钢筋混凝土拱承载力分析的齐次广义屈服函数

为了解决弹性模量调整法应用于钢筋混凝土(RC)结构的难题，建立了矩形截面RC偏压构件的通用齐次广义屈服函数。充分考虑RC偏压构件的破坏机理，并利用二次函数建立了矩形截面RC构件的分段光滑压弯承载力相关方程。通过回归分析建立分区表达的截面特征函数，以综合考虑钢筋混凝土偏压构件的截面几何和材料性能对承载力的影响，在此基础上采用分数指数幂的一阶多项式建立矩形截面RC偏压构件的齐次广义屈服函数。利用单元承载比定义高承载单元的自适应识别准则，通过有策略地缩减高承载单元的弹性模量模拟RC拱结构高应力区域的刚度退化，并根据线弹性迭代分析确定RC拱的极限承载力，据此提出了RC结构承载力分析的弹性模量缩减法。通过与模型试验及增量非线性有限元法对比分析，验证了该文方法具有较高的计算精度与计算效率。     

中厚板的一般精确解研究

本文选取由三角级数和多项式组成的挠度函数和应力函数，函数满足方程和边界条件，因而得到矩形厚板的一般精确解。     

受边缘非线性分布荷载作用矩形薄板的面内应力分析

矩形薄板边缘受非线性分布面内载荷作用的情况在工程中经常遇到,精确的应力分析也是薄板稳定性分析的基础,由于问题的复杂性目前还没有精确解.该文根据弹性力学理论,采用里兹法求解矩形薄板边缘受非线性分布载荷作用的面内应力,应力函数采用切比雪夫多项式并满足所有应力边界条件.结合数学计算软件Mathematica,分析了不同长宽比...     

∏形梁剪力滞效应的解析解

精确分析∏形梁在纵横向荷载共同作用下，其横断面上正应力分布规律对于计算其有效宽度有重要意义，应用力法原理，先将∏形梁和翼板截开成矩形截面梁和平面应力板，在截面上代之以赘余的分布剪力，对于平面应力板，通过利用板变形的对称性来简化其边界条件，然后假设一个满足板的控制方程的Airy应力函数求得板的应力和位移，再利用Timoshenko梁理论求得梁的挠度和转角，根据截面上梁与板的纵向位移相等的变形协调条件便可最终确定截面上的分布剪力，给出的数值算例验证了方法的有效性，并与铜陵长江公路大桥主梁的模型有限元结果和试验结果作了对比，解析解法还可用来检验其他各种数值计算方法的精度，并可推广到其他多跨薄壁结构梁桥的膜应力分析中。     

矩形截面毛坯挤压矩形工件的上限研究

应用上限法建立了由矩形毛坯正挤压矩形截面工件的等挤压比流动模型,推导出了三次多项式表示的流线方程,给出了变形区的动可容速度场、应变速率场及上限功率的表达式,获得了挤压力的上限数值解;分析了变形程度、工件截面形状等参数对挤压力的影响,并获得了相对挤压应力与截面形状系数之间的近似关系式.研究证明采用流线速度场进行上限分析比其他方法更符合实际情况,根据流线设计的凹模优于常规凹模,如平底模.     

弹性基支自由边矩形板的非线性振动问题

弹性地基上四边自由矩形板的非线性振动分析是板理论中一个相当困难的问题，到目前为止这个问题还没有得到解决。本文首先给出一个包含三角函数和多项式组成的挠度函数和应力函数，这些函数满足在四个自由边上的全部边界条件。然后利用伽辽金法得到Ｄｕｆｉｎｇ方程。     

高层建筑层风力特性实验研究

对9种矩形截面的高层建筑物模型进行了风洞实验．观测了模型的层风力特征。通过对大量实验数据的处理和分析．研究了层风力系数和层风力功率谱密度函数在建筑物高度方向上的变化特征．分析了结构高、宽比和矩形截面长、宽比对高层建筑物层风力系数和局部功率谱密度函数特性的影响，并探讨了层风力的空间相关特征。     

ㄇ形梁剪力滞效应的解析解

精确分析ㄇ形梁在纵横向荷载共同作用下,其横断面上正应力分布规律对于计算其有效宽度有重要意义,应用力法原理,先将ㄇ形梁和翼板截开成矩形截面梁和平面应力板,在截面上代之以赘余的分布剪力,对于平面应力板,通过利用板变形的对称性来简化其边界条件,然后假设一个满足板的控制方程的Airy应力函数求得板的应力和位移,再利用Timoshenko梁理论求得梁的挠度和转角,根据截面上梁与板的纵向位移相等的变形协调条件便可最终确定截面上的分布剪力,给出的数值算例验证了方法的有效性,并与铜陵长江公路大桥主梁的模型有限元结果和试验结果作了对比,解析解法还可用来检验其他各种数值计算方法的精度,并可推广到其他多跨薄壁结构梁桥的膜应力分析中。     

电磁水表的异径管道流场仿真研究

采用Fluent软件对圆形截面渐变为小圆形截面和矩形截面的异径管道流场进行三维建模和数值仿真,在中间截面面积基本相同的情况下,模拟了异径管中的流场分布,并分析了中间横截面的速度分布,中心截面的平均速度及进出水口的压力损失。研究表明,圆形截面和矩形截面的速度分布在两端管道为10倍直管段时都是呈中线对称分布的,而当水表两端直接为弯管时,圆形截面呈偏离分布,矩形截面呈中线对称分布。另外,中间截面为矩形的中心面的平均速度比中间截面为圆形的平均速度增幅大,在压力损失方面,矩形截面和圆形截面都没有超出国家标准。由上述分析可知,利用Fluent软件可对电磁水表的结构设计起到指导作用。     

矩形孔径上折射率均匀性数据拟合研究

泽尼克圆多项式在圆形光瞳的正交性和能够代表经典像差而被广泛应用到波前分析中,用泽尼克圆多项式作为矩形光瞳基底函数,通过推导得到在矩形光瞳上正交的多项式.这个在矩形光瞳上正交的多项式不仅是唯一的,而且也能够表示经典像差,就像泽尼克圆多项式在表示圆形光瞳时具有这样的特性一样.矩形光瞳上正交多项式像泽尼克圆多项式一样即可以用...     

Stress distribution around a slender notch in a beam

A detailed two dimensional photoelastic investigation is made of the stress distribution around a slender notch in a simply supported beam subjected to a central load. It is found that the shear stress attains a maximum when the notch axis is inclined at 30° with the centroidal axis of the beam.     

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.     

Buckling characteristics of nanocrystalline nano-beams

The buckling and the postbuckling characteristics of nanocrystalline nano-beams with/without surface stress residuals are investigated. A hybrid model is proposed where a non-classical beam model is incorporated with a size-dependent micromechanical model. The micromechanical model has the merit of accounting for the beam material structure effects, i.e. the grain size and the grain boundary effects. To account for the beam size effects, the couple stress theory is implemented where some measures are added to capture the grain rigid rotation effects. The proposed hybrid model is harnessed to derive the governing equations of a nano-beam subjected to an axial compressive load accounting for the mid-plane stretching according to von-Karman kinematics and the surface stress residuals. Analytical solutions for the prebuckling and postbuckling configurations and natural frequencies as functions of the applied compressive axial load are derived. The effects of the beam material structure and the beam size on the beam’s prebuckling characteristics and the postbuckling configurations and natural frequencies are studied. The obtained results reveal that both the size and the material structure of nanobeams have great impacts on their buckling characteristics.     

Exact solution of elasto-plastic stresses in a metal-matrix composite beam of arbitrary orientation subjected to transverse loads

An analytical elasto-plastic stress analysis is presented for a metal-matrix composite beam of arbitrary orientation subjected to a single transverse force applied to the free end of the beam and a uniformly distributed load. The material is assumed to be perfectly plastic in the elasto-plastic solution. A composite consisting of stainless-steel-reinforced aluminum was produced for this work. Sample problems are given for various orientation angles. Elastic, elastoplastic and residual normal and shear stresses are calculated. The location of the elasto-plastic boundary of the beam is obtained according to the x coordinates of the beam.     

Analytical solution for bi-material beam with graded intermediate layer

Using the Airy stress function, an analytical solution is obtained for a bi-material beam with a graded intermediate layer, which is subjected to a uniform load on the upper surface and has different boundary conditions at the two ends. Young’s modulus of the graded intermediate layer is assumed to be an arbitrary function of the thickness coordinate and its Poisson’s ratio is kept a constant. The solution can easily degenerate into the ones of the tri-material beam, the bi-material beam, the homogeneous beam, and the graded beam, and some of them coincide with the available solutions. The analytical and numerical (finite-element-based) results are in agreement with each other for several examples. The influence on the stress distribution for the cantilever beam is discussed when Young’s modulus of the graded intermediate layer takes different functions.     

均布荷载作用下榫卯连接木梁的解析解

基于弹性力学的半逆解法,在均布荷载作用下的简支木梁、铰接木梁和固接木梁解答的基础之上,结合中国古建筑榫卯节点半刚性连接的特点,通过引入两个表示半刚性的参数,得到了榫卯连接木梁内应力分布的多项式解答。通过对一个随梁实例的计算,分析了两个半刚性参数对梁内应力分布的影响,又通过比较榫卯梁和简支梁、铰接梁及固接梁内应力分布的特点,发现剪应力对于木梁尤其是榫卯木梁的影响不能被忽略。该文最后指出,榫卯节点的刚度随荷载的增大是在不断变化的,并给出了变荷载作用下半刚性参数的确定方法。     

插值振型函数法求解移动荷载作用下等截面连续梁的动态响应

根据哈密顿原理,应用插值振型函数法,分析了多跨连续梁在移动荷载作用下的车桥耦合振动动态响应。经实例讨论分析,给出了多跨等截面连续梁在不同速度移动荷载作用下的数值结果。实例分析表明,该方法具有很好的收敛性和很高的精度。具通过对结果的分析讨论,得到了多跨连续梁在移动荷载作用下的一些规律。     

The stochastic finite element method in structural reliability

First-order reliability and finite element methods are used to develop a methodology for reliability analysis of structures with stochastically varying properties and subjected to random loads. Two methods for discretization of random fields are examined and the influence of the correlation length of random property or load fields on the reliability of example structures are investigated. It is found that the correlation length of load fields has significant influence on the reliability against displacement or stress limit states. The correlation length of property fields is significant for displacement limit states, but may not be significant for stress limit states. Examples studied include a fixed ended beam with stochastic rigidity and a plate with stochastic elasticity.     

高温下张弦梁结构力学特征解析解

在实腹钢梁或钢桁架下部张拉预应力高强钢索形成预应力张弦梁结构,然而钢索的预应力对温度变化敏感,因此火灾是危及张弦梁结构安全性的重要灾害,求解高温下结构的力学特征解析解是进一步研究其火灾安全性能的理论基础。考虑高温下钢材材性的衰减、非线性热应变以及几何形变的耦合,建立张弦梁结构高温下梁单元与索单元建立基本平衡微分方程,分别推导出在均布荷载作用下张弦梁结构在均匀温度场及非均匀温度场中,结构跨中挠度、预应力索水平张力和撑杆轴力的解析解;并且基于张弦梁结构力学特征解析解,对比分析了张弦梁结构热力耦合数值分析模型的可靠性,可为后继设计张弦梁受火试验方案及研究其受火破坏机理提供参考。     

The creep of an elastoviscoplastic beam under a bending loading

Thermoplastics start to manifest a nonlinear mechanical behavior from relatively low loading levels. Under a bending solicitation, which generates a nonuniform stress field, the material behavior becomes more challenging. Indeed, a flexed specimen may have different behaviors from one point to another according to the local stress state. In the present work, a six-parameter rheological model is used to simulate the nonlinear behavior of an elastoviscoplastic beam, subjected to a three-point bending load. In the framework of Euler–Bernoulli theory, the mathematical formulation of a bent beam behavior involves the bending curvature function. This function allows the determination of the strain and stress fields along and through the beam. However, when the beam reaches the viscoplastic stage, the differential equation providing the bending curvature of the beam requires a numerical integration, which has been accomplished in this work. This theoretical modeling approach is supported by experimental creep tests carried out on polyamide specimens (PA6). The testing results are qualitatively consistent with the predictions of the proposed rheological model.