考虑约束扭转的薄壁梁单元刚度矩阵

推导了薄壁空间梁单元刚度矩阵 ,考虑了双向弯曲及截面约束扭转对杆件轴向变形的影响 ;计算了截面的翘曲变形 ,以及二次剪应力对翘曲变形的影响 ,可适用于任意截面 (包括开口、闭口和混合剖面 )的薄壁杆件。计算结果表明 ,考虑约束扭转的薄壁梁单元刚度矩阵有相当好的精确度 ,可以用于薄壁杆件的静动力分析。     

开口薄壁梁的扭转理论与应用

以Vlasov薄壁构件理论为基础, 推导了开口薄壁构件一阶扭转理论. 该理论考虑了翘曲剪应力对截面转角的影响, 截面的转角分为自由翘曲转角和约束剪切转角, 在约束扭转中, St.Venant扭矩仅仅与自由翘曲转角有关, 而翘曲扭矩仅与约束剪切转角有关. 利用半逆解方法求出了约束扭转中薄壁构件的St.Venant扭矩表达公式; 依据能量方法, 建立了约束剪切转角和翘曲扭矩之间的关系, 并提出了翘曲剪切系数概念, 给出了一阶扭转理论的微分方程. 为了有效求解微分方程, 给出了求解微分方程的初参数法方程和相应的影响函数矩阵; 当St.Venant扭矩可以忽略时, 得到与一阶弯曲理论(Timoshenko梁理论)相似的一阶扭转理论简化形式. 最后利用算例证明了一阶扭转理论和简化理论的有效性.      

开口厚壁截面短构件的约束扭转1）

为了分析开口厚壁截面短构件的约束扭转问题,采用统一分析梁模型与有限节线法,对T形和L形厚壁截面短构件约束扭转时横截面的翘曲和应力分布情况等问题进行了分析研究.算例计算结果表明：开口厚壁截面短构件存在与其横截面形心位置不一致的扭转（弯曲）中心,构件在不过扭转中心的外力作用下会产生弯扭耦合变形,其横截面将产生不均匀翘曲,横截面上的翘曲正应力和扭转剪应力均呈非线性分布.     

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.     

开口厚壁截面短构件的约束扭转

为了分析开口厚壁截面短构件的约束扭转问题,采用统一分析梁模型与有限节线法,对T形和L形厚壁截面短构件约束扭转时横截面的翘曲和应力分布情况等问题进行了分析研究.算例计算结果表明:开口厚壁截面短构件存在与其横截面形心位置不一致的扭转(弯曲)中心,构件在不过扭转中心的外力作用下会产生弯扭耦合变形,其横截面将产生不均匀翘曲,横截面上的翘曲正应力和扭转剪应力均呈非线性分布.     

薄壁箱梁的翘曲连续性条件

基于薄壁杆件理论,分析了薄壁箱梁弯曲剪流和约束扭转翘曲剪流计算时的翘曲连续性 条件. 从翘曲连续性条件出发,推导了薄壁箱梁约束扭转翘曲剪流的一般公式,此外,还指 出了有关文献中的错误并进行了更正. 最后对一个悬臂箱梁的约束扭转翘曲剪流进行了计算 比较.     

变截面双帽箱型横截面点焊薄壁构件的扭转问题

提出沿构件长度方向截面尺寸发生缓慢变化时双帽箱型横截面点焊薄壁构件扭转特性的分析方法,并利用此方法讨论了变截面等焊点间隔构件和变截面非等焊点间隔构件的翘曲扭转问题并得到如下结论:①变截面构件长度越长,扭转刚度越小,其刚度下降率与等截面构件几乎相等;②采用变截面构件,不仅保持一定刚度,还可以减少焊点数目,降低焊接成本;③若右半部分的焊点间隔p2对左半部分的焊点间隔p1的变化范围小于25%,则其传递剪力变化不大。仿真结果与实验值以及利用cosmos/m而得到的数值解相比较吻合得较好,完全满足工程精度要求。此研究为解决实际车体结构的设计问题,具有有益的参考价值。     

复合材料单闭室薄壁梁弯曲与扭转分析

本文主要讨论复合材料单闭室薄壁梁的弯曲与扭转，重点研究横向剪切和限制翘曲的影响。在复合材料薄壁梁弯曲与扭转经典分析理论的基础上，建立了一种能够考虑横向剪切和限制翘曲影响的复合材料单闭室薄壁梁弯曲与扭转分析方法。     

一种新的薄壁杆件单元扭转刚度矩阵

本文提出一种新的薄壁杆件单元扭转刚度矩阵,它能够计及二次剪应力对翘曲变形的影响,并适用于任意剖面(包括开口,闭口和混合剖面)的薄壁杆件。计算表明,这个新的扭转刚度矩阵有相当好的精确度,可以代替Kawai或Gunnlaugsson-Pedersen的刚度矩阵,用于薄壁杆件的有限元静动力分析。     

复室开闭口混合薄壁截面翘曲座标的计算

本文试图对复室开闭口混合薄壁截面翘曲座标的计算作一简介。应用了广义扇形座标计算的原则,对二种类型的上述截面的计算,作了示例。翘曲座标值,仍以计算公式表示之。本文并简述了复室混合截面薄壁杆件和复室闭合截面薄壁杆件扭转计算的异同。     

Optimization of a Thin-Walled,Anisotropic Curved Bar for Maximum Torsional Stiffness∗

ABSTRACT

ABSTRACT A curved bar in the form of a circular ring sector is under uniform torsion when acted upon by two equal and opposite forces directed alone the axis passing through the center of the ring and perpendicular to its plane, i.e., forces acting along the axis of rotation. The exact torsion theory can be extended to this case when the material of which the bar consists is cylindri-cally anisotropic, with the axis of anisotropy directed along the axis of rotation and having an elastic symmetry about any plane of the transverse cross section. In this paper, a thin-walled curved bar having the loading conditions and material properties described above is optimized so as to maximize its torsional stiffness. The optimization is carried out with respect to the cross-sectional shape of the bar subject to constraints on the transverse area (single-purpose design) and bending stiffness (multipurpose design). In the special case of an orthotropic material, the angle of inclination of the ortho-tropy axes with respect to the middle plane is optimally determined for a cross section with constant thickness. A perturbation method is used to obtain analytical solutions, and numerical results are presented indicating the efficiency of the designs and the optimal cross-sectional shapes.     

Non-linear elastic non-uniform torsion of bars of arbitrary cross-section by BEM

In this paper an elastic non-uniform torsion analysis of simply or multiply connected cylindrical bars of arbitrary cross-section taking into account the effect of geometric non-linearity is presented employing the boundary-element(BE) method. The torque-rotation relationship is computed based on the finite-displacement (finite-rotation) theory, that is the transverse displacement components are expressed so as to be valid for large rotations and the longitudinal normal strain includes the second-order geometric non-linear term often described as the “Wagner strain”. The proposed formulation does not stand on the assumption of a thin-walled structure and therefore the cross-section's torsional rigidity is evaluated exactly without using the so-called Saint-Venant's torsional constant. The torsional rigidity of the cross-section is evaluated directly employing the primary warping function of the cross-section depending on its shape. Three boundary-value problems with respect to the variable along the beam axis angle of twist, to the primary and to the secondary warping functions are formulated. The first one, employing the Analog Equation Method (a BEM-based method), yields a system of non-linear equations from which the angle of twist is computed by an iterative process. The remaining two problems are solved employing a pure BE method. Numerical results are presented to illustrate the method and demonstrate its efficiency and accuracy. The developed procedure retains most of the advantages of a BEM solution over a pure domain discretization method, although it requires domain discretization.     

THE USE OF VACUUM PRESSURE IN STRUCTURAL TESTING

This paper presents an experimental setup for the method of simulating uniformly and varying distributed loads on structural members and roofing materials. The applications of this setup can be used for the study of beams, such as the lateral, torsional buckling behavior of cold-formed thin-walled structures. In addition, the method of measuring bending stiffness of composite materials in semimonocoque structures is illustrated. With a little modification to the setup, the study could possibly be extended to the investigation of elastic foundations and beam-column interaction.     

Zur Berechnung der Schnittkräfte in Zylinderschalen nach der Balkenmethode bei Berücksichtigung der gemischten Torsion

Übersicht Es wird eine erweiterte Theorie der dünnwandigen Träger vorgelegt, in der die Veränderlichkeit der Normal- und Schubspannungen über die Wanddicke berücksichtigt wird, und zwar unter Vernachlässigung der Krümmungen der Wölbfläche in Schnitten rechtwinklig zur Querschnittsmittellinie. Dadurch lassen sich die Anteile der Biegesteifigkeit der Stabwandungen an der Gesamtbiegesteifigkeit, vor allem aber die des De Saint-Venantschen Torsionswiderstandes an der Gesamtverdrehungssteifigkeit erfassen. Es werden Gleichungen für die Querschnittswerte des Stabes, für die Belastungs-Verschiebungszusammenhänge im Gesamtsystem und für die Schalenschnittkräfte in Längs- und Querrichtung abgeleitet. Die Bedeutung der mitgeteilten Ergänzungen zur Theorie der dünnwandigen Stäbe für die Schnittkräfte wird an zwei Beispielen gezeigt.

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Summary This paper deals with the extended theory of thin-walled beams, taking into account the variability of normal and shear stresses over the thickness of the walls. The curvature of the warped cross-sectional surface perpendicular to the center-line of the wall is neglected. This permits to arrive at the component of the overall flexural rigidity which results from the flexural rigidity of the beam walls; furthermore one can establish that part of the overall torsional resistance which results from De Saint-Venant's torsional resistance. Equations are derived for the properties of the cross-sectional area of the shell beam for the relation between loads and displacements in the overall-system, and for the stress-resultants in longitudinal and transverse directions. Two examples are attached in order to show how the internal forces of certain structures are influenced by the additional members of the equations.

     

The approximate analytical solution for the buckling loads of a thin-walled box column with variable cross-section

1.IntroductionThin-walledboxcolumnswithvariablecross-sectionareextensivelyusedascompressionmembersforhighbridgepiers,waterandtelevisiontowersandothersimilarstructures.Atpresent,however,fewpapersdealingwiththecriticalloadsoftorsional-fie-curalbucklingforthiskindofstructurescanbeseen.Inthispaper,bymeansoftheenergyprincipleandtheGalerkin'smethod,theapproximateexpressionsforcalculatingthecriticalloadsoffie-curalandtorsionalbucklingaredevelopedrespectively.Anapplicablecomputerprogramisworkedout,an…     

A new beam element for analyzing geometrical and physical nonlinearity

Based on Timoshenko＇s beam theory and Vlasov＇s thin-walled member theory, a new model of spatial thin-walled beam element is developed for analyzing geometrical and physical nonlinearity, which incorporates an interior node and independent interpolations of bending angles and warp and takes diversified factors into consideration, such as traverse shear deformation, torsional shear deformation and their coupling, coupling of flexure and torsion, and the second shear stress. The geometrical nonlinear strain is formulated in updated Lagarange （UL） and the corresponding stiffness matrix is derived. The perfectly plastic model is used to account for physical nonlinearity, and the yield rule of von Mises and incremental relationship of Prandtle-Reuss are adopted. Elastoplastic stiffness matrix is obtained by numerical integration based on the finite segment method, and a finite element program is compiled. Numerical examples manifest that the proposed model is accurate and feasible in the analysis of thin-walled structures.     

Improved torsional analysis of laminated box beams

The improved torsional analysis of the laminated box beams with single- and double-celled sections subjected to a torsional moment is performed by introducing 14 displacement parameters. For this, a thin-walled laminated box beam theory considering the effects of shear and elastic couplings is presented. The governing equations and the force-displacement relations are derived from the variation of the strain energy. The system of linear algebraic equations with non-symmetric matrix is constructed by introducing the displacement parameters and by transforming the higher order simultaneous differential equations into first order ones. This numerical technique determines eigenmodes corresponding to 12 zero and 2 non-zero eigenvalues and derives displacement functions for displacement parameters based on the undetermined parameter method. Finally, the element stiffness matrix is determined using the member force-displacement 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 using the Lagrangian interpolation polynomials and three-dimensional analysis results using the shell elements of ABAQUS for coupled laminated beams with single- and double-celled sections.     

Buckling of thin-walled columns accounting for initial geometrical imperfections

The paper is devoted to the effect of some geometrical imperfections on the critical buckling load of axially compressed thin-walled I-columns. The analytical formulas for the critical torsional and flexural buckling loads accounting for the initial curvature of the column axis or the twist angle respectively are derived. The classical assumptions of theory of thin-walled beams with non-deformable cross-sections are adopted. The non-linear differential equations are derived and the critical buckling loads are approximated by means of the Galerkin’s method. Comparison of analytical results to numerical analysis of simply supported I-columns by means of finite element method (FEM) is provided. Moreover the analytical formulas is adapted to I-columns with lipped flanges and satisfactory agreement of analytical and numerical results of stability analysis is observed.     

A new finite element of spatial thin-walled beams

Based on the theories of Timoshenko＇s beams and Vlasov＇s thin-walled members, a new spatial thin-walled beam element with an interior node is developed. By independently interpolating bending angles and warp, factors such as transverse shear deformation, torsional shear deformation and their Coupling, coupling of flexure and torsion, and second shear stress are considered. According to the generalized variational theory of Hellinger-Reissner, the element stiffness matrix is derived. Examples show that the developed model is accurate and can be applied in the finite element analysis of thinwalled structures.