矩形截面杆的翘曲正应力

矩形截面杆的翘曲正应力申向东，康德基（内蒙古农牧学院水利系，呼和浩特０１００１８）杆在平面弯曲时，因剪切使横截面翘曲而产生的正应力，这里称为翘曲正应力，在材料力学教材中一般未给出计算表达式。本文用材料力学的一般方法求得了矩形截面杆在任意分布荷载作用下...     

用材料力学公式计算任意截面短梁正应力时的修正项研究

对材料力学中梁的弯曲应力公式增加一修正项,以反映短梁弯剪翘曲变形对应力分布的影响。提出一种根据短梁横截面边界形状及艾瑞应力函数求解应力修正项的方法,应用弹性力学空间问题的一般理论,通过应力平衡方程、应变相容方程及应力边界条件,建立了关于任意截面短梁的应力修正项及剪应力的基本方程。在所建立的基本方程基础上,导出了矩形截面和圆形截面短梁修正应力的具体计算公式,该修正应力与均布荷载大小及弹性模量与剪切模量之比均成正比,但与截面惯性矩成反比。数值算例表明,本文方法计算的应力与通用有限元软件ANSYS计算的结果吻合良好,从而验证了本文方法及其基本公式的正确性。     

锥形杆轴向拉伸的材料力学解答

对于锥形杆受轴向均匀载荷拉伸的模型,本文基于横截面上轴向正应力均匀分布的假设,给出了其应力及截面变形的材料力学解答。结合ANSYS有限元分析结果及弹性力学精确解进行对比。发现锥角较小时,对于工程实际,材料力学解的误差可以接受。而锥角较大时,需要对轴向正应力公式作修正以使得材料力学解仍然适用。     

工字型截面弯曲切应力分布辨析

工字型截面是材料力学薄壁结构的典型代表,部分教材与教学PPT素材在弯曲切应力分布部分存在问题与争议,本文利用简化模型与力平衡条件给出理论分析结果,同时给出了有限元分析结果作为研讨性教学素材.     

复杂应力状态应力坐标点的简单界定

复杂应力状态应力坐标点的简单界定薛福林（哈尔滨工业大学哈尔滨１５０００６）在材料力学中，为了导出复杂应力状态正应力和剪应力的最大值，需要说明在应力坐标平面中，主单元体的任意斜截面的应力坐标点必在图１的阴影区域内。为此，现在的材料力学书中的办法是推导出...     

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。     

直梁弯曲切应力的讨论

针对矩形截面直梁横力弯曲,讨论了弯曲切应力推导的假设条件,给出了弯曲切应力公式的适用范围.并通过图像的方式展示了不同截面形状下弯曲切应力的分布模式,为学生全面认识与理解弯曲切应力分布提供课堂教学补充材料.     

开口和闭合薄壁截面连接处的近似相容条件

本文证明:对于薄壁杆件,偏心弯曲会引起约束扭转.假设翘曲位移w(z,s)=-θ(z)·Q(s),在开闭截面相接处,有θ_(?)(z)=αθ_l(z),并允许有相对刚体位移.在弥合翘曲差异时,局部应力系Δσ起了作用,从轴向力平衡、弯矩平衡、双力矩平衡决定待定常数α,使翘曲位移在连接处"有可能"连续.实例表明,与有限元法结果符合甚好.     

变截面梁弯曲切应力分析

从一般情况出发在继承经典的弯曲正应力公式前提下,应用静力边界条件与微体平衡方程导出变截面梁的弯曲切应力公式.结果与有限元解基本吻合,而传统材料力学方法与之相差甚远.     

梁的弯曲正应力的材料力学方法修正

从矩形截面梁的剪应力公式出发,推导了在横力弯曲情况下梁的弯曲正应力的近似公式．当梁上的分布荷载可用单一的多项式表示时,该公式在取泊松比v=0时与弹性力学的精确解一致,在其他情况下有些误差,但比传统的材料力学解精确很多．提供了简支梁部分受均布荷载作用的算例,给出了材料力学中梁的正应力公式、该近似公式的计算结果及精确解并做了比较．讨论了公式和方法的普适性．     

Assembly stress for the reduction of stress concentration

A systematic study utilizing the experimental method of reflected photoelasticity was undertaken to determine the effects of assembly stress on the stresses around circular holes under uniaxial tension. The assembly stresses are the result of the contact and bearing stresses between the bolts and the member. It has been concluded that assembly stress contributes to reducing the stresses around the hole.     

Relations between stress growth and stress relaxation functions

The stress relaxation function after steady shear flow and the stress growth function at inception of steady flow are derived for several constitutive equations of the integral and differential types. Relationships between these functions are deduced and discussed.     

The stress subspace of hybrid stress element and the diagonalization method for flexibility matrixH

The following is proved: 1) The linear independence of assumed stress modes is the necessary and sufficient condition for the nonsingular flexibility matrix;2. ) The equivalent assumed stress modes lead to the identical hybrid element The Hilbert stress subspace of the assumed stress modes is established So, it is easy to derive the equivalent orthogonal normal stress modes by Schmidt’s method Because of the resulting diagonal flexibility matrix, the identical hybrid element is free from the complex matrix inversion so that the hybrid efficiency is improved greatly The numerical examples show that the method is effective.     

The general stress strain relation of soils involving the rotation of principal stress axes

1.IntroductionThestudyofsoils'constitutiverelationismostlylimitedinsuchStressstatethattherotationofprincipalstressaxesisabletobeignored.Soonlythevalueofprincipalstressneedtobeconsideredandthedirectionofprincipal'stressisregardedtobeunchangeable.Onthiscondition,theprincipalaxesof'stressincrement,strainincrementjstressandstrainarethesame.Therelevantexperimentsandengineeringsshowthattherotationofprincipalstressaxeswillgeneratesignificantplasticdeformationandthenoncoaxalityofstressandstrain.First…     

多重应力奇异性及其强度系数的数值分析方法

以具有两个应力奇异性次数的平面问题为例,提出了一种利用普通的数值分析结果确定奇异点附近多重应力奇异性的各阶次数以及相应的应力强度系数的数值分析方法,计算实例表明,本方法可以精确地求得各阶应力奇异性的次数,并且可以很方便地应用外插法确定出对应的应力强度系数。     

A piezoelectric stress gauge for measuring dynamic stress in soil and rock media

A piezoelectric stress gauge is described in this paper. Its major performance data are: measuring range 10⁶–10⁸ Pa, response time less than 7μs; non-linearity within ±1% and total stress measurement error within ± 10%. It can be used for measuring dynamic stress in soil, rock and concrete media as well as dynamic force and dynamic pressure in fluids.     

The measurement of the yield stress of liquids

An analysis has been made of different methods of measuring the yield stress of liquids. In the experimental program, a comparison is made of measurements of the yield stress using an Instron 3250 Rheometer in several geometries (cone-plate, parallel plate and eccentric disk) in shear flow and stress relaxation, a laboratory vane and a cone penetrometer. Good agreement has been obtained between the shear flow data and the laboratory vane, while stress relaxation appears to underestimate the yield stress.     

A study on stress intensity factors and singular stress fields of three-dimensional interface crack

By using the finite-part integral concepts and limit technique, the hypersingular integrodifferential equations of three-dimensional (3D) planar interface crack were obtained; then the dominant-part analysis of 2D hypersingular integral was further used to investigate the stress fields near the crack front theoretically, and the accurate formulae were obtained for the singular stress fields and the complex stress intensity factors. After that, a numerical method is proposed to solve the hypersingular integrodifferential equations of 3D planar interface crack, and the problem of elliptical planar crack is then considered to show the application of the method. The numerical results obtained are satisfactory. Project supported by the Foundation of Solid Mechanics Open Research Laboratory of State Education Commission at Tongji University and the National Natural Science Foundation.     

A physical decomposition of the stress tensor for complex flows

Traditionally, the components of the stress with respect to a relevant coordinate system are used for the purpose of stress visualisation and interpretation. A case for using a flow dependent measure to interpret and visualise stress is made for two dimensional flow, together with a suggestion for extending the idea to three dimensions. The method is illustrated for Newtonian and Oldroyd B fluids in both the eccentrically rotating cylinder and flow past a cylinder benchmark problems. In the context of a generalised Newtonian fluid, the relation between the flow-dependent stress measure to other field variables under certain flow conditions, is examined and is indicative of its importance in complex flow.

Inversion of speckle interferometer fringes for hole-drilling residual stress determinations

Speckle interferometric fringe patterns record stress-relief displacements induced by the drilling of blind-holes into prestressed objects. The quantitative determination of residual stress state from such stress patterns is difficult because of the ambiguity in the order of the observed fringes. The plane stress magnitudes are provided directly from selected fringe positions using a stochastic, iterative least squares minimization approach. The inversion requires prior knowledge of the experimental geometry and an appropriate uniaxial stress-relief displacement basis function derived from three-dimensional finite element calculations. Superpositioning of the rotated and scaled displacement basis functions allows the stress-relief relaxation for any biaxial state of stress to be determined. In this paper, fringe patterns were forward modeled from a large ensemble of calculated biaxial stress-relief displacement fields. Inversion of these noise-free fringe patterns reproduced the biaxial stresses with negligible error. Analysis of more realistic fringe patterns that include speckle noise gave stress magnitude errors that diminished rapidly with the number of selected points to better than 3 percent for 100 points. Sensitivity of the optical method is influenced by a number of factors, but the ensemble of model fringe patterns studied indicates that the stress magnitudes (nomalized with respect to the material's Young's modulus) from 3×10^–4 to 10^–2 can accurately be determined with visible laser radiation. The method is amenable to automation and can easily be extended to study near surface gradients in the residual stresses or applied to other optical recording techniques such as moiré and phase-shifting interferometry.