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.     

叠梁的变形与弯曲切应力影响的关系讨论

梁的弯曲切应力分析是材料力学中的一个重要内容，但是通过叠梁与整体梁不同弯曲变形形式的演示实验来说明梁层间存在切应力容易造成概念上的混淆。本文仍然采用材料力学方法分析了层间粘接后两层之间的相互作用，指出其本质是约束两层的拉伸与压缩变形而非约束层间剪切变形。正是这种约束作用使得横截面弯曲正应力重新分布，造成两种梁弯曲变形的明显差异。这一分析过程能够启发学生思考实验现象背后的力学本质，理解相关力学概念。     

准静载作用下弹塑性微弯裂纹尖端塑性区

研究了准静载荷作用下的弹塑性弯曲延伸裂纹的塑性区.通过分析,比较精确地确定了弯曲裂纹尖端塑性区域边界上正应力与切应力的分布状态.综合考虑了准静态作用应力,塑性区域边界上正应力与切应力,利用二阶摄动方法,研究分析了弯曲裂纹尖端塑性区域的范围;预测了弹塑性裂纹的扩展路径.     

重新认识横力弯曲梁的切应力强度效应

通过多层叠合梁的横力弯曲问题分析, 证明弯曲切应力不仅直接导致 多层叠合梁的脱层, 而且这种脱层还会进一步引发弯曲正应力的急剧增加. 这种由弯曲切应 力引发的连锁效应和潜在危害, 理应引起同学们的足够重视.     

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。     

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.     

层合梁弯曲正应力的测试与计算

运用电测技术对双金属层合梁的弯曲正应力进行了测试, 并且基于层合梁弯曲的 Timoshenko理论, 计算了均布载荷作用下简支层合梁的弯曲正应力. 通过对结果的比较, 弯曲 正应力的实测值、理论分析值和有限元计算三者结果较为接近, 相互佐证了本文实验方法与 理论分析的正确性. 本文的实验方法和理论分析可以直接引入材料力学的课程教学中, 可作为对传统的弹性梁纯 弯曲实验的扩展和弯曲正应力公式推导的延伸. 有利于加深学生对中性轴和复合材料概念的 理解, 是针对材料力学难点进行教学科研的有益尝试.     

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.     

用切比雪夫多项式研究短梁的弯曲计算

考虑剪切效应,利用切比雪夫多项式构造严格满足表面切应力边界条件的轴向位移表达式,建立了短梁弯曲问题的新理论．利用奇异函数把作用在短梁上的复杂外载荷表示为分布载荷,推导出了短梁弯曲时的截面正应力公式及挠曲线表达式．把采用切比雪夫多项式推导出短梁的弯曲计算公式计算结果与弹性理论计算结果进行比较,可知该方法的计算精度较高．研究结果表明：在复杂外载荷作用下,当长高比小于等于6时,剪切变形对梁的弯曲挠度影响较大,而当长高比小于3时,剪切变形对梁的弯曲应力影响较大;因此建议采用切比雪夫多项式方法给出的挠度表达式、弯曲应力进行计算,因为切比雪夫多项式方法不但给出了复杂外载荷作用下梁截面挠度、弯曲应力的计算通式,而且该方法具有计算过程简便、精度高的优点．     

组合梁中性轴位置确定方法及应力分析

中性轴是梁弯曲分析的重要概念,其位置的确定是组合梁弯曲变形与应力分析的关键.采用相当截面法、加权平均法分析不同材料组合梁中性轴位置.采用相当和加权的概念进行组合截面的正应力与切应力分析.分析可知相当截面法概念清晰、加权平均法简单高效.相当截面法和加权平均法可简化组合梁的应力分析.分析过程有助于加深学生对梁弯曲相关概念的...     

Bending of thin circular rings

The basic equations for the bending of circular rings are deduced from a set of accurate equations for circular cylindrical shells. The advantages in using these differential equations as compared with the customary energy method are shown through examples. It turns out that solutions of these equations can be as easily obtained as solutions of the well-known differential equation for straight beams. It is also shown that the center line of the ring is essentially inextensible, which is assumed ab initio in the classical ring theory.     

Bending instabilities of elastic tubes

The present paper examines instabilities of long thin elastic tubes. Both initially straight and initially bent tubes are analyzed under in-plane bending. Tube response, a combination of ovalization instability and bifurcation instability (buckling), is investigated using a nonlinear finite element (FE) technique, which employs polynomial functions in the longitudinal tube direction and trigonometric functions to describe cross-sectional deformation. It is demonstrated that the interaction between the two instability modes depends on the value and the sign of the initial tube curvature. The ovalization of initially bent tubes is examined in detail and, in particular, the case of opening moments. Furthermore, the paper emphasizes on bifurcation instability. It is shown that buckling may occur prior to or beyond the ovalization limit point, depending on the value of the initial curvature. Using the nonlinear FE formulation, the location of bifurcation on the primary path is detected, post-buckling equilibrium paths are traced, and the corresponding wavelengths of the buckled configurations are calculated. Moreover, results over a wide range of initial curvature values are presented, extending the findings of previous works. Finally, several analytical approaches, introduced in previous research works, are also employed to estimate the moments causing ovalization and bifurcation instability. These approaches are based on nonlinear flexible shell theory or simplified ring analysis. The efficiency and accuracy of those analytical methods with respect to the nonlinear FE formulation are examined.     

Bending of inhomogeneous curved bars

The stress distribution across an inhomogeneous circular beam subjected to pure bending is considered. In previous treatments the spatial variation of the elastic stiffness has been modeled by a power law and here a slight generalization for the form of the elastic stiffness is given. It is shown that the standard curved beam approximation exhibits excellent agreement with the exact results. A method of engineering the stiffness gradient to produce a specified stress profile is presented.     

Bending of a composite beam-column

Summary The paper deals with the bending of a composite beam-column of variable cross-section. The governing equation is developed under usual assumptions concerning the beam-column deformation (the deformation is not small enough to neglect its effect on the equilibrium equations, but it is sufficiently small for geometrical linearization to be carried out) and it refers to any given creep function. A simply supported beam-column of constant cross-section under particular external load is considered as example to show the application of the developed equation and the solution method. Introducing a particular creep function and geometrical properties of cross-section into the general result the known interval in which the values of Euler's critical force lie is obtained as well as the safe load limit.

---

Biegung mit Normalkraft von Verbundträgern bei Berücksichtigung des Einflusses der Systemverformung

Übersicht Die Biegung mit Normalkraft von Verbundträgern mit veränderlichem Querschnitt bei Berücksichtigung des Einflusses der Systemverformung wird betrachtet. Es gelten die üblichen Voraussetzungen, d. h. die Systemverformung ist nicht so klein, daß man sie in den Gleichgewichtsbedingungen vernachlässigen kann, doch so klein, daß man die geometrische Linearisation durchführen kann, und die Grundgleichungen gelten für beliebige Kriechfunktionen. Als Beispiel wird ein exzentrisch gedrückter Balkenträger mit konstantem Querschnitt behandelt, um die Anwendung der Gleichungen und die Lösungsmethode zu zeigen. Für eine spezielle Kriechfunktion und einen gewählten Querschnitt wird das Intervall, in welchen die Euler-Knicklast liegt, gefunden und zudem die Grenzlast.

---

---

Presented at the Euromech Colloquium 231, Constitutive equations in viscoelasticity: Applications and methods of solution, held in Smolenice Castle (Czechoslovakia), Oktober 6–9, 1987     

Method to Calculate Bending Center and Stress Intensity Factors of Cracked Cylinder Under Saint-Venant Bending

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｅｓｔｒｅｎｇｔｈｏｆｍａｔｅｒｉａｌｓ[1],ｉｎｏｒｄｅｒｔｏｅｌｉｍｉｎａｔｅｔｈｅａｄｄｉｔｉｏｎａｌｔｏｒｓｉｏｎｉｎａｔｈｉｎ＿ｗａｌｌｅｄｃｙｌｉｎｄｅｒｗｉｔｈｏｐｅｎｃｒｏｓｓ＿ｓｅｃｔｉｏｎｕｎｄｅｒｂｅｎｄｉｎｇｂｙａｔｒａｎｓｖｅｒｓｅｆｏｒｃｅ,ｉｔｉｓｓｕｆｆｉｃｉｅｎｔｔｏｒｅｍｏｖｅｔｈｅｔｒａｎｓｖｅｒｓｅｆｏｒｃｅａｔｔｈｅｂｅｎｄｉｎｇｃｅｎｔｅｒ.Ｔｈｅｒｅｆｏｒｅａｎａｐｐｒｏｘｉｍａｔｅｍｅｔｈｏｄｔｏｃａｌｃｕｌａｔｅｔｈｅ…     

Bending of corrugated thick rectangular plates

An approximate analytical solution describing the bending of hinged corrugated thick plates is obtained using the second variant of the boundary shape perturbation method and taking into account the first three approximations. The effect of the shape of the boundary surfaces in the zone of maximum external load on the magnitude and nonlinear variation of the displacements and stresses throughout the thickness of a corrugated thick plate depending on the corrugation amplitude and spatial frequency is analyzed. The results are compared to the exact solution for a flat plate     

Bending of edge-bonded dissimilar rectangular plates

This study develops the extended Kantorovich method (EKM) to provide a closed form semi analytical solution for the bending analysis of two edge-bonded thin rectangular plates. The constituent plates could be different in thickness, length, material, loading conditions, and Winkler foundation’s stiffness. A combination of clamp, free, and simply supports are applied to the structure. The shared edge in the composite plate is assumed to be perfectly bonded. By applying the EKM together with the idea of weighted residual technique, two sets of ODEs are obtained. Bending is assumed to remain continuous on the bonded edge. The EKM procedure is modified by applying the coordinate of an arbitrary shared point in the boundary conditions for the shared edge, to relate the bending of the two plates. The ODEs are solved iteratively to obtain the deflection function in a fast convergence trend. Two examples of aluminium-steel plate and functionally graded material-steel plate are considered. The deflection results from the boundary modified EKM (BM-EKM) are in high agreement with the finite element solution results. The bending of stepped plates is a special case of the current study. The suggested BM-EKM strengthens the EKM’s ability for solving complex jointed/bonded structures in structural analyses.

     

Bending of layers weakened by cuts

In the present paper, a method proposed by one of the authors is extended to a class of skew-symmetric elastic problems for the stress analysis of a layer supported by sliding fixed supports and weakened by several stress raisers. The corresponding boundary value problem is reduced to an infinite system of one-dimensional singular integral equations of the second kind. The expressions for the stress components in an elastic layer weakened by stress raisers are presented. Based on the developed analytical algorithm, extensive numerical investigations have been conducted. The results of these investigations are illustrated graphically exposing some novel qualitative and quantitative knowledge about stress concentration in the layer depending on some geometric parameters of stress raisers and Poisson’s ratio of a layer material.