实心圆柱外表面受热冲击作用的轴对称平面应变热弹性动力学解

利用分离变量法，成功地给出了各向同性实心圆柱外表面受热冲击作用的轴对称平面应变热弹性动力学问题的解析解．运用此方法，可以避免积分变换且易于实现数值计算．在数值结果中，与拟静态问题和均匀热冲击情形进行了比较，表明惯性项对中心处应力响应影响不大，而热传导的过程能大大减低中心处的热应力．     

圆柱正交异性体三维弹性问题的一个解法

本文从三维弹性力学基本方程出发,导出了圆柱正交异性体三维弹性静、动态问题的状态方程,并进而求得以位移表达的控制方程.还对横观各向同性体的轴对称问题给出了一个完备闭合解.文中算例计算了一个横观各向同性组合圆柱体的轴对称问题.     

圆柱壳在两种非轴对称同步移动载荷作用下的动力响应

本文根据工程实例计算的需要,研究了有限长弹性圆柱薄壳在两种非轴对称同步移动载荷作用下的动力响应问题。两种非轴对称同步移动载荷作用是指非轴对称移动的集中载荷,以及同步移动且作用范围随移动位置增加的均布载荷的共同作用。建立了在上述两种不同类型载荷作用下的具有对称形式的动力学微分方程组;分别采用Dirac函数与Heaviside函数表示移动的均布载荷与集中载荷,设定位移函数的基础上,应用Galerkin法及Laplace变换,求得了圆柱薄壳应力与位移动态响应的解析解;通过具体算例,将所得到解析解的计算结果与ANSYS数值解进行了对比分析,验证了解析解的可靠性。     

磁-电-弹性半空间在轴对称热载荷作用下的三维问题研究

考虑力-电-磁-热等多场耦合作用, 基于线性理论给出了磁-电-弹性半空间在表面轴对称温度载荷作用下的热-磁-电-弹性分析, 并得到了问题的解析解. 利用Hankel 积分变换法求解了磁-电-弹性材料中的热传导及控制方程, 讨论了在磁-电-弹性半空间在边界表面上作用局部热载荷时的混合边值问题, 利用积分变换和积分方程技术, 通过在边界表面上施加应力自由及磁-电开路条件, 推导得到了磁-电-弹性半空间中位移、电势及磁势的积分形式的表达式. 获得了磁-电-弹性半空间中温度场的解析表达式并且给出了应力, 电位移和磁通量的解析解. 数值计算结果表明温度载荷对磁-电-弹性场的分布有显著影响. 当温度载荷作用的圆域半径增大时, 最大正应力发生的位置会远离半无限大体的边界; 反之当温度载荷作用的圆域半径减小时, 最大应力发生的位置会靠近半无限大体的边界. 电场和磁场在温度载荷作用的圆域内在边界表面附近有明显的强化, 而磁-电-弹性场强化区域的强化程度跟温度载荷的大小和作用区域大小相关. 本研究的相关结果对智能材料和结构在热载荷作用下的设计和制造具有指导意义.      

圆柱壳的非线性动力屈曲分析

本文研究在轴向冲击作用下，具有初始几何缺陷的圆柱壳的非线性弹性动力屈曲问题。由于冲击过程中作用时间极短，应力波的影响变得相当重要，同时认为圆柱壳经历大挠度变形。分析中不仅考虑圆柱壳的径向惯性力，而且也考虑轴向惯性力和几何非线性的影响。假设圆柱壳中位移和薄膜力可分成轴对称分量和非轴对称分量之和，并引入应力函数表示非轴对称内力，对平衡方程应用伽辽金方法，将导出的和冲击物体的质量对动屈曲性能的影响很大。     

偏场作用下不可压缩软电弹性圆柱壳的轴对称波动

基于Dorfmann-Ogden非线性电弹性框架及其线性增量理论,研究了在偏场作用下的不可压缩各向同性软电弹性圆柱壳中的轴对称波,获得了以贝塞尔函数表示的波动解和精确的频散方程。针对已有文献提出的非线性软电弹性材料模型,研究了偏场下电弹性圆柱壳的波动特性。结果表明:预加电场与预拉伸对软电弹性圆柱壳中波动的影响显著,二者可用于对波动特性的调控。另外,对比研究了不同结构形式、考虑和不考虑真空情况下电场对波动特性的影响,结果表明:这两个因素的变化会使弥散曲线形状发生较大的改变。     

冲击载荷下含表面裂纹圆柱壳体的动态断裂

动态载荷下含表面裂纹的有限尺寸构件的断裂问题在工程实践中有着重要意义,但由于此类问题非常复杂,目前还不能求得解析解。本文针对含轴向半椭圆盘状表面裂纹的圆柱壳体,应用有限元法研究了动态载荷下其断裂问题,计算了动态应力强度因子与静态应力强度因子的比值KdIyn(t)/KsIta。从计算结果可以得出,比值KdIyn(t)/KsIta与结构和裂纹的尺寸有关,而与冲击载荷的大小无关。本文所得结果在一定程度上揭示了圆柱壳体表面、裂纹面、物质惯性和弹性波的相互作用及其对动态断裂的影响。     

弹性圆柱壳在轴向应力波传播过程中的非对称屈曲

讨论弹性圆柱壳端部受冲击载荷作用，在应力波传播过程中的非对称屈曲问题。通过求解扰动方程得到了动态屈曲的分叉条件、临界载荷和屈曲模态。数值结果表明，当壳壁厚不很薄时，轴对称屈曲临界载荷比非对称临界载荷高；反之，轴对称临界载荷会比非对称临界载荷低。不同的冲击载荷，屈曲模态也将不同。     

弹／粘塑性柱体扭转问题的函数Laplace变换解

在应力Ｌａｐｌａｃｅ变换分析粘塑性轴对称问题基础上，对弹性－弹／粘塑性圆柱体扭转全过程进行分析，根据柱体扭转的应力分布，构造应力函数与位移函数，并对函数进行Ｌａｐｌａｃｅ变换。相应求出圆柱体、空心圆柱体的Ｌａｐｌａｃｅ变换解，以及圆柱体的弹性－粘塑性交界线值     

在轴向应力波传播和反射过程中弹性有限长圆柱壳非对称动态屈曲

本文讨论弹性有限长圆柱壳端部受冲击载荷作用，在轴向应力波传播和反射过程中的非对称动态屈曲问题。通过建立和求解扰动方程得到了动态屈曲的分叉条件，临界载荷和屈曲模态。数值结果表明：当壳壁厚不很薄时，轴对称屈曲临界载荷比非轴对称临界载荷高；反之，轴对称临界载荷会比非对称临界载荷低；由于应力波的反射，临界载荷降低，因而更容易发生屈曲，屈曲模态也有其不同特点。     

Magneto–thermo–electro–elastic transient response in a piezoelectric hollow cylinder subjected to complex loadings

The article presents an analytical solution for magneto–thermo–electro–elastic problems of a piezoelectric hollow cylinder placed in an axial magnetic field subjected to arbitrary thermal shock, mechanical load and transient electric excitation. Using an interpolation method solves the Volterra integral equation of the second kind caused by interaction among magnetic, thermal, electric and mechanical fields, the electric displacement is determined. Thus, the exact expressions for the transient responses of displacement, stresses, electric displacement, electric potential and perturbation of the magnetic field vector in the piezoelectric hollow cylinder are obtained by means of Hankel transforms, Laplace transforms, and inverse Laplace transforms. From sample numerical calculations, it is seen that the present method is suitable for a piezoelectric hollow cylinder subjected to arbitrary thermal shock, mechanical load and transient electric excitation, and the result carried out may be used as a reference to solve other transient coupled problems of magneto–thermo–electro–elasticity.     

Transient thermal elastic fracture of a piezoelectric cylinder specimen

A finite piezoelectric cylinder with an embedded penny-shaped crack is investigated for a thermal shock load on the outer surface of the cylinder. The theory of linear electro-elasticity is applied to solve the transient temperature field and the associated thermal stresses and electrical displacements without crack. These thermal stresses and electrical displacements are added to the surfaces of the crack to form an electromechanical coupling and mixed mode boundary-value problem. The electrically permeable crack face boundary condition assumption is used, and the thermal stress intensity factor and electrical displacement intensity factor at the crack border are evaluated. The thermal shock resistance of the piezoelectric cylinder is evaluated for the analysis of piezoelectric material failure in practical engineering applications.     

Elasto-plastic analysis of an internally pressurized thick-walled cylinder using a strain gradient plasticity theory

An analytical solution for the stress, strain and displacement fields in an internally pressurized thick-walled cylinder of an elastic strain-hardening plastic material in the plane strain state is presented. A strain gradient plasticity theory is used to describe the constitutive behavior of the material undergoing plastic deformations, whereas the generalized Hooke’s law is invoked to represent the material response in the elastic region. The solution gives explicit expressions for the stress, strain and displacement components. The inner radius of the cylinder enters these expressions not only in non-dimensional forms but also with its own dimensional identity, unlike classical plasticity-based solutions. As a result, the current solution can capture the size (strengthening) effect at the micron scale. The classical plasticity-based solution of the same problem is shown to be a special case of the present solution. Numerical results for the maximum effective stress in the cylinder wall are also provided to illustrate applications of the newly derived solution.     

Exact Electromagnetothermoelastic Solution for a Transversely Isotropic Piezoelectric Hollow Sphere Subjected to Arbitrary Thermal Shock

This paper presents analytical study for electromagnetothermoelastic transient behavior of a transversely isotropic hollow sphere, placed in a uniform magnetic field, subjected to arbitrary thermal shock. Exact solutions for the transient responses of stresses, perturbation of magnetic field vector, electric displacement and electric potential in the transversely isotropic piezoelectric hollow sphere are obtained by means of the Hankel transform, the Laplace transform and their inverse transforms. An interpolation method is used to solve the Volterra integral equation of the second kind caused by interactions among electric, magnetic, thermal and elastic fields. From the sample numerical calculations, it is seen that the present method is suitable for the transversely isotropic hollow sphere, placed in a uniform magnetic field, subjected to arbitrary thermal shock. Finally, the result can be used as a reference to solve other transient coupling problems of electromagnetothermoelasticity.     

The crack tip fields of orthotropic composite plate under bending

1MechhacalModelThefractUreproblemwhichisthesameasthatinpaper[I]isfurtherdiscussedinthispaper.TheanalysisoffractUrebehavioursnearcracktipforinfinitelinearelasticorthotropiccompositeplatewithacentralthroughcrackoflengthZaiscarriedout.ThegeometryandloadingcondihonsareshowninFig.1.Tosolvesuchaproblem,weneedtosolvethepanaldifferentialequationwiththefollowingboundaryconditions:wherewisdeflectionofcoddleplane;M.andM,arebendingmoment,Ma.istwistingmoment,andstiffnessmatrixFromthetheoryofplateL'],w…     

Transient temperature fields in functionally graded materials with different shapes under convective boundary conditions

This paper presents analyses of the transient temperature fields in an infinite plate, an infinite solid cylinder and a solid sphere made of functionally graded materials (FGMs) under convective boundary conditions. The composition and the thermo-physical properties of the infinite FGM plate, the infinite FGM solid cylinder and the FGM solid sphere are of planar symmetric, axially symmetric and spherically symmetric distributions, respectively. The analytical formulae of the one-dimensional transient temperature fields for the three FGM solids are obtained respectively by using the separation-of-variables method and the variable substitution method. Numerical results reveal that the transient temperature fields of the FGM components exhibit similar shape effect to that of homogeneous components. The present work provides valuable basis for the investigation of the thermal shock resistance of FGMs with various shapes.     

圆柱外表面受热冲击问题的广义热弹性分析

基于 L-S 广义热弹性理论, 针对实心圆柱体在外表面受均匀热冲击作用下的一维广义热弹性问题进行研究分析. 利用热冲击的瞬时特征, 借助于 Laplace 正、反变换技术及柱函数的渐近性质, 推导了热冲击作用周期内温度场、位移场和应力场的渐近表达式. 通过计算, 得到了热冲击条件下各物理场的分布规律以及延迟效应和耦合效应对热弹性响应的影响规律. 结果表明: 当考虑延迟效应和耦合效应时, 热扰动将以两组速度不同的波的形式向前传播, 延迟效应和耦合效应对各物理场的建立时间, 阶跃间隔和阶跃峰值均产生影响, 且延迟效应和耦合效应均在一定程度上削弱了热冲击的作用效果.      

The elastic sphere under nonsymmetric loading

Existing solutions to boundary value problems arising from an elastic sphere subjected to a body force have been primarily restricted to axisymmetric, conservative loading. In this paper, a method for solving the displacement equations governing the static equilibrium of an elastic sphere subjected to an arbitrary body force and surface displacement is presented. The solutions are obtained in terms of three vector spherical harmonics and expressions for the displacement and stress fields are presented. Additionally, a short discussion indicating extension of these solutions to dynamic problems is included.This research was supported in part by an Organized Research Grant, Southwest Texas State University, 1979.     

Bond-based peridynamic modelling of singular and nonsingular crack-tip fields

A static meshfree implementation of the bond-based peridynamics formulation for linearly elastic solids is applied to the study of the transition from local to nonlocal behavior of the stress and displacement fields in the vicinity of a crack front and other sources of stress concentration. The long-range nature of the interactions between material points that is intrinsic to and can be modulated within peridynamics enables the smooth transition from the square-root singular stress fields predicted by the classical (local) linear theory of elasticity, to the nonsingular fields associated with nonlocal theories. The accuracy of the peridynamics scheme and the transition from local to nonlocal behavior, which are dictated by the lattice spacing and micromodulus function, are assessed by performing an analysis of the boundary layer that surrounds the front of a two dimensional crack subjected to mode-I loading and of a cracked plate subjected to far-field tension.     

Thermo-electro-elastic transient responses in piezoelectric hollow structures

The paper presents an analytical method to solve thermo-electro-elastic transient response in piezoelectric hollow structures subjected to arbitrary thermal shock, sudden mechanical load and electric excitation. Volterra integral equation of the second kind caused by interaction between elastic deformation and electric field is solved by using an interpolation method. Thus, the exact expressions for the transient responses of displacement, stresses, electric displacement and electric potential in the piezoelectric hollow structures are obtained by means of Hankel transform, Laplace transform, and their inverse transforms. In Section 2, based on spherical coordinates, the governing equation of thermo-electro-elastic transient responses in a piezoelectric hollow sphere is found and the associated numerical results are carried out. In Section 3, based on cylindrical coordinates, the governing equation of thermo-electro-elastic transient responses in a non-homogeneous piezoelectric hollow cylinder is found and the corresponding numerical results are carried out. The results carried out may be used as a reference to solve other transient coupled problems of thermo-electro-elasticity in piezoelectric structures.