasov’s assumptions. The equilibrium equations and the force–deformation relations are derived from the energy principle. A system of linear algebraic equations with non-symmetric matrices is constructed by introducing fourteen displacement parameters and by transforming the higher order simultaneous differential equations into first-order ones. This numerical technique determines eigenmodes corresponding to multiple zero and non-zero eigenvalues and derives exact displacement functions for displacement parameters based on the undetermined parameter method. Finally, the exact stiffness matrix is determined using the member force–deformation relations. The theory developed by this study is validated by comparing several torsional responses from the present approach with those from the finite element beam model that uses third-order Hermitian polynomials and detailed two-dimensional analysis results using the shell elements of ABAQUS for coupled composite beams with single- and double-celled sections.