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。     

双悬臂梁试样恒位移K_1计算公式

双悬臂梁(Double Cantilever Beam简称DCB)试样是一种单边裂纹、裂纹面弯曲加载的试样。早期用于测量材料的表面能,近来应用于断裂韧性的测量、裂纹体动态止裂和裂纹扩展动力学等研究工作中,恒位移的DCB试样尤其广泛用来研究金属材料应力腐蚀断裂性能和机理,因此需恒位移条件下的K_1表达式。     

一维六方准晶弹性层合悬臂梁的解析解

本文利用一维六方准晶的平面本构关系,以及简化为平面问题的物理方程,在悬臂梁的弹性应力解的基础上,假设准晶层和弹性层的应力分布,求出了各自的位移表达式,再利用层间连续条件和放松的边界条件,推导出一维六方准晶层合悬臂梁仅在自由端受集中力作用下声子场和相位子场的位移解析解,为研究准晶涂层材料的力学性质提供参考。     

梯度功能压电悬臂梁的一组基本解及其应用

采用应力函数解法,研究了弹性参数和体积力同时呈梯度变化时压电材料悬臂粱的力-电响应,得到了应力函数和电位移函数的解析表达式及梯度功能压电悬臂梁的一组基本解．作为一种应用形式,给出了梯度功能压电执行器的尖端位移和制动力的确定方法、此外,利用该基本解,可以方便地确定悬臂梁在多种不同典型荷载单独或联合作用下的解答。     

自由端受集中力作用下压电悬臂梁弯曲问题解析解

本文对由横观各向同性压电介质构成的悬臂梁，在自由端受集中力作用下的弯曲问题进行了研究。首先根据问题的特点，得到简化的线弹性压电悬臂梁的基本方程。然后根据正交各向异性材料悬臂梁应力分布特点，采用逆解法，建立了该问题的应力函数与电势分布函数，进而得到精确多项式解析解。该解析解形式简单，便于应用。文中对自由端受集中力的常规材料和压电材料悬臂梁的挠度也进行了比较。     

光纤传感器在悬臂结构中应用的分析

本文用有限元方法研究Ｍａｃｈ—Ｚｅｈｎｄｅｒ式光纤干涉传感器在测量时光纤对位移因子的影响，光纤对裂纹的感知，并对悬臂梁和双悬臂梁中光纤的铺设进行了分析。     

应用半权函数法计算界面裂纹的应力强度因子

应用半权函数法求解双材料界面裂纹的应力强度因子，得到以半权函数对参考位移与应力加权积分的形式表示的应力强度因子。针对特征值为复数λ的双材料界面裂纹裂尖应力和位移场，设置与之对应特征值为-λ的位移函数，即半权函数。半权函数的应力函数满足平衡方程，应力应变关系，界面的连续条件以及在裂纹面上面力为0；半权函数与裂纹体的几何尺寸无关，对边界条件没有要求。由功的互等定理得到应力强度因子KⅠ和KⅡ的积分形式表达式。本文计算了多种情况下界面裂纹应力强度因子的算例，与文献结果符合得很好。由于裂尖应力的振荡奇异性已经在积分中避免，只需考虑绕裂尖远场的任意路径上位移和应力，即使采用该路径上较粗糙的参考解也可以得到较精确的结果。     

基于改进SPH方法的平面动态应力模拟

为了探讨在动态激励作用下材料的局部力学行为,本文将改进的光滑粒子流体动力学方法(Smoothed Particle Hydrodynamics)应用于平面应力问题求解.引入速度、密度及应力修正项,对在简谐外部激励作用下的弹性悬臂梁运动及应力情况进行模拟.本文通过编写FORTRAN程序,计算了弹性悬臂梁的运动周期、运动幅值,并将悬臂梁自由端中点的位移情况与有限元计算结果进行了对比.此外,本文还对梁内典型位置处的正应力及密度变化情况进行显示跟踪.研究结果表明,本文采用的改进光滑粒子流体动力学方法不仅能够较为准确的模拟悬臂梁振动问题,且能持续显示跟踪各物质点的物理量,对结构强度的长期监测有一定的工程应用潜力与现实意义.     

用双悬臂梁（DCB）试样测定JR曲线的实验方法

本文首先建立了双悬臂梁(DCB)试样的 J 积分和加载点位移Δ的半解析解,然后提出了一种利用 CDB 试样测定材料.J_R 阻力曲线的单试样方法,并对40Cr 钢材进行了实际测试.结果表明,该方法不仅简单易行、结果可靠,而且获得的材料 J_R 曲线的Δα范围较宽.     

柔性基/硅层合悬臂梁振动响应的有限元分析

应用ABAQUS建立了柔性基/硅层合悬臂梁有限元模型,计算了在位移载荷下,柔性基/硅层合悬臂梁中硅层的应力变化,分析了层厚比的变化对柔性基/硅层合悬臂梁低阶固有频率以及振动响应的影响,并与铝基层合悬臂梁进行了对比。结果表明:柔性基可以大幅减小硅层上的应力;封装层和硅层的层厚比越大,柔性基/硅层合悬臂梁的低阶固有频率越大;同时,位移和速度响应明显减小,响应的周期也减小。表明增大封装层和硅层的层厚比,可以有效地提高柔性基/硅层合悬臂梁的整体性能和稳定性,提高其抗冲击性能。反之,会增大柔性基/硅层合悬臂梁发生共振现象的概率,不利于其整体稳定性的提升。此研究结果可为柔性电子器件结构振动特性的优化设计提供理论参考。     

用等效力系变换矩阵求解静不定桁架极限载荷

采用等效力系变换矩阵研究了双模量静不定桁架极限载荷问题．首先证明了固体的等效力系变换矩阵与等效位移变换矩阵是互为转置的矩阵,采用等效力系变换矩阵求解双模量静不定桁架结构的内力,然后再利用静力方程确定双模量静不定桁架结构的极限载荷．当力的变换关系可以根据物理条件容易求得,而位移的变换关系不容易找出时,用等效力系变换矩阵求解静不定桁架极限载荷,就更能显示出其计算过程简洁、清晰等优点．用等效力系变换矩阵求解静不定桁架极限载荷不涉及材料的性质,对各向同性材料、双模量材料静不定桁架极限载荷的求解都适用．     

An improved Jones-Nelson nonlinear material model and rubber composite lamina analysis

A Jones-Nelson model has been applied to depict nonlinear stress-strain relations of composite laminae, where mechanical properties were expressed by strain energy density. The nonlinear material matrix is only a function of the strain energy density. Then a material model could be conveniently applied under complex stress condition. In this paper, by introducing large displacement stress-strain measurement and varying-Poisson's ratio idea, an improved Jones-Nelson material model is presented, where the expanding problem of material properties and convergence problems are overcome. Meanwhile a discuss of the reorientation of fiber and a material nonlinear analysis of rubber composite lamina under super large deformation conditions are made. The prediction results of improved material model are in fairly good agreement with those of the experiments.     

张拉膜结构的有限元分析

应用有限元程序ANSYS进行了薄膜结构的找形分析和荷载分析．张拉结构受力后将产生较大的位移,因此需要采用非线性理论．通过一系列计算,可以发现影响找形结果的因素有：单元的划分,初始弹性模量的选取,膜的预张力,边索和脊索的预张拉力值及其比值．在实际工程中,由于膜结构建筑要求和边界条件的限制,找到具有极小曲面性质的初始平衡形状较难,因此,一般把应力的差值控制在一定的范围内．工程实例计算结果表明：在风荷载作用下膜结构的竖向位移反应比较大,风吸力通常是索膜结构设计的控制因素．     

高速荷载下多孔饱和地基的动力响应

研究高速荷载作用下梁与多孔饱和半空间的动力响应。由Fourier变换求解多孔饱和固体的动力基本方程，根据梁与半空间的接触条件得出多孔饱和半空间上梁的垂直位移的表达式。文中的数值算例考虑了荷载移动速度对梁的动力位移的影响，并与相应的弹性半空间问题作了对比。从算例中可以发现荷载移动速度对动力位移有很大的影响，当移动速度与半空间的表面波速相近时，地面会当产生很大的振动，同时还发现当速度大于介质的剪切波速时，多孔饱和半空间上梁的动力响应与弹性半空间上梁的动力响应有很大的差别。     

The illustration calculations of second order effects in elastic half-space acted upon by a non-uniform shear load

I.IllustrationsThegeneralsolutionofsecondordereffectsinelastichalfspaceacteduponbyanon-uniformshearloadpresentedbypaperIl]areapplicableforallvalueof6>-l,butareverycomplicated.Asani1lustrationofthemethodwegivebelowthelinearandsecondordersolutionsfor8=l/2.T…     

Deformation of thin straight pipes under concentrated forces or prescribed edge displacements

The purpose of this paper is to present an efficient analytic method for obtaining the deformation of thin straight pipes, subjected to prescribed edge displacements or concentrated loads.The approach uses the mixed formulation where unknown functions are combined with trigonometric terms. A variational procedure is used to obtain the system of ordinary differential equations. For the applied load a Fourier approach is used to represent the load as an analytical function. For the prescribed displacement, three solutions for the ovalization are evaluated and a method based on energy contribution of each term is used to obtain their superposition.In contrast to finite element method the proposed method is efficient and can be applied to other boundary condition problems leading to continuous displacement and stress fields with a low number of unknowns. Comparisons with experimental and finite element procedures show good agreement that enhances the merits of the analytical solutions proposed.The value of this method is based on solving the differential equations rather than using commercial codes. So far, the solution of prescribed edge displacements has been limited to one term. This paper discusses how to add further terms using the mixed formulation, thus, presenting a novel procedure.     

Analysis of an Anisotropic Finite Wedge under Antiplane Deformation

The antiplane deformation of an anisotropic wedge with finite radius is considered in this paper within the classical linear theory of elasticity. The traction-free condition is imposed on the circular segment of the wedge. Three different cases of boundary conditions on the radial edges are considered, which are: traction-displacement, displacement-displacement and traction-traction. The solution to the governing differential equation of the problem is accomplished in the complex plane by relating the displacement field to a complex function. Several complex transformations are defined on this complex function and its first and second derivatives to formulate the problem in each of the three cases of the problem corresponding to the radial boundary conditions, separately. These transformations are then related to integral transforms which are complex analogies to the standard finite Mellin transforms of the first and second kinds. Closed form expressions are obtained for the displacement and stress fields in the entire domain. In all cases, explicit expressions for the strength of singularity are derived. These expressions show the dependence of the order of stress singularity on the wedge angle and material constants. In the displacement-displacement case, depending upon the applied displacement, a new type of stress singularity has been observed at the wedge apex. This revised version was published online in August 2006 with corrections to the Cover Date.     

Torsion of an elastic solid cylinder with a radial variation in the shear modulus

A Green's function approach is used to formulate and obtain the stress field, under torsional loads in a radially finite solid cylinder with radially variable elastic modulus. With this approach a certain dual static-geometric analogy in the solution is readily proved and applied to generate the solution with stress boundary conditions from that with displacement boundary conditions and vice-versa.The problem is solved using both boundary conditions and for an exponentially varying shear modulus. In particular, under displacement boundary conditions, the stress field in the solid with a generalised Reissner-Sagoci boundary condition is easily deduced. With stress boundary conditions, the criteria for crack propagation in such elastic models are also obtained using the Griffith-Irwin condition of rupture.     

Stress channelling in extreme couple-stress materials Part II: Localized folding vs faulting of a continuum in single and cross geometries

The antiplane strain Green's functions for an applied concentrated force and moment are obtained for Cosserat elastic solids with extreme anisotropy, which can be tailored to bring the material in a state close to an instability threshold such as failure of ellipticity. It is shown that the wave propagation condition (and not ellipticity) governs the behaviour of the antiplane strain Green's functions. These Green's functions are used as perturbing agents to demonstrate in an extreme material the emergence of localized (single and cross) stress channelling and the emergence of antiplane localized folding (or creasing, or weak elastostatic shock) and faulting (or elastostatic shock) of a Cosserat continuum, phenomena which remain excluded for a Cauchy elastic material. During folding some components of the displacement gradient suffer a finite jump, whereas during faulting the displacement itself displays a finite discontinuity.     

The viability of a simple procedure for determining the criterion for the instability of circumferential growth of a through-wall crack in a stainless steel piping system, Part 2: The applied displacements produce bending and tensile deformation

Against the background of the technological problem of integranular stress corrosion cracking of Type 304 stainless steel Boiling Water Reactor piping systems, the stability of a circumferential through-wall crack is examined, for the case where the cracked section is at a position where the pipe enters a larger component. The paper presents a general methodology for determining the instability criterion for fixed displacement loadings, which are appropriate for an accident condition, the criterion being expressed in terms of the applied and material tearing moduli, or equivalently in terms of an effective pipe length. The methodology is applied to models which simulate bends in a piping system, and general conclusions are drawn with regards to the effect of pipe bends on crack instability.