也谈矩形截面梁剪应力公式推导

也谈矩形截面梁剪应力公式推导罗开彬（重庆建筑大学，重庆６３００４５）文献［１］对矩形截面梁剪应力公式在变剪力情况下进行了推导，文献［２］对该推导提出了质疑，对此笔者也谈点粗浅的看法．材料力学中，该公式是在无分布荷载梁段（即剪力Ｑ＝ｃｏｎｓｔ）的情况下...     

也谈矩形截面梁剪应力公式推导

也谈矩形截面梁剪应力公式推导罗开彬（重庆建筑大学，重庆６３００４５）文献［１］对矩形截面梁剪应力公式在变剪力情况下进行了推导，文献［２］对该推导提出了质疑，对此笔者也谈点粗浅的看法．材料力学中，该公式是在无分布荷载梁段（即剪力Ｑ＝ｃｏｎｓｔ）的情况下...     

我看“矩形截面梁剪应力计算公式的严格推导”

我看“矩形截面梁剪应力计算公式的严格推导”薛福林（哈尔滨工业大学，哈尔滨１５０００６）文［１］给出一个在梁的剪力不是常量时弯曲剪应力公式的推导，并认为这个推导是严格的。笔者认为该文的推导存在矛盾。该文在假定剪力、弯矩和剪应力都是截面位置坐标的函数时，...     

我看“矩形截面梁剪应力计算公式的严格推导”

我看“矩形截面梁剪应力计算公式的严格推导”薛福林（哈尔滨工业大学，哈尔滨１５０００６）文［１］给出一个在梁的剪力不是常量时弯曲剪应力公式的推导，并认为这个推导是严格的。笔者认为该文的推导存在矛盾。该文在假定剪力、弯矩和剪应力都是截面位置坐标的函数时，...     

关于螺栓或销钉连接构件的弯曲应力分析

由于螺栓或销钉连接构件是一个静不定问题,相关材料力学教材把螺栓或销钉连接构件作为静定问题来处理,有时会导致螺栓或销钉连接构件的弯曲应力及螺栓或销钉剪力计算存在很大的计算误差.因此,按静不定问题来研究螺栓或销钉连接构件弯曲变形,推导出了螺栓或销钉连接构件的弯曲应力及螺栓或销钉剪力计算公式,对工程技术人员理解和掌握螺栓或销钉连接构件的弯曲应力及螺栓或销钉剪力计算有理论指导意义.     

工字形薄壁梁翼缘弯曲切应力的进一步分析

本文通过梁相邻两横截面间轴向的平衡条件,进一步推导了工字形薄壁梁翼缘与腹板交接区域垂直于剪力的切应力和翼缘上平行于剪力的切应力计算公式。结果表明,所得公式完全满足横截面对称性条件和应力边界条件。在此基础上,绘制了工字形薄壁梁横截面上新的切应力分布图。本文的研究成果可作为学生全面学习工字形薄壁梁上弯曲切应力的重要补充。     

箱形梁剪力滞效应分析中的翘曲位移函数及广义内力研究

以薄壁箱梁的弯曲计算理论为基础,从分析翼缘板的面内剪切变形和弯曲剪力流的分布规律入手,从理论上证明二次抛物线是箱形梁剪力滞效应分析中的合理翘曲位移函数。选取剪力滞效应引起的附加挠度作为广义位移,用基于最小势能原理的能量变分法建立箱形梁剪力滞效应分析的控制微分方程和边界条件。对箱梁横截面上新出现的广义内力给出严密定义,并建立了剪力滞翘曲应力的简便计算公式,它与初等梁弯曲应力公式具有相同的形式。对一个简支箱梁模型的计算表明,计算值与实测值吻合良好,从而证实了本文的分析方法和建立的公式是正确的。不同于弯矩的分布,剪力滞广义力矩具有快速衰减的分布特征。对集中荷载作用下的简支箱梁算例,剪力滞效应使其跨中挠度增大达12%,工程实践中必须认真对待。     

剪力公式的论证与应用

 在结构力学中对梁和刚架绘制内力图时一般是先绘制弯矩图,再绘制剪力图. 根据 上述特点，寻求了一种应用弯矩图绘制剪力图的数值方法，即剪力公式. 该公式主要特点是： 把剪力计算的平衡问题转化为几何问题. 并且通过例题的应用，叙述了剪力公式的使用方法. 适用于静定结构和超静定结构.     

均布荷载作用下四角点支承的有梁矩形板弯曲问题

本文将有梁矩形板分为梁和矩形板两部分．对梁写出挠度方程；对矩形板，引用广义简支边的概念和叠加法，写出矩形板的弯曲解及板边的分布剪力．然后将板边的分布剪力代入梁的挠度方程，即得有梁矩形板的定解方程．最后以正方形有梁板为例，做数值计算，说明这种解法是正确的．     

梁格法计算双室箱梁剪力滞效应的精度研究

为研究梁格法计算双室箱梁剪力滞效应的精度,采用梁格法建立单箱双室简支箱梁的梁格分析模型,研究了单箱双室箱梁在竖向集中力以及均布荷载作用下的弯曲效应。采用有机玻璃模型进行实测研究,并建立基于板壳有限元的数值计算模型。将梁格解的剪力滞系数与板壳数值解、实验实测的剪力滞系数进行比较,得出的结论主要有:1采用梁格法计算单箱双室箱梁的剪力滞效应时,横截面的剪力滞系数呈台阶状分布,由于台阶数量过少,使得梁格法很难真实反映单箱双室箱梁的剪力滞效应;2集中荷载作用下,梁格法计算的峰值剪力滞系数偏小,跨中顶板截面与实验值最大相差10.5%;3均布荷载作用下,梁格解与板壳数值解的剪力滞系数在跨中顶板截面最大相差20.7%,峰值剪力滞系数的最大差率为-12.9%,且随着宽跨比的减小,梁格解的剪力滞系数逐渐增大。     

On the solution of the Darboux problem

We consider the problem of determining the angular position of a rigid body in space from its known angular velocity and initial position (the Darboux problem) in quaternion setting. For an arbitrary angular velocity vector of the body, we present a solution based on Lappo-Danilevskii’s recursion relations [1]. New special cases of solvability of the Darboux problem in closed form are obtained.     

On the solution of the sector problem

A rigorous study of the sector problem is presented by using the Mellin transform technique. The stress function is obtained as an asymptotic expansion of the complex inversion integral. The number of terms of this expansion, as well as the differentiability of the stress function, depend on the differential properties of boundary conditions on the radial edges. If these boundary conditions belong toC , this asymptotic expansion is transformed to a uniformly convergent infinite series. The coefficients of the series, which depend only on the boundary conditions along the circumferential edges, are calculated by applying a bi-orthogonality condition, or, by a technique based on the Betti formula.

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Résumé En utilisant la technique de la transformation de Mellin on présente une étude rigoureuse du problème d'un secteur. La fonction des contraintes est obtenue par un développement asymptotique de l'intégral complexe d'inversion. Le nombre de termes de ce développement, ainsi que la differentiabilité de la fonction des contraintes, dépendent de proprietés différentielles des conditions aux limites sur les bords radiaux. Si ces conditions aux limites sont dansC , ce développement asymptotique est transformé en série infinie uniformement convergente. Les coefficients de cette série, qui dépendent uniquement de conditions aux limites sur le bord circulaire, sont calculés à l'aide d'une condition de bi-orthogonalité que nous démontrons, ou, à l'aide d'une technique basée sur la formule de Betti.

     

Numerical solution of the entrainment equation

An equation describing the change in body shape as a result of intense mass entrainment from the surface under the effect of convective aerodynamic heating under the simplest assumptions (dependence of the pressure on only the local slope of the surface, the method of local similarity to compute the heat fluxes) is considered. Mathematical questions originating during its numerical solution are investigated. The instability of explicit schemes is proved in the neighborhood of the stagnation point. A stable explicit-implicit scheme, suitable for a through computation of unsmooth solutions, is proposed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 147–154, March–April, 1978.The author is grateful to V. V. Lunev for constant attention to the research and for useful discussions.     

Exact solution of the Boltzmann equation

We build up immediate connection between the nonlinear Boltzmann transport equation and the linear AKNS equation, and classify the Boltzmann equation as the Dirac equation by a new method for solving the Boltzmann equation out of keeping with the Chapman, Enskog and Grad’s way in this paper. Without the effect of other external fields, the exact solution of the Boltzmann equation can be obtained by the inverse scattering method.     

有界弦的行波解及其与驻波解的关系

 有界弦的振动是介绍数学物理方程求解方法和了解 连续体振动、波动运动形态的一个典型例子. 给出了它的行波解, 并揭示了行波 解与驻波解的关系, 可以帮助加深对弦的运动形态的了解.     

A solution for the narrow rectangular punch

This paper considers the problem of a rectangular flat ended punch acting on an elastic half-space. An approximate solution is generated through application of the elastic line integral equations. The results produced by this method are then compared with another approximate solution already available.

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Zusammenfassung Dieser Aufsatz behandelt das Problem eines starren, flachen Stempels mit rechteckigen Grundriss, der in einen elastischen Halbraum gepresst wird. Eine Näherungslösung wird erzeugt mittels der Integralgleichung des elastischen Linienkontakts. Die auf dieser Weise gewonnene Ergebnisse werden mit einer schon bekannten Näherungslösung verglichen.

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Résumé Dans ce rapport, on considère le problème d'un cachet rigide à base plane rectangulaire qui est poussée dans une semi-espace élastique. Une solution approximative est générée par application de l'équation integrale du contact élastique de ligne. Les résultats produits par cette méthode sont comparés à une solution approximative déjà connue.

     

One approximate solution of the Nekrasov problem

An approximate solution ω = A[ω, μ] of the nonlinear integral Nekrasov equation is obtained by successive replacement of the kernel of the integral operator by a close one. The solution is sought not directly at the bifurcation point μ₁ = 3 of the linearized equation ω = μL[ω] but at the point μ = 1 at which operator A[ω, μ], remaining nonlinear in ω, is linear in μ. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 6, pp. 50–56, November–December, 2007.     

A particular solution for the chaplygin equation

In the theoretical studies of several gasdynamic problems a major role is played by the hodograph plane, where the equations in terms of velocity component variables are linear. In these studies a primary role is played by the Chaplygin equation for the stream function . Chaplygin [1] obtained a general solution for the equation of motion in the hodograph plane. Particular exact solutions of the hodograph are also known [2]: radial flow, spiral flow, etc. Below we consider a particular solution of the Chaplygin equation.     

An exact solution of the Navier-Stokes equations

Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 168–169, July–August, 1989.