变惯矩梁变形的函数解

<正> 一般说来,任何一个变惯矩梁(包括线性变惯矩梁和非线性变惯矩梁)的变形问题,都可以通过对梁的挠曲线微分方程y″=M(x)/EJ(x) (1)进行二次直接积分来求得其函数解.力学与实践     

对"用奇异函数法求解某些变截面梁的变形"一文中线性变惯矩梁的变形问题的看法

读了王燮山同志"用奇异函数法求解某些变截面梁的变形"(力学与实践,Vol.6,1984.4.)一文后,对于文中的第三个问题,即线性变惯矩梁的变形问题提出异议.文中提出用奇异函数法求解线性变惯矩梁的变 ...     

对"用奇异函数法求解某些变截面梁的变形"一文中线性变惯矩梁的变形问题的看法

读了王燮山同志“用奇异函数法求解某些变截面梁的变形”(力学与实践,Vol.6,1984.4.)一文后,对于文中的第三个问题,即线性变惯矩梁的变形问题提出异议.文中提出用奇异函数法求解线性变惯矩梁的变     

确定变惯矩梁变形函数解的一般方法

本文利用泰勒公式，推导出同一类载荷作用下的变惯矩梁变形函数解的一般表达式，较之积分法更加快捷、实用．     

1988年全国青年力学竞赛复赛试题解答

材料力学部分1.一体重为W的跳水运动员站在厚2a长为L的悬臂梁跳水板之端部,已知梁的许用应力为σ_B,惯矩为J,弹性模量为E.允许他起跳的高度在()之...     

任意变刚度梁变形的通用方程

<正> 工程实际中常遇到阶梯形和锥形等变截面变刚度梁,求其复杂载荷作用下的变形多采用近似的数值解法.文[1]给出阶梯形变截面梁第 n 段变形的通用方程,需计算各段端点的转角多项式和挠度多项式的值.文[2]采用直接积分法求解变惯矩梁变形,要确定若干积分常数.本文利用 Heaviside 函数,将任意变刚度化为阶梯刚度,导出了任意变刚度梁变形的一种通用方程     

1988年全国青年力学竞赛复赛试题

材料力学部分1.一体重为 W 的跳水运动员站在厚2a 长为 L 的悬臂梁跳水板之端部,巳知梁的许用应力为 σ_B,惯矩为 J,弹性模量为 E.允许他起跳的高度在()以内.2.两端简支,长为 l 的直圆管中,定常地以速度v 流动着液体.已知管的弹性模量 E,转动惯量 J=     

一维六方准晶层合简支梁自由振动与屈曲的精确解

伪Stroh型公式能够将多场耦合材料的控制方程转化为线性特征系统来求解，从而获得多层结构简支边界条件的精确解.本文利用伪Stroh型公式，研究一维六方准晶层合简支梁的自由振动和屈曲问题，通过传递矩阵法，获得准晶层合梁自由振动固有频率与临界屈曲载荷的精确解.通过与已有梁的剪切变形理论结果比较，验证了本文伪Stroh型公式的正确性和有效性.通过数值算例，分析由两种不同准晶材料组成的三明治层合梁的叠层方式、高跨比、层厚比及层数对梁的固有频率、临界屈曲载荷及其模态的影响规律.结果表明，叠层顺序和梁的高跨比、层厚比对准晶层合梁的自由振动固有频率和临界屈曲载荷有很大影响，可通过调整梁的几何尺寸和叠层顺序得到准晶层合梁的最佳固有频率和临界屈曲载荷.本文给出的精确解可为工程上研究准晶梁的各种数值解法和实验方法提供理论参考.     

沙漠砂混凝土梁抗弯性能研究

为研究沙漠砂混凝土梁的受弯性能,通过7根沙漠砂混凝土梁与1根普通混凝土梁的对比试验,分析了沙漠砂混凝土梁的正截面承载力、试件的变形性能和破坏特征;并对采用现行混凝土规范公式计算的沙漠砂混凝土梁的开裂弯矩、抗弯承载力和挠度进行了探讨。研究结果表明:平截面假定仍然适用于沙漠砂混凝土梁,且沙漠砂混凝土梁的破坏特征以及跨中挠度曲线与普通混凝土梁构件相近;现行规范中梁的开裂弯矩公式、极限承载力公式和挠度计算公式不适用于沙漠砂混凝土梁。因此,本文通过引入与沙漠砂替代率相关的修正系数,提出了适宜于沙漠砂混凝土梁的建议公式,并通过理论分析证明了其可行性。     

复合砂浆钢绞线网加固RC梁受弯性能计算研究

分析了复合砂浆钢绞线网加固钢筋混凝土梁的受弯性能, 不同材料加固梁的受弯性能可采用同一公式进行计算, 研究表明加固梁受弯性能受本体梁的初始受力状态和是否采用三面U型加固影响较大. 采用正截面极限平衡法, 推导出复合砂浆钢绞线网加固钢筋混凝土梁极限抗弯承载力计算公式; 在混凝土结构设计规范公式基础上, 提出加固梁裂缝宽度和裂缝间距计算公式, 加固梁公式计算值与试验值吻合较好.     

Force Action of a Body with a Permeable Boundary on a Wall in a Fluid

The ideal fluid flow due to fluid penetration through the boundary of an infinitely long solid cylinder in contact with a solid wall is determined. A formula is derived according to which the force exerted by a finite-length part of the cylinder on the wall is directed into the wall and can thus have an arbitrarily large absolute value. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 1, pp. 82–84, January–February, 2006.     

Torsion problems for a cylinder with a rectangular hole and a rectangular cylinder with a crack

Using the method of singular integral equation and the crack-cutting technique, the rigorous solutions are obtained for a cylinder with a rectangular hole and a rectangular cylinder with a crack, which exactly satisfy the boundary conditions and the conditions at the corner points. After that the torsional rigidities and the stress intensity factors at the crack tip are determined. Next, for the doubly connected circular cylinder with a rectangular hole the expressions for the singular stresses around the concave corner points are derived and the generalized stress intensity factors are then defined. Since the crack-cutting technique is used in this paper, the solution of the matching rectangular cylinder is also obtained and its numerical results coincide with those in references. Thus the method proposed here is verified. The project supported by National Natural Science Foundation of China     

Unsteady-state filtration of a liquid in a fractured-porous stratum to a well with a hemispherical end-face

A study is made of the motion of a liquid toward a well with a hemispherical end-face with unsteady-state spherical-radial filtration in a fractured-porous stratum consisting of hemispherical regions with different values of the permeability of the system of cracks, superposed one on another. A Laplace transform is used to find exact solutions to the problem of the lowering of the stratum pressure as a function of time and distance as well as of the output of a well working with a constant end-face pressure. The article discusses partial cases corresponding to the exploitation of closed and bounded open fractured-porous strata by a central well with a hemispherical end-face. On the basis of numerical calculations, the effect of the parameters of fractured-porous strata on the change in the indices of the process of their exploitation is established. It is established that, with the exploitation of fractured-porous strata, the process of the lowering of the end-face pressure of the well and its output become stabilized with sufficiently large values of the time.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 115–123, November–December, 1973.     

Interaction of a cylinder with a free surface and a jet

The problem of the asymmetric flow around a cylinder of a nonviscous jet is considered and, in particular, of flow with one free boundary. The problem of the choice of circulation is posed, based on a generalization of the Zhukovskii-Chaplygin postulate. Several possibilities are considered and the principle of the minimum of the maximum velocity on a contour is proposed, which qualitatively and quantitatively truly reflects certain aspects of the interaction of the cylinder with the flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 50–58, September–October, 1977.     

Simulation by a source of a thin jet from a body

An exact analytic solution is found to the following plane hydrodynamic problem. An unbounded flow of an ideal incompressible fluid flows around a plate BB' placed at right angles to the velocity vector of the flow at infinity. The pressure on the free boundary P is equal to the pressure in the flow. From an opening in the center of the plate, a jet with flow rate Q from a cavity with pressure P₀ encounters the flow head-on. As a result of the solution, it is found that for fixed width of the opening the values of Q allowed by the scheme are limited. In the limiting case Q = 0 Chaplygin's flow is obtained with stagnation region at the front [1], and in the limiting case Q = Q_max a jet out of a cavity with pressure P₀ into a cavity with pressure P. As Q varies in this interval, the total drag, regarded as the drag of the plate and the chamber from which the jet emerges, takes a minimal value at a certain point. If the width of the opening tends to the length of the slab, the problem of the collision of two jets is obtained; if the width of the opening tends to zero (Q o), the problem of jet flow past a slab with a source is obtained. It is shown that the replacement of the jet by the source gives a good approximation in both the sense of the force characteristics and in the sense of the behavior of the free streamlines.Translated from Izvestiya Akademii Nauk SSSR, Hekhanika Shidkosti i Gaza, No. 5, pp. 47–54, September–October, 1979.We thank L. I. Sedov for his interest in the work and G. Yu. Stepanov for proposing the method of solution and for a helpful discussion.     

On a Paradox in the Motion of a Rigid Particle along a Wall in a Fluid

The results of an experimental investigation of spherical particles with different surface roughnesses rolling under their own weight down an inclined pipe wall in a Newtonian fluid at low Reynolds numbers, both with (friction should be taken into account) and without contact with the wall, are presented. It is shown that a fixed particle moves differently in different fluids with similar viscosities and densities. This fact, as well as the possibility of particle motion without contact with the wall, cannot be explained within the framework of the usual hydrodynamic theories. An example is the dependence of the particle motion on the static pressure.