Cross-sectional warping and precision of the first-order shear deformation theory for vibrations of transversely functionally graded curved beams

The warping may become an important factor for the precise transverse vibrations of curved beams.Thus,the first aim of this study is to specify the structural design parameters where the influence of cross-sectional warping becomes great and the first-order shear deformation theory lacks the precision necessary.The outof-plane vibrations of the first-order shear deformation theory are compared with the warping-included vibrations as the curvature and/or thickness increase for symmetric and asymmetric transversely-functionally graded(TFG)curved beams.The second aim is to determine the influence of design parameters on the vibrations.The circular/exact elliptical beams are formed via curved mixed finite elements(MFEs)based on the exact curvature and length.The stress-free conditions are satisfied on three-dimensional(3D)constitutive equations.The variation of functionally graded(FG)material constituents is considered based on the power-law dependence.The cross-sectional warping deformations are defined over a displacement-type FE formulation.The warping-included MFEs(W-MFEs)provide satisfactory 3D structural characteristics with smaller degrees of freedom(DOFs)compared with the brick FEs.The Newmark method is used for the forced vibrations.

The Effects of the Longitudinal Axis of Loading upon Bending, Shear and Torsion of a Thin-Walled Cantilever Channel Beam

Three aluminium channel sections of US standard extruded dimension are mounted as cantilevers with x-axis symmetry. The flexural bending and shear that arise with applied axial torsion are each considered theoretically and numerically in terms of two longitudinal axes of loading not coincident with the shear centre. In particular, the warping displacements, stiffness and stress distributions are calculated for torsion applied to longitudinal axes passing through the section’s centroid and its web centre. The stress conversions derived from each action are superimposed to reveal a net sectional stress distribution. Therein, the influence of the axis position upon the net axial and shear stress distributions is established compared to previous results for each beam when loading is referred to a flexural axis through the shear centre. Within the net stress analysis is, it is shown how the constraint to free warping presented by the end fixing modifies the axial stress. The latter can be identified with the action of a ‘bimoment’ upon each thin-walled section.

Theory of Flexural Shear, Bending and Torsion for a Thin-Walled Beam of Open Section

Aspects of the general Vlasov theory are examined separately as applied to a thin-walled channel section cantilever beam under free-end end loading. In particular, the flexural bending and shear that arise under transverse shear and axial torsional loading are each considered theoretically. These analyses involve the location of the shear centre at which transverse shear forces when applied do not produce torsion. This centre, when taken to be coincident with the centre of twist implies an equivalent reciprocal behaviour. That is, an axial torsion applied concentric with the shear centre will twist but not bend the beam. The respective bending and shear stress conversions are derived for each action applied to three aluminium alloy extruded channel sections mounted as cantilevers with a horizontal principal axis of symmetry. Bending and shear are considered more generally for other thin-walled sections when the transverse loading axes at the shear centre are not parallel to the section = s centroidal axes of principal second moments of area. The fixing at one end of the cantilever modifies the St Venant free angular twist and the free warping displacement. It is shown from the Wagner-Kappus torsion theory how the end constrained warping generates an axial stress distribution that varies with the length and across the cross-section for an axial torsion applied to the shear centre. It should be mentioned here for wider applications and validation of the Vlasov theory that attendant papers are to consider in detail bending and torsional loadings applied to other axes through each of the centroid and the web centre. Therein, both bending and twisting arise from transverse shear and axial torsion applied to each position being displaced from the shear centre. Here, the influence of the axis position upon the net axial and shear stress distributions is to be established. That is, the net axial stress from axial torsional loading is identified with the sum of axial stress due to bending and axial stress arising from constrained warping displacements at the fixing. The net shear stress distribution overlays the distributions from axial torsion and that from flexural shear under transverse loading. Both arise when transverse forces are displaced from the shear centre.

SOLUTION OF GENERALIZED COORDINATE FOR WARPING FOR NATURALLY CURVED AND TWISTED BEAMS

A theoretical method for static analysis of naturally curved and twisted beams under complicated loads was presented, with special attention devoted to the solving process of governing equations which take into account the effects of torsion-related warping as well as transverse shear deformations. These governing equations, in special cases, can be readily solved and yield the solutions to the problem. The solutions can be used for the analysis of the beams, including the calculation of various internal forces, stresses, strains and displacements. The present theory will be used to investigate the stresses and displacements of a plane curved beam subjected to the action of horizontal and vertical distributed loads. The numerical results obtained by the present theory are found to be in very good agreement with the results of the FEM results. Besides, the present theory is not limited to the beams with a double symmetric cross-section, it can also be extended to those with arbitrary cross-sectional shape.

Exact solution for warping of spatial curved beams in natural coordinates

The purpose of the paper is to present an exact analytical solution of a spatial curved beam under multiple loads based on the existing theory. The transverse shear deformation and torsion-related warping effects are taken into account. By using this solution, a plane curved beam subjected to uniform vertical loads and torsions is analyzed. Accuracy and efficiency of present theory are demonstrated by comparing its numerical results with Heins＇ solution. Furthermore, the effects of the transverse shear deformation and torsion-related warping on deformation of the beam are discussed.

L波段全向天线研究与设计

在实际应用中,有时需要全向天线在水平面以上覆盖较广的空域,针对这一需求,文章提出了两种工作在L频段的波束上翘的全向天线。其中一种为使用同轴转平行双线结构进行馈电的串联印刷偶极子天线,且加入反射板保证波束上翘,实测结果表明该天线在工作频段内,电压驻波比(voltage stanting wave ratio,VSWR)小于1.5,水平面增益大于2dBi,俯仰角0°~70°(定义水平方向为0°)增益大于-7dBi,不圆度小于2dB。另一种为双锥天线,使用上下锥体不对称结构保证波束上翘,同时引入固定套环保证天线的稳定性。实测结果表明该天线在工作频段内,VSWR小于2,俯仰角0°~20°增益大于1dBi,俯仰角0°~70°增益大于-7dBi,不圆度小于2.5dB。该天线结构稳定,性能优良,可应用于车载通信或其他通信场景中。

Application of stiffness matrix of a beam element considering section distortion effect

According to the stationary principle of potential energy and the generalized coordinate method, a stiffness matrix of a beam element considering distortion effects is derived. Using the stiffness matrix of the beam element, a finite element program for computing thin-walled box steel beams is developed. And the program can take the section distortion and warping effects into account. The influences of diaphragm spacing on the mechanical behavior of thin-walled box beams are analyzed by the program. The numerical analysis shows that setting diaphragms have the greatest influence on the distortion normal stress, while there is very little influence on the bending normal stress. Only when the distance of adjacent diaphragms decreases to a certain value, will the distortion normal stress in the thin-walled box beam obviously reduce under the distortion load. Finally, a distortion-warping coefficient γ is introduced for simplifying the calculation of the longitudinal normal stress of thin-walled box beams. When the ratio of diaphragms adjacent space L to the maximum section dimension H is less than 2, the distortion-warping coefficient γ tends to one, which means that the distortion normal stress of the thin-walled box beam tends to zero, and the effect of the section distortion can be ignored.

2024中国国际纺织机械展览会暨ITMA亚洲展览会经编设备述评

介绍2024年中国国际纺织机械展览会暨ITMA亚洲展览会经编机及整经机的参展情况及技术特征。重点分析参展经编机与整经机、经编设备配件的核心技术特点,包括:超大针距横移控制技术、智能生产管理与远程服务系统、经编高机号精密加工技术、宽幅化与高效生产技术等高新技术运用到经编设备上,极大提高了经编机的生产效率。结果表明,经编企业在经编机的制造水平上有明显提升,在设备数智化方面也得到显著加强,数字纺织、智慧纺织、精密加工制造进一步实现,并提出我国经编机应进一步向智能化方向发展。

某地铁桥梁箱梁下挠及开裂检测评估处治技术

某地铁高架桥为65 m+120 m+65 m预应力混凝土变截面连续梁桥,建成后运营不久发现主梁产生较大的竖向下挠,并且主梁跨中底板出现较多延伸至腹板的横向裂缝。为了解主梁下挠和裂缝产生的原因以及目前桥梁的技术状况,对该桥梁进行了专项检测,并采用有限元软件进行结构验算。检测及验算结果表明:该桥梁体下挠和开裂的主要原因主要是梁体跨中预应力的损失,特别是底板束预应力损失过大或张拉不足而导致的梁体抗弯承载力不足。根据检测评估结果主要采用了体外预应力钢束进行维修补强。维修处治后的荷载试验表明,桥梁强度、刚度及动力性能均满足规范要求,桥梁加固处治效果良好。

THE ANALYSIS OF THIN WALLED COMPOSITE LAMINATED HELICOPTER ROTOR WITH HIERARCHICAL WARPING FUNCTIONS AND FINITE ELEMENT METHOD

In the present paper, a series of hierarchical warping functions is developed to analyze the static and dynamic problems of thin walled composite laminated helicopter rotors composed of several layers with single closed cell. This method is the development and extension of the traditional constrained warping theory of thin walled metallic beams, which had been proved very successful since 1940s. The warping distribution along the perimeter of each layer is expanded into a series of successively corrective warping functions with the traditional warping function caused by free torsion or free beading as the first term, and is assumed to be piecewise linear along the thickness direction of layers. The governing equations are derived based upon the variational principle of minimum potential energy for static analysis and Rayleigh Quotient for free vibration analysis. Then the hierarchical finite element method. is introduced to form a,. numerical algorithm. Both static and natural vibration problems of sample box beams axe analyzed with the present method to show the main mechanical behavior of the thin walled composite laminated helicopter rotor.

基于剪切变形宽翼薄壁工字形梁剪滞效应的分析

分析了宽翼薄壁工字形梁竖向弯曲时的翼缘和腹板剪力流分布规律,利用剪切变形来定义剪滞翘曲位移函数,采用基于最小势能原理的能量变分法,建立了宽翼薄壁工字形梁剪滞效应分析的剪力滞控制微分方程和边界条件。以剪力滞广义位移、竖向挠度、竖直平面内转角、剪力、弯矩及剪力滞广义力矩作为6个初参数,给出了任意集中荷载作用下微分方程的初参数解。对简支工字形截面梁模型进行计算,应力和挠度计算结果与有限元较吻合,证明该方法有效。

基于一维高阶梁理论的薄壁箱梁非线性弥散波特性

当薄壁箱梁在受到动扭转载荷时,其截面产生翘曲和畸变形变且同时与扭转形变产生耦合。由于耦合效应的影响,应力波沿薄壁箱梁轴线的的传播变得很复杂。然而,现在对弥散现象的研究还不够深入,用三维弹性动力学方程的数值解很难观察出频散曲线各分支之间的相互关系。因此,采用能够表达这3种位移形变的一维高阶梁理论来研究色散关系。通过该研究,揭示了低频频散关系的虚、实分支之间的相互联系。在算例分析中,研究了薄壁箱梁几何效应引起的非线性色散影响,可知薄壁箱梁壁厚越大其极限波速越小;横截面宽高比越大,分支1的频率越大,而分支2和分支3的频率越小。

经编间隔织物增强硅橡胶基复合材料压缩行为的数学模型

为研究经编间隔织物增强硅橡胶基复合材料(silicone-rubber-matrix composite reinforced by warp-knitted spacer fabric,SWSF)在20%变形内的压缩机理,基于Euler-Bernoulli梁理论和Spence不变量本构理论,建立了SWSF的压缩细观力学理论模型,该模型由硅橡胶的力学模型和经编间隔织物(warp-knitted spacer fabric,WSF)的压缩模型组成。根据相应力学试验的结果,在MATLAB软件中计算了SWSF压缩细观力学理论模型的参数。利用复合材料的压缩试验,验证压缩细观力学理论模型的可行性。结果表明,建立的细观压缩力学理论模型能够较好地模拟SWSF试样在20%变形内的压缩行为。此外,该理论模型有助于理解SWSF的压缩机理,优化SWSF的产品设计。

一种适用于回字形截面梁的新型翘曲形状函数

回字形截面梁是本科力学课程教学中常见的一种梁结构,本文提出一种适用于回字形截面的翘曲形状函数,基于此,建立了适用于回字形截面梁的高阶剪切变形梁模型。所提理论同时考虑了横截面剪切变形和转动惯量的影响,且不需引入剪切修正系数,对于回字形截面梁的动静态力学行为计算精度高。同时,计算过程简单,易于工程应用,可以作为材料力学、弹性力学和有限元法课程教学实例,也可基于所提理论发展新的一维高精度有限元梁模型。

薄壁梁剪切挠曲性能解耦分析方法研究

为快速准确地获得薄壁梁的挠曲应力及位移,提出一种考虑各板剪切变形影响的薄壁梁挠曲分析方法。从薄壁板剪应变与位移关系出发,推导出具有明确力学机制的挠曲纵向位移函数;选取剪切变形引起的挠度作为广义位移,通过解耦挠曲性能提出剪切翘曲应力及挠度的一种简化分析方法;基于矩形板条的平面应力解,导出翼板翘曲应力修正系数的表达式;利用中支点的变形连续条件及简化分析理论,提出薄壁连续梁的剪切挠曲简化分析方法。数值算例结果表明,本文方法求得的应力结果与3D FEM结果最大误差在3%以内,挠度最大误差为6%以内,说明所提方法可靠且精度较高;参数分析表明,材料泊松比及板宽比对翼板的翘曲应力影响较大。

剑杆小样织机上机工艺参数对纬密的影响

针对剑杆小样织机的性能,对后梁高度、提综提前时间、经纱张力、打纬提前时间、钢筘停留时间等工艺参数进行调节,探究工艺参数的调节对织物纬密的影响,并探究出较优工艺,为大车生产提供参考依据。

薄壁箱梁抛物线系列剪滞翘曲位移函数的精度选择分析

为了探讨抛物线系列剪滞翘曲位移函数的设置对薄壁箱梁力学性能分析计算精度的影响,选择了符合箱梁翼板纵向翘曲位移模式的抛物线函数,同时考虑剪力滞效应和剪切变形等因素,利用能量变分法建立箱梁的控制微分方程,基于简支和连续边界条件计算出不同翘曲位移函数箱梁的自振频率,进而根据箱梁自振频率的大小对所设置翘曲位移函数的精确度进行选择。研究结果表明:二次抛物线函数能够更准确地反映薄壁箱梁翼板剪力滞效应以及由其引起的箱梁纵向翘曲位移的分布特征;当箱梁跨宽比较小时,同一箱梁应用不同翘曲位移函数计算得到的自振频率相差很小,但箱梁翼板剪力滞系数却相差较大,故在对跨宽比较小的箱形梁桥进行力学分析时翘曲位移函数的选择更为重要。

自行走上轴车的研制及应用效果

总结在高密度织机布局车间中自行走上轴车的结构、原理及其应用效果。介绍了自行走上轴车的各组成部分,包括车架、运输行走系统、纺织器材升降系统和控制系统。简述了自行走上轴车的具体工作流程。应用效果表明:自行走上轴车可实现在高密度织机车间内对穿经完成的成品及带纱经轴的灵活行走,并实现经轴上机功能。认为:自行走上轴车可提升生产效率,降低用工成本,提高操作安全性。

基于新型广义位移的箱形梁扭转单元及应用

为了改进变截面连续箱梁桥的扭转分析理论,将截面总扭转角分解为自由翘曲扭转角和约束剪切扭转角,选取自由翘曲转角扭率作为广义位移,提出一个2节点8自由度的扭转梁段单元。从约束扭转控制微分方程出发,推导单元刚度矩阵及等效节点荷载列阵。引入应力增大系数,以反映约束扭转对初等梁应力的增大效应。数值算例验证了本文梁段单元的可靠性。最后对一个三跨变截面连续箱梁桥进行分析,结果表明,双力矩影响线与弯矩影响线较为类似,按双力矩影响线进行最不利荷载加载时最大应力值偏小;应力增大系数在集中荷载作用截面出现极值,均发生在腹板与顶板交点处;利用偏载放大系数来考虑扭转附加效应时,不宜考虑弯曲正应力较小及翘曲正应力出现极值的梁段区域。

H形钢梁考虑有限翘曲约束刚度的扭转效应分析

为考虑半刚性连接对H形钢梁翘曲变形的有限约束,引入翘曲约束刚度的概念,提出介于简单支承和固定支承之间的半刚性连接H形钢梁约束扭转计算方法。结合数值算例,验证本文方法的正确性,详细分析翘曲约束刚度变化对翘曲正应力和二次剪应力的影响。研究结果表明:翘曲约束刚度引起的双力矩沿跨度呈线性变化,翘曲正应力随翘曲约束刚度的增大而减小,二次剪应力随翘曲约束刚度的增大而增大。