功能梯度材料纯弯曲梁的弹塑性分析

假设功能梯度材料为一理想弹塑性材料,其弹性模量和屈服强度沿梁高度方向按照幂函数变化,在小变形及平截面假设下研究功能梯度材料纯弯曲梁的弹塑性性能.根据Mises屈服准则导出了纯弯曲梁的弹性极限弯矩的解析表达式,建立了梁在弹塑性状态时截面弯矩与截面弹、塑性区分布之间的关系式,给出了梁进入塑性极限状态时中性轴的位置以及塑性极限弯矩的解析计算公式.数值算例的结果表明,功能梯度材料梁的弹塑性性能与均匀材料梁不同,其屈服不一定首先产生于截面最大应力点,而可能有多种不同的屈服模态及相应的塑性扩展.弹性模量及屈服强度的梯度变化对功能梯度材料纯弯曲梁的中性轴位置、截面弹塑性应力分布以及塑性极限弯矩均有较大影响.研究结果可为功能梯度材料梁的弹塑性分析提供一定的参考.     

功能梯度梁纯弯曲特性研究

根据陶瓷和金属的体积分布,利用TTO模型,得到了功能梯度材料力学参数沿梁高度方向变化的规律。在小变形及平面假设下研究了功能梯度矩形截面梁纯弯曲特性。结果表明:弹性模量、屈服应力、切线模量的梯度分布使梁截面的应力呈现明显的不对称;在加载的弹性阶段,中性轴偏向陶瓷一侧并保持恒定;随着载荷的增大,在陶瓷一侧率先出现单边塑性区,中性层的高度先降低后增大;卸载阶段,中性层的高度、梁截面上的应力分布受卸载初始时的弯矩影响;功能梯度纯弯曲梁截面应力及弹塑性边界呈现出明显的不对称性。     

均布荷载作用下功能梯度简支梁弯曲的解析解

利用应力函数半逆解法,研究了均布载荷作用下、材料属性在厚度上任意变化的功能梯度简支梁弯曲的解析解,给出了各向应力应变与位移的解析显式表达式.首先根据平面应力状态的基本方程,得出了功能梯度梁的应力函数应满足的偏微分方程,并根据应力边界条件得出了各应力分布的表达式;进而根据功能梯度材料的本构方程和位移边界条件,得出了应变和位移的分布.最后,通过将本文的解退化到均质各向同性梁并与经典弹性解比较,证明了本文理论的正确性,并求解了材料组分呈幂律分布的功能梯度梁的应力和位移分布,分析了上下表层材料的弹性模量比λ与组分材料体积分数指数n对应力和位移分布的影响.     

形状记忆合金梁纯弯曲的理论分析

基于已有实验得到的形状记忆合金非线性的应力-应变关系,引入拉压不对称系数研究了形状记忆合金纯弯曲梁的力学性能。在平截面假定下,建立了梁在不同弯矩作用下截面应力、相变百分含量、相边界的解析表达式。对两端受弯的简支梁进行数值分析,结果表明:纯弯曲的过程中,平截面假定仍然成立,中性层的移动和表层材料相变状况有关;表层材料发生相变后,中性层偏离截面中心向受压侧移动,直至受压侧表层材料相变完成,完全转变为马氏体相;之后随弯矩的增大,中性层开始反向移动。材料本身的拉压不对称性使得形状记忆合金纯弯曲梁截面应力的分布以及相边界的移动呈现出明显的不对称性。     

具有梯度界面层的双材料悬臂梁解析解

采用应力函数法,求得了具有弹性模量沿高度线性变化的梯度界面层的双材料悬臂梁在均布载荷作用下的应力和位移解析解。该解可退化为双材料梁、弹性模量沿整个梁高线性变化的梯度梁以及均质材料梁的情况,退化为均质材料梁时与已有结果一致。通过一具体算例将得到的解析解与有限元解进行了比较,两者吻合较好。并讨论了梯度界面层的高度变化对梁中的应力和梁端挠度的影响。结果表明,在梁的总高度不变的情况下,增加梯度界面层的高度可减小弯曲应力和梁端挠度,而对挤压应力和切应力的影响很小。     

平行于功能梯度材料夹层的币型裂纹起裂条件

分析了功能梯度材料中币型裂纹的扩展问题．裂纹平行于无限域中功能梯度材料夹层,受有与裂纹面成任意角度的拉应力．假定功能梯度材料夹层与两个半无限域均匀介质完全粘合,其弹性模量沿厚度方向变化．采用基于层状材料广义Kelvin基本解的边界元方法分析裂纹问题,给出了均布正应力和剪应力作用下裂纹的应力强度因子、将应力强度因子耦合于应变能密度断裂判据,讨论了裂纹体在拉伸应力作用下的起裂条件．     

用Laplace变换分析弹┐粘塑性梁的弯曲

在弹塑性梁弯曲变形理论基础上，本文用Ｌａｐｌａｃｅ变换进一步分析了弹－粘塑性梁的弯曲问题．并以矩形截面梁为例，说明弹－粘塑性梁弯曲时的弹性与粘塑性区的应力，梁的挠度及弹－粘塑性交线的计算     

梯度多孔材料单轴压缩弹塑性变形的宏微观数值分析

针对闭孔的密度梯度多孔材料,建立含球形孔洞的三维数值分析模型,研究其单轴压缩力学行为。首先,研究密度梯度对多孔材料宏观力学行为(如弹性模量和屈服强度)的影响;其次,研究密度梯度与材料局部力学性能的关系,得到了沿梯度方向弹性模量和屈服强度的分布规律;最后,讨论梯度多孔材料单轴压缩变形局部化机制。结果表明:当梯度材料与均质材料的总体相对密度相同时,梯度材料的宏观弹性模量和屈服强度均低于均质材料水平,其宏观应力-应变关系曲线降低;梯度多孔材料沿梯度方向的力学性能发生急剧变化,等效弹性模量沿梯度方向呈线性分布,屈服强度呈非线性曲线分布,导致沿梯度方向应力、应变呈现高度的不均匀性;多孔材料的变形局部化产生于孔隙率较大的薄弱位置,再逐渐向孔隙率较小的位置发展。由此可知,孔隙率的梯度变化影响多孔材料的力学性能,通过改变孔隙率的分布可实现材料预期的力学性质。     

斜侵彻混凝土靶的刻槽弹体的结构响应

基于刚塑性理论和侵彻载荷理论分析，将刻槽弹体简化为空间自由变截面梁，给出了弹体在侵彻混凝土早期的刚体响应行为，得到了弹体任一截面弯矩、剪力以及屈服函数的分布规律。基于此理论分析，得到了刻槽弹体壁厚、材料屈服强度、初速及倾角对弹体弯曲的影响规律。     

任意梯度分布功能梯度涂层平面裂纹分析

提出可以分析任意梯度功能梯度材料的分层模型,并采用该模型研究功能梯度涂层平面裂纹问题.采用Fourier变换和传递矩阵法将该混合边值问题化为奇异积分方程组,通过数值求解获得应力强度因子.考察了分层模型的有效性,以及材料梯度变化形式、结构几何尺寸和材料梯度参数对裂纹应力强度因子的影响,发现结构几何尺寸、材料梯度变化形式、...     

界面特性对功能梯度智能梁静动态响应的影响研究

采用状态空间法分析了两边简支的含压电夹层的功能梯度梁的静力弯曲和自由振动问题．为了考虑中间压电层与上、下功能梯度层之间的粘结效果,采用线性弹簧模型以模拟界面性能．假设上下功能梯度层的材料参数沿厚度连续变化,而压电层则是均匀材料,并且它们都是正交各向异性的．由于功能梯度梁的不均匀性使得直接求解比较困难,文中用层合模型来进行近似．数值算例中,分别考虑了压电层用于传感器或作动器的情形,分析了粘结界面完美程度对组合梁静力弯曲和自由振动频率的影响．     

纵横载荷作用下功能梯度梁的弯曲和过屈曲

基于一阶非线性梁理论和物理中面概念,导出了纵横向载荷作用下功能梯度材料(FGM)梁非线性弯曲和过屈曲问题的控制方程,并获得了该问题的精确解;据此解研究了梯度材料性质、外载荷、横向剪切变形以及边界条件等因素对功能梯度材料梁非线性力学行为的影响,分析中假设功能梯度材料性质只沿梁厚度方向,并按成分含量的幂指数函数形式变化。结果表明:纵横载荷共同作用下,功能梯度梁的弯曲构形将有无限多个;随着梯度指数的增大,梁的变形减小,临界载荷升高;随着长高比的增大,横向剪切变形的影响减小。     

Semi-analytical elasticity solutions for bi-directional functionally graded beams

Elasticity solutions are presented for bending and thermal deformations of functionally graded beams with various end conditions, using the state space-based differential quadrature method. The beams are assumed to be macroscopically isotropic, with Young’s modulus varying exponentially along the thickness and longitudinal directions, while Poisson’s ratio remaining constant. The state space method is adopted to obtain analytically the thickness variation of the elastic field and, when coupled with differential quadrature, the longitudinal discretization can be analyzed in an approximate manner. This approach is then validated by comparing the numerical results with the exact solutions for a special functionally graded beam and with finite element solutions. The influences of material gradient indices on the response of bi-directional functionally graded beams are finally investigated.     

Nonlinear vibration analysis of functionally graded beams considering the influences of the rotary inertia of the cross section and neutral surface position

In the paper work, the nonlinear vibration response of functionally graded (FG) Euler–Bernoulli beam resting on elastic foundation is studied. Based on von Kármán’s geometric nonlinearity, the partial differential governing equations describing the nonlinear vibration of FG Euler–Bernoulli beam are derived from Hamilton’s principle and are reduced to an ordinary nonlinear differential equation with quadratic and cubic nonlinear terms via Galerkin’s procedure. Due to unsymmetrical material variation along the thickness of FG beam, the neutral surface concept is proposed to remove the stretching and bending coupling effect and the rotary inertia of the cross section is incorporated to obtain an analytical solution. Numerical results are presented to show the effects of the nonlocal parameters and vibration amplitude on the frequency responses. This results may be useful in design and engineering applications.     

Analysis of curved beams using a new differential transformation based curved beam element

Differential transformation method is used to obtain the shape functions for nodal variables of an arbitrarily non-uniform curved beam element including the effects of shear deformation considering axially functionally graded material. The proposed shape functions depend on the variations in cross-sectional area, moment of inertia, curvature and material properties along the axis of the curved beam element. The static and free vibration of axially functionally graded tapered curved beams including shear deformation and rotary inertia are studied through solving several examples. Numerical results are presented for circular, parabolic, catenary, elliptic and sinusoidal beams (both forms—prime and quadratic) with hinged-hinged, hinged-clamped and clamped-clamped and clamped-free end restraints. Three general taper types (depth taper, breadth taper and square taper) for rectangular cross section are studied. Out of plane vibration is studied and the lowest natural frequencies are calculated and compared with the published results. Out of plane buckling is investigated for circular beams due to radial load.     

Homogenized and classical expressions for static bending solutions for functionally graded material Levinson beams

The exact relationship between the bending solutions of functionally graded material (FGM) beams based on the Levinson beam theory and those of the corresponding homogenous beams based on the classical beam theory is presented for the material properties of the FGM beams changing continuously in the thickness direction. The deflection, the rotational angle, the bending moment, and the shear force of FGM Levinson beams (FGMLBs) are given analytically in terms of the deflection of the reference homogenous Euler-Bernoulli beams (HEBBs) with the same loading, geometry, and end supports. Consequently, the solution of the bending of non-homogenous Levinson beams can be simplified to the calculation of transition coefficients, which can be easily determined by variation of the gradient of material properties and the geometry of beams. This is because the classical beam theory solutions of homogenous beams can be easily determined or are available in the textbook of material strength under a variety of boundary conditions. As examples, for different end constraints, particular solutions are given for the FGMLBs under specified loadings to illustrate validity of this approach. These analytical solutions can be used as benchmarks to check numerical results in the investigation of static bending of FGM beams based on higher-order shear deformation theories.     

Bending of functionally graded nanobeams incorporating surface effects based on Timoshenko beam model

The bending responses of functionally graded(FG) nanobeams with simply supported edges are investigated based on Timoshenko beam theory in this article. The Gurtin-Murdoch surface elasticity theory is adopted to analyze the influences of surface stress on bending response of FG nanobeam. The material properties are assumed to vary along the thickness of FG nanobeam in power law. The bending governing equations are derived by using the minimum total potential energy principle and explicit formulas are derived for rotation angle and deflection of nanobeams with surface effects. Illustrative examples are implemented to give the bending deformation of FG nanobeam. The influences of the aspect ratio, gradient index, and surface stress on dimensionless deflection are discussed in detail.     

Buckling of an elastoplastic bar

Buckling of a bar of an elastoplastic material is studied. It is shown that for any (σ-?) diagram of the bar material, the limit load (the longitudinal external force) in dimensionless variables that the bar can withstand does not exceed the current bending stiffness of the most loaded (in terms of the bending moment) section.     

Elasticity solutions for functionally graded plates in cylindrical bending

The plate theory of functionally graded materials suggested by Mian and Spencer is extended to analyze the cylindrical bending problem of a functionally graded rectangular plate subject to uniform load. The expansion formula for displacements is adopted. While keeping the assumption that the material parameters can vary along the thickness direction in an arbitrary fashion, this paper considers orthotropic materials rather than isotropic materials. In addition, the traction-free condition on the top surface is replaced with the condition of uniform load applied on the top surface. The plate theory for the particular case Of cylindrical bending is presented by considering an infinite extent in the y-direction. Effects of boundary conditions and material inhomogeneity on the static response of functionally graded plates are investigated through a numerical example.