单箱双室简支箱梁剪切变形及剪力滞双重效应分析

基于各个翼板选取不同的最大剪切转角差为剪力滞广义位移,应用能量变分原理分别推导出了考虑和不考虑剪切变形时单箱双室截面控制微分方程组,结合边界条件给出了箱梁纵向应力和竖向挠度的初参数解,从力学、数学角度上证实了剪切变形和剪力滞效应是两个相对独立的力学行为,进一步阐述了二者对箱梁的影响,即剪切变形对箱梁截面纵向应力无影响,但是对竖向挠度有很大的影响.数值算例表明,利用该文解和数值解分析跨中截面剪力滞系数横向分布规律,二者吻合程度良好,其横向分布规律与单室箱梁类似,唯独不同之处是边腹板处的剪力滞效应比中腹板处的剪力滞效应略微大一些;挠度计算表明,剪切效应使得该箱梁在集中和均布荷载作用下跨中挠度分别增大4.6%和2.7%.     

翼板变厚度箱形梁的剪力滞效应分析

针对翼板厚度沿截面宽度方向线性变化的混凝土箱形梁，利用势能变分原理对其进行剪力滞效应分析.选取剪力滞效应引起的附加挠度作为描述剪力滞变形状态的广义位移，并考虑轴力平衡条件对剪力滞效应的影响.将简支箱梁在均布荷载和集中荷载作用下的理论计算值与有限元值进行对比，结果表明:采用该文分析方法得到的计算值与有限元值吻合良好，证实了该文分析方法的正确性.与将翼板变厚度箱梁简化为等厚度箱梁的计算方法相比，考虑翼板厚度变化的计算方法可提高计算精度，误差减小量最大达到了5.65%.     

箱形梁剪力滞效应的分离求解方法及参数影响分析

选取剪力滞效应引起的附加挠度为广义位移,将箱梁的剪力滞变形状态从初等梁挠曲变形状态中分离出来,作为一种独立的变形状态进行分析,运用能量变分法建立了以附加挠度为未知量的截面控制微分方程及边界条件;结合简支边界条件分别导出了集中荷载和均布荷载作用下箱梁的附加挠度和纵向应力计算公式.纵向应力分析表明:该文方法计算的应力结果和样条函数法计算的应力结果吻合良好,从而验证了其方法的正确性.挠度研究表明:剪力滞附加挠度由跨中向两侧支点递减;针对于该文算例而言,均布荷载和集中荷载作用下跨中截面的剪力滞附加挠度分别占初等梁挠度的2. 57%和3. 03%;随着高跨比和宽跨比的增大,相应箱梁跨中截面的附加挠度逐渐减小,且宽跨比对附加挠度的影响远大于高跨比的影响.     

波形钢腹板-钢底板-混凝土顶板连续组合箱梁的剪力滞效应

考虑混凝土顶板和钢底板不同的模量,结合变分法推导了波形钢腹板-钢底板-混凝土顶板(CSWSBCT)组合箱梁剪力滞效应的控制微分方程组和边界条件,建立了CSWSBCT两跨连续箱梁跨中集中荷载、均布荷载作用下剪力滞系数的计算公式,采用模型试验梁对两种荷载工况下连续组合箱梁的剪力滞效应进行了分析.结果表明:其理论计算值与模型试验实测值和有限元值在波形钢腹板的顶底板上三者吻合较好,变化趋势一致,验证了计算公式的正确性;均布荷载作用下中间支点截面处顶底板的剪力滞系数最大值大于集中荷载工况下最大值,且在两种荷载工况下中间支点截面处波形钢腹板和混凝土顶板、钢底板交界处的剪力滞效应突出.     

集中弯矩作用下箱梁剪力滞效应的解析解

以承受集中弯矩的简支梁结构为对象,基于能量变分法,获得了剪力滞效应计算的解析解通式.分别对仅跨内承受集中弯矩和单侧梁端承受集中弯矩简支梁,以及两侧梁端承受相反弯矩的纯弯梁,提出了剪力滞效应计算的理论公式,揭示了该类型结构的剪力滞规律.通过简支箱梁算例,研究了3种集中弯矩工况下的剪力滞效应,并和有限元板壳数值解进行对比分析.研究表明,该解析方法可以有效计算简支梁承受集中弯矩时的剪力滞效应.简支梁在集中弯矩作用部位存在较为突出的剪力滞效应.     

基于抽象翘曲位移函数的箱形梁剪力滞效应分析

针对薄壁箱梁剪力滞问题,基于抽象的翘曲位移函数,通过对控制微分方程的形式进行分析研究,构造出剪力滞翘曲位移函数的基本形式;对翼板引入边界约束影响的修正系数,然后通过能量变分原理推导出了箱形梁剪力滞的控制微分方程及其解析解.根据有限元结果确定翼板边界约束影响修正系数的具体值,以带翼板的简支箱形梁分别作用集中荷载和均布荷载为数值算例,进行了计算分析.分析结果表明:采用该文方法计算的结果与有限元结果总体吻合良好,并且该文的计算结果也反映出了翼板应力小于顶板应力的分布规律,从而验证了该文分析方法的正确性.     

宽翼缘组合梁结构剪滞效应计算分析与试验研究

剪滞效应将导致钢-混凝土组合梁翼缘板纵向正应力沿翼板宽度方向分布不均,从而产生不利的横向裂缝.因此,有必要深入研究剪滞效应对宽翼缘组合梁结构的作用机理,以便加以防范.根据组合翼板微元的变形协调条件和平衡微分方程,建立了薄壁双箱组合梁翼板横截面法向应力微分方程.在考虑两端简支的边界条件下,利用解析解法求得其解析应力解.最后给出算例,通过与室内试验结果进行比较,表明该文方法具有较好的精度和实用性.     

波形钢腹板箱梁畸变应力分析

在对梯形截面箱梁的畸变角给出一般定义的基础上,根据传统混凝土箱形梁的理论及波形钢腹板的力学特性,对波形钢腹板组合箱梁的畸变翘曲应力进行推导,应用基于势能驻值原理的能量变分法,建立了以所定义的畸变角为未知量的控制微分方程,并给出其初参数解.采用初参数法求出波形钢腹板组合箱梁的畸变角和畸变双力矩,最终得到纵向畸变翘曲应力.通过算例对比分析了传统混凝土箱梁和波形钢腹板组合箱梁顶板与腹板及底板与腹板交点处的畸变翘曲应力,分析结果表明:由于波形钢腹板组合箱梁腹板的纵向刚度很小几乎为零,所以在波形钢腹板组合箱梁底板与腹板交点处产生的翘曲应力大于混凝土箱梁底板与腹板交点处的对应值.     

波形钢腹板箱梁的约束扭转剪应力分析

基于周边不变形理论,结合闭口薄壁杆件约束扭转的计算分析,研究了波形钢腹板箱梁在约束扭转时混凝土悬臂板上扭转剪应力的分布,并进行了计算.通过对悬臂板在约束扭转中剪力流计算公式的推导,进一步阐述了其自由扭转剪应力及翘曲扭转剪应力的分布,指出了相关文献在这部分计算中存在的问题.通过一个简支波形钢腹板组合箱梁算例,将该文方法计算结果与ANSYS有限元计算结果进行比较.结果表明:在波形钢腹板箱梁截面中,主要由波形钢腹板承受扭转剪应力,其次是混凝土底板,底板剪应力最大值发生在底板中心处,其数值近似等于腹板剪应力的一半,而混凝土顶板和悬臂部分的扭转剪应力很小;该文计算的扭转剪应力结果在总体上符合有限元得到的扭转剪应力分布规律,在悬臂自由端为0,随着离开悬臂自由端距离的增大,扭转剪应力逐渐增大并达到峰值.     

双室组合箱梁剪力滞分析的偏泛函微分方法

工程中普遍存在的剪力滞问题可能导致工程结构构件发生大变形以致严重损坏,对工程安全造成极为不利的影响.为了深入研究其作用机理,通过构建抛物型偏泛函模型,利用偏泛函微分系统对双室组合箱梁进行了推导研究.求得了在特殊外荷载(跨中集中荷载)下的特解,进一步得到了4种模式下的剪力滞偏泛函系数表达式.并从混凝土材料参数、钢梁材料参数等影响因素出发,选取模型结构,对该类型双室组合箱梁进行了参数特性研究以及对比分析.通过该研究,可为薄壁箱室结构的设计计算提供一定的指导作用和参照价值.     

Natural damped vibrations of anisotropic box beams of polymer composite materials. 2. Numerical experiments

The influence of the orientation of reinforcing fibers on the natural frequencies and mechanical loss coefficient of coupled vibrations of unsupported symmetric and asymmetric box beams, as evaluated in numerical experiments, is discussed. The calculations were performed under the assumption that the real parts of the complex moduli and mechanical loss coefficient are frequency-independent. Vibration modes were identified by their surface shapes. The boundaries of the regions of mutual transformation of interacting vibration modes were determined by the joint analysis of the dependences of the coupled and partial eigenfrequencies and the mechanical loss coefficients on the orientation angle of reinforcing fibers. It is established that vibrations of a symmetric box beam give rise to two primary interactions: bending–torsional and longitudinal–shear ones, which are united into a unique longitudinal–bending–torsional–shear interaction by the secondary interaction caused by transverse shear strains. Vibrations of an asymmetric box beam give rise to longitudinal–torsional and bending–bending (in two mutually orthogonal planes) interactions. It is shown that in a number of cases variation in the orientation angle of reinforcing fibers is accompanied with a mutual transformation of coupled vibration modes. If the differential equations for natural vibrations involve odd-order derivatives with respect to the spatial variable (a symmetric beam and the bending–bending interaction of an asymmetric beam), then, with variation in the orientation angle of reinforcing fibers, the mutual transformation of coupled vibration modes proceeds. If the differential equations for natural vibrations involve only even-order derivatives (the longitudinal–torsional interaction of an asymmetric beam), no mutual transformation of coupled vibration modes occurs.     

Finite element analysis of pressure vessel using beam on elastic foundation analysis

In this study, we first applied the variation principle to derive a new finite element method (FEM) based on the theory of beam on elastic foundation using line element. The derived FEM was then applied to solve, for the first time, the pressure vessel problems with uniform thickness. Our FEM results, obtained even by using only one line element, agreed exactly with the available closed-form solution, confirming the validity and computing efficiency of our finite element formulation. Moreover, we have applied our new FEM to solve pressure vessel problems with non-uniform thickness where no exact analytical solution is known to exist. The distributions of discontinuity stress in the cylindrical part were obtained. We found that shear force and bending moment were indeed discontinuous at the geometrically discontinuous juncture, due to the bending rigidity and elastic constant change by the non-uniform thickness. Finally, the case of discontinuity stresses in a bimetallic joint was also studied. The locations of maximum shear force and bending moment were found to be affected by the bending rigidity of the material.     

CFRP修复缺陷钢板应力解析模型

在使用碳纤维复合材料(carbon fiber reinforced polymer, CFRP)修复钢结构腐蚀缺陷的修复方式中,CFRP应力及胶层应力是确定碳纤维修复结构承载能力的关键。基于平截面假设,得到弯矩作用下应力与应变分布;基于胶层剪切模型,得到胶层剪应力与CFRP和钢板位移间的关系;基于力的平衡,得到CFRP和钢板的应力关系。结合得到的各种材料之间关系,推导出轴力和弯矩联合作用状态下CFRP双面修复钢板的CFRP与胶层应力分布解析解。采用数值分析对CFRP双侧粘贴修复缺陷钢板进行分析,分析结果与解析结果具有一致性,同时获得了CFRP双侧粘贴修复缺陷钢板的应力分布特点,以及构件可能发生破坏的位置,为计算构件极限承载力提供了基础。     

Vibration and flutter of stiff-inplane elastically tailored composite rotor blades

Aeroelastic response, blade and hub loads, and shaft-fixed aeroelastic stability is investigated for a helicopter with elastically tailored stiff-inplane composite rotor blades. A free wake model for nonuniform rotor inflow is integrated with a recently developed finite-element-based aeroelastic analysis for helicopters with tailored composite blades. Pitch-flap and pitch-lag elastic couplings, introduced through the anisotropy of the plies in the blade spar, have a significant effect on the dynamic elastic torsion response. Positive and negative pitch-flap couplings reduce vertical hub shear forces approximately 20% in the high vibration transition flight regime, however, negative pitch-flap elastic coupling significantly increases inplane hub shear forces at all flight speeds. The influence of pitch-flap, pitch-lag, and extension-torsion elastic couplings on the rotating frame blade bending moments is small. Ply-induced composite couplings have a powerful effect on blade stability in both hover and forward flight. Positive pitch-flap, positive pitch-lag, and positive extension-torsion couplings each have a stabilizing effect on lag mode damping. Negative pitch-lag coupling has a strong destabilizing effect on blade lag stability, resulting in a mild instability at moderate flight speeds.     

蠕变损伤材料中缺口尖端稳定扩展的应力场

研究了在拉伸载荷和反平面载荷作用下蠕变损伤材料缺口尖端稳定扩展的应力场．假设材料的应力及位移势函数,得到了缺口尖端场的各参数分量,进而在小范围蠕变条件下,建立了缺口尖端稳定扩展的蠕变损伤控制方程,并考虑缺口尖端蠕变钝化作用和问题的边界条件,对控制方程进行了数值分析,得到了缺口尖端的应力场,并讨论了缺口尖端应力场随各影响参数的变化规律．结果表明,缺口尖端的应力具有r1/(1-n)的奇异性,应力率具有rn/(1-n)的奇异性,n是蠕变指数．     

Hamilton力学下框筒结构剪滞翘曲位移模式研究北大核心CSCD

以等效连续化方法为基础,在Hamilton力学体系下进行框筒结构剪滞翘曲位移函数精度研究.选用不同类型的函数描述翼缘板的剪滞翘曲位移,考虑等效板的剪切变形以及纵向翘曲,得到不同位移函数下结构的总势能及对应的Lagrange函数.区别于传统变分法,该文在Hamilton力学体系下进行问题研究,导出框筒结构弯曲问题的Hamilton正则方程并利用精细积分法求解,进而计算出柱轴力并进行精度分析.算例验证结果表明:使用该方法分析框筒结构的剪力滞后效应是简单可行的;不同翘曲位移函数的选择对侧移计算结果影响不大,对轴力求解结果影响较大,二次抛物线最能反映等效翼缘板的实际翘曲位移;对比不同形式荷载作用下等效翼缘板中应力分布可知,随着外荷载合力作用点位置的升高,结构顶部负剪力滞后效应逐渐减弱至消失.     

护环柱面上受线性分布压力，端面上有不同的剪力和弯矩作用下的弹性解

对护环在柱面上受线性分布压力，并在两端面上有不同的剪力和弯矩作用的情况，应用一个新的位移函数，推出了弹性解．     

Creep and long-time strength of oriented glass-reinforced plastics in interlaminar shear

The creep and long-time strength in interlaminar shear and the creep in compression in the direction of the reinforcement have been experimentally investigated for certain types of oriented glass-reinforced plastics. The specimens in the interlaminar creep tests took the form of short beams loaded in bending. The experimental creep data for shear and compression are well described by the hereditary theory with a kernel of the Abel type (shear) or in the form of a Rabotnov function (compression). If the stresses are constant in time, good agreement with experiment is also given by Findley's form of the aging theory. A deformation criterion of interlaminar shear strength is also obtained. The experimental curves and values of the creep and long-time strength constants are presented.Translated from Mekhanika Polimerov, No. 6, pp. 1003–1012, November–December, 1971.