带后浇段的约束梁在集中力作用下的抗剪强度试验研究

本文通过对10根承受集中荷载作用下带后浇段的矩形截面钢筋混凝土约束梁的试验结果与已有的普通矩形截面钢筋混凝土约束梁的试验和理论计算结果的对比,发现了带后浇段的约束梁在集中力作用下抗剪强度与普通约束梁的差别,分析了后浇段对抗剪承载力的影响。     

矩形截面梁受多项式分布载荷的应力解

本文根据弹性力学半逆解法，对矩形截面梁的主要边界上受高次多项式分布力，提出一个统一的应力函数模式，运用此应力函数可以求解矩形截面梁受５次以内多项式分布载荷时的应力分量．文章以矩形截面梁受５次分布截荷为例，给出了材料力学弯曲正应力公式的修正项．     

点载静力梁函数在求解矩形薄板自振特性中的应用

本文选择一组点载静力梁函数作为基函数，应用李兹法近似求解矩形薄板的自振特性，计算了多种边界条件下各种长宽比的矩形薄板的自振频率，与其它方法相比，本文方法具有很好的精度和收敛性，且计算非常简单直接。     

轴向压力和分布载荷联合作用下压杆屈曲问题的实用算法EI北大核心CSCD

采用渐进积分法研究了压杆在轴向集中力和轴向分布载荷联合作用下的弹性屈曲问题。推导出了在各种边界条件下,承受轴向集中力和轴向分布载荷时临界力的计算公式。建立了轴向集中力和轴向分布载荷联合作用下压杆的四阶微分方程,用均布载荷作用下梁的四阶微分方程比拟压杆,得到压杆屈曲函数的初函数。将挠度函数代入压杆的四阶微分方程进行积分得到下一次迭代挠度函数。利用相邻两次迭代屈曲模态函数最大挠度相等准则,推导出了临界压力公式。与集中力和分布载荷单独作用下的欧拉临界力公式和贝塞尔函数精确解相比,二、三次迭代就可以达到令人满意的工程要求精度。在轴向压力和分布载荷联合作用下,经过三次迭代,可得到临界力的简洁表达式,对实际工程中的压杆具有重要的指导意义。     

移动载荷作用下简支梁的动态响应及裂纹损伤识别研究

基于小波多分辨率分析的方法,根据移动载荷作用下简支梁动态响应特性,利用梁上一点振动信号对裂纹梁进行损伤识别。移动载荷经过梁上裂纹处时,必然导致梁响应时间历程曲线的奇异性,这种奇异性不能直接被观察到,但是可以通过小波多分辨率分析进行识别。利用有限元Ansys软件的瞬态分析方法进行裂纹梁移动载荷作用下的损伤识别数值模拟,通过梁上某一点挠度、速度和加速度的振动信号,利用小波多分辨率分析有效地识别出单个及多个裂纹,同时扩展到多个同向和相向移动载荷作用下裂纹梁的损伤识别。最后,通过不同小波函数的分析结果比较,寻找更加有效的小波函数。以上的损伤识别方法均在较低的移动载荷速度作用下有效,随着速度的增加,裂纹梁损伤识别的有效性越差     

一类考虑温度效应的截面插值梁模型

提出了一种截面插值梁模型,利用该模型求解梁在非均匀热载荷作用下的动静态响应,解决了传统梁理论无法处理受不均匀温度场的梁的问题。利用拉格朗日插值函数对梁单元的截面和轴向分别插值,构造梁的位移场。将位移场代入热弹性动力学方程,得到单元应变和应力,再依据虚功原理推导出单元刚度矩阵、质量矩阵以及等效节点载荷列阵,求解得到热应力。利用热应力的横向剪切力更新单元刚度矩阵,计算梁在热载荷作用下的振动特性。计算结果表明,该方法得到的结果与实体单元模型结果吻合,并且更易于处理受非均匀热载荷作用的细长结构,同时能很好地反映截面的形状、受载及响应结果。     

矩形大开孔薄壁圆筒真空室的强度及屈曲分析

本文运用三维有限元分析方法，对薄壁圆筒真空室上有大面积矩形开孔和接管的一类真空室进行了应力分析，并依据第三强度理论给出了应力及变形情况。此外，本文还应用特征值法对真空室进行了屈曲分析，得到了其一阶临界载荷和波形。结果表明真空室在承受工作载荷条件下满足强度和稳定性要求。     

四边弹性梁支承的矩形板非线性弯曲

本文给出四边弹性梁支承的矩形板在横向荷载作用下的非线性弯曲的重级数解。通过把板内的横向位移展成重傅里哀级数,在边界上的位移展成单傅里哀级数以及把应力函数展成广义傅里哀级数,使边界条件转化成了无穷线性代数方程,控制微分方程转化成了无穷非线性代数方程。文后给出了四边弹性梁支承和对边简支对边弹性梁支承的矩彤板非线性弯曲的计算结果。     

点支撑预应力中厚矩形板的横向振动

基于Reissner-Mindlin一阶剪切变形板理论,讨论在预加面内机械荷载或温度场作用下,点支撑中厚矩形板的横向振动。温度场假定沿板表面为均布,沿板厚方向为线性分布的。利用考虑剪切变形影响的Timoshenko梁函数,采用Rayleigh-Ritz法给出不同边界条件下点支撑中厚板的自振频率。结果表明,温度升高与预加面内压力将使板的自振频率下降,支撑点位置的变化、边界约束条件和横向剪切变形效应都对板的自振频率有显著影响。     

含矩形内部分层的复合材料圆柱壳块 三维问题的片条合成能量解法

根据叠加原理将含有矩形分层的复合材料圆柱壳块在横向载荷作用下的受力状态进行分解,将分层问题归结为在分层表面受附加剪切载荷作用时附加状态的分析,并据此建立了一个仅包含分层区的力学模型。通过切取纵横切片,利用含分层层合直梁与曲梁的附加位移,构造分层区附加位移模态。最后,应用最小势能原理确定位移幅值的闭合解。     

解析型弹性地基Timoshenko梁单元

采用双参数弹性地基模型和Timoshenko深梁模型,建立了弹性地基一般梁挠度控制方程,求解得到了挠度方程解析通解,构建了双参数弹性地基深梁的挠度、截面弯曲转角及剪切角的解析位移形函数。建立了梁模型、梁基模型等两种势能泛函,利用最小势能原理,构造了两个双参数弹性地基深梁单元,给出了单元列式。分析表明:梁模型单元在均布荷载作用下误差为0.221%,非均布荷载作用下误差为0;梁基模型单元在均布荷载作用下误差为0,在两端集中力作用下误差为6.597%,在跨中集中力作用下误差为102.716%;同时,该文提出的双参数Timoshenko梁模型单元不存在剪切闭锁的问题。     

Unilateral buckling of elastically restrained rectangular mild steel plates

 This paper considers the elastic unilateral buckling of rectangular mild steel plates that are restrained elastically and subjected to bending and axial actions. A variational formulation of the Ritz method using linear combinations of harmonic functions for the buckling deformations is used to establish an eigenproblem to determine the plate local buckling coefficients. The motivation for the study is the retrofit of reinforced concrete beams by gluing and then bolting steel plates to the sides of the beam. Such plates, when acting compositely with the concrete beam, are subjected to predominantly bending and axial actions which may cause unilateral local buckling. Whereas the bolts provide complete restraint against buckling at discrete points, the glue may also inhibit local buckling between these nodal points since it acts as a continuous elastic restraint. The influence of the glue stiffness, support conditions and plate proportions on the unilateral buckling of such plates are assessed.     

广义函数论在厚板动力分析中的应用

本文运用广义函数论处理δ函数的导数,对集中力作用下的厚板进行动力分析。基本方程采用由本文作者推演得到的改进的Donnell厚板振动方程。用样条配点法求解广义坐标,对集中力作用下的厚板弹性动力响应给出解的一般表达式。文中以能形板为例给出了数值结果,对按改进理论和经典理论所预示的结果进行了比较。本文方法可以用于厚板物理非线性和几何非线性动力分析和厚板与连续介质共同作用的场合,文中给出了有关表达式。     

装配式建筑双槽钢组合截面梁整体稳定系数研究

提出了一种模块化装配式柱贯通梁实腹式钢结构框架体系,对板块拼接形成的双槽钢组合截面梁的整体稳定性进行了研究。首先证明了双槽钢组合截面梁有限元模型建立方法的可行性,然后分析了不同螺栓布置方式下螺栓间距对双槽钢组合截面梁静力性能的影响,得到合理的螺栓间距。对比分析了梁截面高度、翼缘宽度和厚度、腹板厚度、梁长、双槽钢间隙宽度、螺栓布置方式和荷载类型等参数对钢梁整体稳定性的影响,用拟合的方法得到了等效弯矩系数的计算公式以及弹塑性稳定系数和弹性稳定系数的关系公式。通过对纯弯荷载作用下弹性稳定系数计算公式的等效弯矩系数修正和弹塑性修正,得到了不同荷载类型下的弹塑性稳定系数的计算公式。     

Fatigue behaviour of CFRP L-shaped plates for shear strengthening of RC T-beams

Prefabricated carbon fibre reinforced plastic (CFRP) L-shaped plates can be used to shear strengthen reinforced concrete (RC) T-beams. Previous investigations by EMPA have shown the suitability of the CFRP L-shaped plates for static shear strengthening.In this paper, a large-scale fatigue test is presented which demonstrated the suitability of the CFRP L-shaped plates for shear strengthening of RC T-beams for fatigue reasons. The test beam was subjected to 5 million load cycles at a high load level and a subsequent failure test. Its behaviour is compared with that of a similar, statically tested beam. A fatigue design proposal is presented for users of the CFRP L-shaped plates.     

Elasticity Solution of a Cantilever Functionally Graded Beam

This paper considers the plane stress problem of a cantilever functionally graded beam subjected to linearly distributed load. The material properties of the functionally graded beam are assumed to vary continuously through the thickness, according to a power-law distribution of the volume fraction of the constituents. First, the partial differential equation, which is satisfied by the stress functions for the axisymmetric deformation problem is derived. Then, stress functions are obtained by proper manipulation. A numerical example is finally presented to show the effect of material inhomogeneity on the elastic field in a functionally graded cantilever beam.     

On buckling of crosswise rigid elastic cantilever plates

Summary The classical two-dimensional equations for the buckling of thin elastic anisotropic plates are reduced, on the basis of an assumption of crosswise rigidity, to a system of one-dimensional equations. The reduction pre-supposes that the crosswise dimension of the plate is small compared to it's spanwise dimension and leads, effectively, to a system of beam buckling equations which automatically associates a warping stiffness effect with the classical beam bending and twisting stiffness effects. In the event that inertia load terms are to be considered the system is of the eight order with respect to the spanwise space coordinate. In the absence of such load terms the system can be reduced to the sixth order, with further reductions possible for suitably specialized load conditions.     

解析型Winkler弹性地基梁单元构造

该文采用Winkler弹性地基梁理论确定了弹性地基梁的挠度方程解析通解; 根据最小势能原理建立了解析型Winkler弹性地基欧拉梁及铁摩辛柯梁的单元刚度及等效节点荷载; 得到了解析型弹性地基欧拉梁单元AWFB-E及铁摩辛柯梁单元AWFB-T。同时,论文还采用传统里兹法求得了相应的Winkler弹性地基欧拉梁及铁摩辛柯梁单元刚度矩阵,得到了里兹法弹性地基欧拉梁单元RWFB-E及铁摩辛柯梁单元RWFB-T。对该文构建的两类单元与一般梁-基体系有限元分析结果及理论解析解进行了对比。对比结果表明,传统里兹法由于其多项式形函数无法精确模拟弹性地基梁变形,因此其结果与理论解析解有误差,但随着单元数量增多其误差减小; 采用解析型单元进行计算时,无论单元数量多少,得到的均为“真实”解,说明解析试函数法求得的位移形函数比一般的多项式形函数精确,得到的弹性地基梁单元具备解析型、精确性的特点,可应用于解决实际工程问题。     

弹性地基上正交各向异性自由矩形板的弯曲

本文运用文所建立的方法,研究Winkler弹性地基上正交各向异性自由矩形板弯曲问题的精确解。以受集中载荷作用的板为例,给出不同弹性系数地基上板的位移和弯矩的数字计算结果。     

Dynamics of elastically connected double-functionally graded beam systems with different boundary conditions under action of a moving harmonic load

This paper studies the dynamic responses of an elastically connected double-functionally graded beam system (DFGBS) carrying a moving harmonic load at a constant speed by using Euler–Bernoulli beam theory. The two functionally graded (FG) beams are parallel and connected with each other continuously by elastic springs. Six elastically connected double-functionally graded beam systems (DFGBSs) having different boundary conditions are considered. The point constraints in the form of supports are assumed to be linear springs of large stiffness. It is assumed that the material properties follow a power-law variation through the thickness direction of the beams. The equations of motion are derived with the aid of Lagrange’s equations. The unknown functions denoting the transverse deflections of DFGBS are expressed in polynomial form. Newmark method is employed to find the dynamic responses of DFGBS subjected to a concentrated moving harmonic load. The influences of the different material distribution, velocity of the moving harmonic load, forcing frequency, the rigidity of the elastic layer between the FG beams and the boundary conditions on the dynamic responses are discussed.