从一个怪例看细长梁理论的基本假定

分别采用欧拉和铁木辛柯梁理论分析了均匀分布力偶作用下的两端固支等截面匀质细长 梁, 并通过ABAQUS有限元分析了一个实例, 验证了铁木辛柯梁理论分析的结果. 对比证明在 这种载荷及边界条件下即使细长梁, 也必须考虑剪切效应的影响.     

细长压杆临界挠度的一级非线性解

给出细长压杆临界挠度的一级非线性解, 从而简单明了地解释了材料力学教学中细长压杆临界挠度不能确定的原因.     

弯压组合中一个不容忽视的问题

提出了在弯压组合问题的强度计算中,轴向压力对最大挠度和最大弯矩的影响不可忽视,并导出了计算这种影响的解析式,以及忽略和考虑这种影响的判别式.     

汽车板弹簧减振与等强度梁教学实验

汽车板弹簧减振是等强度梁优良动力特性在工程应用中的典型例子. 以此为背景,设计了一个等强度梁动载实验,并与相应的等直梁动载实验对比,介绍了实验装置、原理、步骤和实验结果. 实验揭示了汽车板弹簧减振的机理,综合了《材料力学》中“等强度梁”、“动载荷”和《理论力学》中“质点振动”等内容.     

深梁的精确解

抛弃所有梁理论假设, 直接从平面应力理论, 导出深梁的状态方程, 求解了简支梁精确解, 并与有限元解进行比较, 结果吻合较好.     

超静定梁变形计算的积分法

从线性化弯矩和曲率关系出发,将超静定梁多余反力的弯矩叠加到梁截面弯 矩中去,经两次积分得到了包括积分常数和多余反力的分段转角方程和挠曲线方程,利用边界 条件和连续条件确定积分常数和多余反力,进而确定了转角方程和挠曲线方程.文中工作扩大 了积分法的应用范围. 教学实践表明,用积分法解超静定梁的变形能够起到帮助学生学习和 掌握固体力学的边值问题解题思想的作用.     

细长柔韧压杆弹性失稳后挠曲线形状的计算机仿真

采用Maple编程对细长柔韧压杆弹性失稳后挠曲线形状进行了计算机仿真,进行了细长柔韧压杆弹性失稳后最大挠度和挠曲线封闭两种情况下的挠曲线形状仿真和详细的解答.分析计算了失稳后屈曲的力学特征,给出了解析表达式;分析计算了失稳后屈曲的平衡状态曲线的几何特征,绘出了计算机仿真曲线.结果表明:失稳后最大挠度和挠曲线封闭是属于两个完全不同的屈曲状态.     

关于弹性梁的数学模型

叙述和比较一维弹性体的两种不同建模方法, 即弹性梁的传统建模方法和基于Kirchhoff-Cosserat模型的建模方法. 应用精确Cosserat模型分析梁的三维运动. 考虑中心线的拉伸压缩变形、截面的剪切变形、截面转动的惯性和端部载荷影响等因素, 建立精确的弹性梁动力学方程. 讨论梁的静态和动态平衡稳定性. Kirchhoff杆、铁摩辛柯梁和欧拉--伯努利梁等为Cosserat模型在各种简化条件下的特例.     

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.     

从理论力学的教学谈过程式启发教育

以力系平衡为例,提出了在理论力学教学中使用过程式启发教育的方法.%主要过程是：通过精心备课形成知识结构树和认识逻辑树,设置适当的问题情境以引发思考,%启发诱导以引导思维流程,激发头脑风暴以让大多数学生享受思考的乐趣,归纳总结以形成%学生对自己思维特点的再认识.     

任意有限个平行移动荷载作用下简支梁绝对最大挠度的解析算法研究

利用能量原理中的最小势能原理以及多元函数的极值原理,得到了简支梁在任意有限个平行移动荷载作用下的挠度方程与绝对最大挠度的解析算式。建立的可能位移函数既满足了位移几何边界条件,又满足了静力边界条件,故足可以保证简支梁的挠度计算精度。     

Numerical analysis of large elasto-plastic deflection of constant curvature beam under follower load

This paper describes a method to analyze the elasto-plastic large deflection of a curved beam subjected to a tip concentrated follower load. The load is made to act at an arbitrary inclination with the tip tangent. A moment-curvature based constitutive law is obtained from linearly hardening model. The deflection governing equation obtained is highly non-linear owing to both kinematics and material non-linearity. It is linearized to obtain the incremental differential equation. This in turn is solved using the classical Runge–Kutta 4^th order explicit solver, thereby avoiding iterations. Elastic results are validated with published literature and the new results pertaining to elasto-plastic cases are presented in suitable non-dimensional form. The load to end angle response of the structure is studied by varying normalized material and kinematic parameters. It is found that the response curves overlap at small deflection corresponding to elastic deformation and diverge for difference in plastic property. The divergent response curves intersect with each other at higher deflection. The results presented also show that the approach may be used to obtain desired non-uniformly curved beam by suitably loading a uniform curvature beam.     

Simplest differential equation of stock price,its solution and relation to assumption of black-scholes model

1　TheSituationofMathematicalAnalysisofStockMarketandTwoAnalyticSystems　　Mostpublicationsunderthetitleofstockmarket,includinghundredsofauthoritativeguidetocontemporaryinvestmenttheories[1],belongtodatacollection ,summinguptheexperienceofmakingprofits,operatingskills,qualitativeanalysis,andtechnicalanalysisusingsimplemathematics,etc .Thework ,cannotbeconsidered ,ingeneral,asrulequantitativeinvestigationandisstillinadescribingstage.Theliteraturesonbehaviorofstockmarketinvestigatedbyanalytic…     

基于晶体塑性理论研究铝材料高压高应变率下的强度特性

为了了解金属材料在极端加载下复杂动态响应过程中的多种机制和效应,重点针对Al材料在高压、高应变率加载下的塑性变形机制,在经典晶体塑性模型的基础上,对其中的非线性弹性、位错动力学和硬化形式进行改进,建立适用于高压、高应变率加载下的热弹-黏塑性晶体塑性模型。该模型可以较好地描述单晶铝和多晶铝材料屈服强度随压力的变化过程,相比宏观模型,用该模型还获得了多晶Al材料在冲击加载下的织构演化规律,揭示了织构择优取向行为和压力的关系。     

Bending of functionally graded cantilever beam with power-law non-linearity subjected to an end force

A realistic beam structure often exhibits material and geometrical non-linearity, in particular for those made of metals. The mechanical behaviors of a non-linear functionally graded-material (FGM) cantilever beam subjected to an end force are investigated by using large and small deformation theories. Young's modulus is assumed to be depth-dependent. For an FGM beam of power-law hardening, the location of the neutral axis is determined. The effects of depth-dependent Young's modulus and non-linearity parameter on the deflections and rotations of the FGM beams are analyzed. Our results show that different gradient indexes may change the bending stiffness of the beam so that an FGM beam may bear larger applied load than a homogeneous beam when choosing appropriate gradients. Moreover, the bending stress distribution in an FGM beam is completely different from that in a homogeneous beam. The bending stress arrives at the maximum tensile stress at an internal position rather than at the surface. Obtained results are useful in safety design of linear and non-linear beams.     

A new method for the non-linear deflection analysis of an infinite beam resting on a non-linear elastic foundation

The aim of this paper is to develop a new method of analyzing the non-linear deflection behavior of an infinite beam on a non-linear elastic foundation. Non-linear beam problems have traditionally been dealt with by semi-analytical approaches that involve small perturbations or by numerical methods, such as the non-linear finite element method. In this paper, in contrast, a transformed non-linear integral equation that governs non-linear beam deflection behavior is formulated to develop a new method for non-linear solutions. The proposed method requires an iteration to solve non-linear problems, but is fairly simple and straightforward to apply. It also converges quickly, whereas traditional non-linear solution procedures are generally quite complex in application. Mathematical analysis of the proposed method is performed. In addition, illustrative examples are presented to demonstrate the validity of the method developed in the present study.     

On the uniform boundedness of solutions of some non-autonomous differential equations of the fourth order

In this paper, sufficient conditions are established under which all solutions of some non-autonomous differential equations of the fourth order are bounded and uniformly bounded.     

On the Floquet Multipliers of Periodic Solutions to Non-linear Functional Differential Equations

For periodic solutions to the autonomous delay differential equation

Principal parametric resonances of a slender cantilever beam subject to axial narrow-band random excitation of its base

The non-linear integro-differential equations of motion for a slender cantilever beam subject to axial narrow-band random excitation are investigated. The method of multiple scales is used to determine a uniform first-order expansion of the solution of equations. According to solvability conditions, the non-linear modulation equations for the principal parametric resonance are obtained. Firstly, The largest Lyapunov exponent which determines the almost sure stability of the trivial solution is quantificationally resolved, in which, the modified Bessel function of the first kind is introduced. Results show that the increase of the bandwidth facilitates the almost sure stability of the trivial response and stabilizes the system for a lower acceleration oscillating amplitude but intensifies the instability of the trivial response for a higher one. Secondly, the first and second order non-trivial steady state response of the system is obtained by perturbation method and the corresponding amplitude–frequency curves are calculated when the bandwidth is very small. Results show that the effective non-linearity of whether the amplitude expectation of the first order steady state response or the amplitude expectation of the second order steady state response is of the hardening type for the first mode, whereas for the second mode the effective non-linearity of whether the amplitude expectation of the first order steady state response or the amplitude expectation of the second order steady state response is of the softening type. Finally, the stochastic jump and bifurcation is investigated for the first and second modal parametric principal resonance. The basic jump phenomena indicate that, under the conditions of system parameters with a smaller bandwidth, the most probable motion is around the non-trivial branch of the amplitude response curve, whereas with a higher bandwidth, the most probable motion is around the trivial one of the amplitude response curve. However, the stochastic jump is sometimes more sensitive to the change of the bandwidth, in other words, a small change of bandwidth may induce a series of stochastic jump and bifurcation.