夹层梁弯曲正应力实验

矩形截面梁弯曲正应力测定,是材料力学实验课的基本实验之一.但由于弯曲正应力公式的推导是从实验现象的叙述开始的,学生通过理论学习,对实验现象和实验结果早已熟悉,再作这简单的验证性实验就     

非线性边界约束下梁的弯曲振动

1.引言从强度或刚度要求出发,经常对线性机械结构加上某些在一定变形情况下才起作用的"预备"性约束,这种约束是否起作用,取决于结构的变形状态,它并不相当于一般的刚度方面的增强,实际上构成了它的强度或刚度取决于系统位移的非线性结构.这样的非线性来自边界条件,它既不同于由材料或大变形等原因造成的非线性现象,又不同于描述方程自身的非     

从优化设计理论谈材料力学中的等强度超静定梁

工程中常用的梁结构因各横截面上的弯矩不同,采用等截面梁时,材料不能得到充分利用,经济性较差。若采用等强度梁,可以使所有截面上的最大应力同时达到材料的许用值,充分挖掘梁结构的承载潜能,提高材料利用率。本文从优化设计角度出发,求解等强度梁截面几何尺寸沿轴线变化的情况,有助于在一般情况下深化对等强度梁设计的理解。

     

基于Euler-Bernoulli梁理论研究热膨胀下梁的非线性振动问题

采用二次摄动法研究了弹性梁在热膨胀状态下的横向非线性振动问题。首先,根据能量原理建立了大挠度梁的非线性振动方程,并对其进行量纲归一化;然后,采用二次摄动法将非线性方程进行离散,得到各阶摄动方程,逐阶求解其渐进解。算例结果表明:应用传统的摄动法(KBM)法分析大幅振动问题的偏差比较大,远不及应用二次摄动法得到的解准确;温度和振幅对梁的固有频率影响显著。     

基于非线性梁理论的有限质点法

有限质点法是以向量式力学为基础,用有限数量的质点来模拟结构的变形行为,质点的运动由牛顿运动定律来计算。在有限质点法中,质点通过构件相连,构件约束着质点的运动,并且其内力由质点的运动变量来描述。基于向量式力学的基本思想和非线性梁理论,提出了一种新的有限质点法,该方法在共旋单元坐标系中描述梁的非线性变形。以空间梁系结构为例,推导了计算构件内力的非线性公式,并考虑了弯扭耦合变形。通过两个连续欧拉角的变换公式得到共旋坐标系的旋转矩阵。与传统的有限质点法相比,本文提出的方法避免了刚体虚转动分析。通过四个结构的数值求解,验证了本文方法在计算结构大变形响应时具有较高的精度。     

计及剪切影响的RC梁的非线性分析

为提高钢筋混凝土RC梁的计算效率和精度,提出了一种基于梁截面弯矩-曲率关系的宏观有限元方法,可用于各种跨高比RC梁的材料非线性分析。首先假定了混凝土和钢筋的非线性应力-应变关系,然后引入经过修正的Rodriguez截面模型,根据边界顶点把截面划分成若干梯形单元,利用quasi-Newton法求解由两个变量耦合而成的截面非线性平衡方程,由此建立RC截面的弯矩-曲率关系。在此基础上利用Timoshenko梁弯曲理论建立考虑横向剪切变形影响的RC梁的有限元分析模型。通过对试验梁的分析对比验证了所提出的分析方法的适用性。     

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．     

直接基于单元平衡的梁非线性分析方法

以单元力平衡条件为基础建立的梁单元在近年来受到广泛关注,与传统的以单元位移相容条件为基础建立的梁单元相比,基于平衡的梁单元可获得较高的精度。针对基于平衡的梁单元,给出了一种几何非线性分析方法,使用该方法进行几何非线性分析时不需进行单元内部位移场的构造,避免了使用现有位移场构造方法时可能引起的振荡问题,同时降低了有限元程...     

一端外伸梁对称弯曲弹性位移的置换法确定

置换法应用于求解一端外伸梁,在对称弯曲的条件下,根据直梁挠曲线所在平面内其与切线所成图形的边角几何关系,推导出求解该形梁的挠度和转角的置换法位移方程,其变量是相应的置换梁自由端的挠度、梁长、梁轴线位置坐标等. 对具体载荷梁的求解过程是：先以具体量值填充左、右置换梁自由端的挠度,再将其代入该置换法位移方程的统一表达式,即得到所求梁段的挠度、转角的方程全解. 所用的计算为代数方程的分式四则运算,只需挠曲线和叠加原理概念,无需积分,一般无需查挠度表,结果精确. 给出工程背景的算例.     

材料力学方法分析带锥度杆和梁的精度

运用楔形体顶点受力的弹性力学精确解和有限元法,研究了材料力学等直杆的拉压和等直梁的弯曲应力公式用于分析带锥度杆和梁时的精度.     

Nonlinear Dynamics of a Beam on Elastic Foundation

The nonlinear dynamics of a simply supported beam resting on a nonlinear spring bed with cubic stiffness is analyzed. The continuous differential operator describing the mathematical model of the system is discretized through the classical Galerkin procedure and its nonlinear dynamic behavior is investigated using the method of Normal Forms. This model can be regarded as a simple system describing the oscillations of flexural structures vibrating on nonlinear supports and then it can be considered as a simple investigation for the analysis of more complex systems of the same type. Indeed, the possibility of the model to exhibit actually interesting nonlinear phenomena (primary, superharmonic, subharmonic and internal resonances) has been shown in a range of feasibility of the physical parameters. The singular perturbation approach is used to study both the free and the forced oscillations; specifically two parameter families of stationary solutions are obtained for the forced oscillations.     

简支饱和多孔弹性梁的非线性弯曲

基于饱和多孔介质理论和弹性梁的大挠度弯曲假设,在多孔弹性梁轴线不可伸长,孔隙流体仅沿轴向方向扩散的限制下,建立了微观不可压饱和多孔弹性梁大挠度拟静态响应的一维非线性数学模型.在此基础上,利用Galerkin截断法,分析了两端可渗透的简支多孔弹性梁在突加横向均布载荷作用下的非线性弯曲,给出了梁弯曲时挠度、弯矩以及孔隙流体压力等效力偶随时间的响应曲线.数值结果表明:当载荷较小时,大挠度非线性与小挠度线性理论的结果相差很小,而当载荷较大时,非线性大挠度理论的结果小于相应线性小挠度理论的结果,并且这种差异随着载荷的增大而增大.同时,在载荷突加于梁上时,多孔弹性梁骨架起初不变形,孔隙流体压力等效力偶由零突增为非零,其值与外载荷保持平衡.随着时间的增加,梁的挠度增加,等效力偶逐渐减小为零,最终多孔梁骨架承担全部的外载荷.     

Theory of Short-Term Microdamageability for a Homogeneous Material under Physically Nonlinear Deformation

The structural theory of short-term damageability is generalized to the case of physically nonlinear deformation of an undamaged material. The stochastic elasticity equations for a porous medium whose skeleton deforms nonlinearly are used. The failure criterion for a microvolume of the material is assumed to be in the Huber–Mises form. The microdamage balance equation for a physically nonlinear material is derived. This equation and the macrostress–macrostrain relation for a porous physically nonlinear material constitute a closed-form system describing the coupled processes of physically nonlinear deformation and microdamage. An algorithm is constructed for computing microdamage–macrostrain relationships and plotting deformation curves. Such curves are plotted for the case of uniaxial tension     

Probabilistic Approaches for Optimal Beam DesignBased on Fracture Mechanics

The questions raised in this paper are related to an important class of problems concerning the shape optimization of brittle or quasibrittle elastic bodies with cracks. The optimization problems taken into consideration consist in finding the boundary of a body in such a way that the cost functional (volume of the body) reaches a minimum, while satisfying prescribed bounds on stress intensity factors. These problems are characterized by incomplete information concerning crack size, location and orientation. In this context the paper presents some possible formulations of optimal structural design problems based on probabilistic approaches. Using these approaches optimal designs for beams with surface and internal cracks have been found.Sommario.Il presente lavoro riguarda un'importante classe di problemi di ottimizzazione di forma di corpi elastici fragili o quasi fragili con fratture. I problemi di ottimizzazione considerati consistono nel trovare la forma di un corpo in modo tale che il suo volume sia minimo nel rispetto di alcune condizioni riguardanti il fattore di intensità di sforzo. Questi problemi sono caratterizzati da informazioni incomplete riguardanti le dimensioni della frattura, la sua posizione ed il suo orientamento. In questo contesto il presente lavoro presenta alcune possibili formulazioni del problema di ottimizzazione strutturale basato sull'approccio probabilistico. Usando tali approcci vengono ricavate le forme di travi ottime con fratture interne e di superficie.     

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．     

用高阶剪切变形理论研究双模量梁的弯曲

利用高阶剪切变形理论研究了双模量梁的弯曲变形问题,推导出了双模量梁的挠曲线方程及弯曲正应力公式．讨论分析了翘曲函数的指数n对挠度、正应力的影响．研究结果表明：拉压弹性模量的差异对梁的弯曲应力有较大影响．把高阶剪切变形理论的计算结果与弹性理论计算结果进行比较,可知该方法计算精度非常高．     

Semianalytic Finite-Element Method in Problems of Nonlinear Continuum Mechanics

A technique for solving problems of nonlinear continuum mechanics associated with contact interaction, plastic distortion, and continuous and discrete fracture of spatial bodies is developed based on the semianalytic finite-element method generalized to noncanonical bodies. Solutions are obtained to new applied problems in various branches of technology. Compared with the traditional FEM, the technique is highly efficient—the amount of computation needed to solve spatial problems reduces by several orders of magnitude     

用无网格局部Petrov-Galerkin法分析非线性地基梁

利用无网格局部Petrov-Galerkin法求解了非线性地基梁。在Petrov-Galerkin方法中，采用移动最小二乘（MLS）近似函数作为场主量挠度的试函数并取移动最小二乘近似函数中的体验函数作为近似场函数的加权函数，采用罚因子法施加本质边界条件。文末给出了两个计算实例，算例的结果表明，Petrov-galerkin法不仅能成功地分析线性地基梁，而且也适用于解非线性地基梁，在分析非线性地基梁时具有收敛快，稳定性好的优点。     

Experimental Nonlinear Identification of a Single Mode of a Transversely Excited Beam

A procedure is presented for using a primary resonance excitation in experimentally identifying the nonlinear parameters of a model approximating the response of a cantilevered beam by a single mode. The model accounts for cubic inertia and stiffness nonlinearities and quadratic damping. The method of multiple scales is used to determine the frequency-response function for the system. Experimental frequency- and amplitude-sweep data is compared with the prediction of the frequency-response function in a least-squares curve-fitting algorithm. The algorithm is improved by making use of experimentally known information about the location of the bifurcation points. The method is validated by using the extracted parameters to predict the force-response curves at other nearby frequencies.We then compare this technique with two other techniques that have been presented in the literature. In addition to the amplitude- and frequency-sweep technique presented, we apply a backbone curve- fitting technique and a time-domain technique to the second mode of a cantilevered beam. Differences in the parameter estimates are discussed. We conclude by discussing the limitations encountered for each technique. These include the inability to separate the nonlinear curvature and inertia effects and problems in estimating the coefficients of small terms with the time-domain technique.