带扩散的广义热弹性固体中移动荷载引起的二维相互作用

当一个移动荷载沿着一个坐标轴作用在介质边界上时,研究了该具有广义热弹性扩散的均匀各向同性介质中的扰动.应用特征值逼近方法,研究了Laplace-Fourier变换域中的二维扰动问题.在Fourier扩展技术的基础上,利用Laplace数值逆变换技术,求解了位移分量、应力、温度场、浓度和化学势的解析表达式.数值计算了铜类材料的这些表达式,并给出有关图形.作为特殊情况,给出了广义热弹性介质和弹性介质中,扩散和热效应的理论结果和数值结果.     

热冲击荷载作用下的含球形空腔的广义热弹性功能梯度球形各向同性体

在带两个松弛时间参数的广义热弹性线性理论(Green和Lindsay理论)意义上,研究含一个球形空腔的功能梯度球形各向同性无限大弹性介质中,热弹性位移、应力和温度的求解方法.空腔表面无应力,但承受一个随时间变化的热冲击荷载作用.在Laplace变换域中,给出了一组矢量-矩阵微分方程形式的基本方程,并用特征值方法求解.应用Bellman方法进行数值逆变换.计算了位移、应力和温度,并给出相应的图形.结果表明,材料热物理性质的变化,对荷载响应的影响非常强烈.并与对应的均匀材料进行了比较和分析.     

层状横观各向同性饱和地基上圆板的非轴对称振动

研究了层状横观各向同性饱和地基上弹性圆板的非轴对称振动问题．首先,通过方位角的Fourier变换,将圆柱坐标系下横观各向同性饱和土的三维动力方程转化为一阶常微分方程组,基于径向Hankel变换,建立问题的状态方程,求解状态方程后得到传递矩阵;其次,利用传递矩阵,结合层状饱和地基的边界条件、排水条件及层间接触和连续条件,给出了任意简谐激振力作用下层状横观各向同性饱和地基动力响应的通解;然后,按混合边值问题建立层状饱和地基上弹性圆板非轴对称振动的对偶积分方程,并将对偶积分方程化为易于数值计算的第二类Fredholm积分方程,并给出了算例．     

横观各向同性饱和弹性多孔介质非轴对称动力响应

应用Fourier展开和Hankel变换求解了简谐激励下横观各向同性饱和弹性多孔介质的非轴对称Biot波动方程,得到了一般解。用一般解给出了多孔介质总应力分量的表达式。最后对求解横观各向同性饱和弹性多孔介质非轴对称动力响应边值问题的方法作了系统说明,并且给出了数值分析特例。     

横观各向同性饱和地基的三维动力响应

首先引入位移函数,将直角坐标系下横观各向同性饱和土Biot波动方程转化为2个解耦的六阶和二阶控制方程;然后基于双重Fourier变换,求解了Biot波动方程,得到以土骨架位移和孔隙水压力为基本未知量的积分形式的一般解,并用一般解给出了饱和土总应力分量的表达式．在此基础上系统研究了横观各向同性饱和半空间体的稳态动力响应问题,考虑表面排水和不排水两种情况,得到了半空间体在任意分布的表面谐振荷载作用下,表面位移的稳态动力响应,文末给出了算例．     

横观各向同性饱和地基与中厚圆板的非轴对称动力相互作用

研究横观各向同性饱和土地基上中厚弹性圆板的非轴对称振动问题,即首先利用Fourier展开和Hankel变换技术,求解了简谐激励下横观各向同性饱和土地基的非轴对称Biot波动方程,然后按混合边值问题建立地基与弹性中厚圆板非轴对称动力相互作用的对偶积分方程,并将对偶积分方程化为易于数值计算的第二类Fredholm积分方程．文末给出了算例．数值结果表明,在一定频率范围内,地基表面的位移幅值随激振频率增加而增大,随距离的增大以振荡形式衰减变化．     

带球形空腔的广义热弹性无限大材料的弹性模量和传热系数与材料参考温度的相关性

利用具某一松弛时间的广义热弹性方程求解了带球形空腔的无限大材料问题．该材料的弹性模量和传热系数是可变的．空腔的内表面没有力作用,但有热冲击作用．利用Laplace变换求得直接逼近解．数值求解了Laplace逆变换．给出了温度、位移和应力的分布图．     

具有立方对称性及两个弛豫时间的微极热弹性介质中调和时间源引起的变形

研究了具有立方对称性及两个弛豫时间的微极热弹性介质在调和时间源中的响应．采用了Fourier变换以及数值逆变换技术．在物理域中,得到了位移、应力、微转动和温度分布的数值结果．将微极立方晶体法向位移、法向力应力、切向耦合应力和温度分布的计算结果,与微极各向同性固体的结果进行比较．绘制了指定材料的数值结果图形．还推断了某些特殊情况的结果．     

在重力作用下的上覆无限热弹性流体对广义热弹性固体转动的影响

计及上覆无限热弹性流体的重力作用,沿界面有不同的外力作用时,研究广义热弹性固体的旋转变形问题.在Laplace和Fourier域内,通过积分变换,得到了位移、应力及温度分布的表达式.然后在物理域内,应用数值逆变换方法,得到这些分量的值,并讨论了该问题的一些特例.结果以图形方式给出,显示了介质的旋转以及重力作用的影响.     

黏性流体与热弹性微极蜂窝结构介质界面上受倾斜荷载作用时的弹性动力分析

研究倾斜荷载作用在黏性流体与热弹性微极蜂窝结构固体界面上时,荷载倾斜角的影响.假设倾斜荷载是法向荷载和切向荷载的线性组合.为求解该问题,对时间变量进行Laplace变换,对空间变量进行Fourier变换.通过引入势函数,获得了变换域中应力、温度分布和压力的表达式.利用数值逆变换技术,求得问题的物理解.同时,得到了频域中的表达式,以及变量适当变化时稳态情况下的表达式.用图形显示不同荷载源和荷载倾角变化时的响应.并且讨论了一些特殊情况.     

An axisymmetric steady-state thermoelastic problem of an external circular crack in an isotropic thick plate

A steady state thermoelastic mixed boundary value problem for an isotropic thick plate is considered in this paper. The faces of an external circular crack situated in the mid-plane of the plate are opened up by the application of temperature while the bounding surface of the plate are maintained at a constant zero temperature. Solution valid for large values of the ratio of the plate thickness to the diameter of the crack has been obtained. Expressions for various quantities of physical interest are derived by finding iterative solutions of the equations and the results are shown graphically.     

De la convection naturelle instationnaire sur une plaque verticale infinie

Summary This paper considers the unsteady laminar free convection produced by heating an infinite vertical flat plate. Analytical solutions in closed forms for the velocity and temperature profiles, when the surface temperature varies stepwise and as a power of time, are obtained for Prandtl numbers close to unity.Results are reported for several values of the Prandtl number in case of a stepwise varying plate temperature.     

Influence of surface mass transfer on mixed convection flows over non-isothermal horizontal flat plates

Non-similar solution of a steady mixed convection flow over a horizontal flat plate in the presence of surface mass transfer (suction or injection) is obtained when there is power-law variation in surface temperature. The surface temperature is assumed to vary as a power of the axial coordinate measured from the leading edge of the plate. A non-similar mixed convection parameter is considered which covers the whole convection regime, namely from pure free convection to pure forced convection. Numerical results are reported here to account the effects of Prandtl number, surface temperature, surface mass transfer parameter (suction or injection) on velocity and temperature profiles, and skin friction and heat transfer coefficients.     

Thermal stresses in a plate with transversely isotropic material

In this paper the thermal stresses in a plate with transversely isotropic material have been obtained by the method of Hankel transforms. Three cases of surface temperature over a circular region of exposure with flux of heat, paraboloidal distribution and constant temperature with surface radiation have been considered. Numerical results are presented for the case of surface radiation.     

The influence of coupled diffusion of heat and moisture on the state of stress in a plate

The fundamental results of previous reports on the coupling of the processes of diffusion of heat and moisture in solids are reviewed. The influence of the coupling on diffusion into an infinite plate from both its surfaces is discussed with the aim of clarifying what can and cannot be learned from such experiments. The nonuniformity of temperature and moisture content tends to cause nonuniform deformation. The stresses set up are computed for a homogeneous, isotropic plate. These self-equilibrating stresses first increase with time and then die out. For some combinations of material constants, the stresses undergo a reversal. For example, in some cases the surface stresses initially become compressive as moisture begins diffusing into the plate. Subsequently, as the interior of the plate increases in temperature due to the coupling effect, the surface stresses become tensile before eventually subsiding to zeroPublished in Mekhanika Kompozitnykh Materialov, No. 1, pp. 53–61, January–February, 1980.     

Hydrodynamic and thermal slip flow boundary layers over a flat plate with constant heat flux boundary condition

In this paper the boundary layer flow over a flat plat with slip flow and constant heat flux surface condition is studied. Because the plate surface temperature varies along the x direction, the momentum and energy equations are coupled due to the presence of the temperature gradient along the plate surface. This coupling, which is due to the presence of the thermal jump term in Maxwell slip condition, renders the momentum and energy equations non-similar. As a preliminary study, this paper ignores this coupling due to thermal jump condition so that the self-similar nature of the equations is preserved. Even this fundamental problem for the case of a constant heat flux boundary condition has remained unexplored in the literature. It was therefore chosen for study in this paper. For the hydrodynamic boundary layer, velocity and shear stress distributions are presented for a range of values of the parameter characterizing the slip flow. This slip parameter is a function of the local Reynolds number, the local Knudsen number, and the tangential momentum accommodation coefficient representing the fraction of the molecules reflected diffusively at the surface. As the slip parameter increases, the slip velocity increases and the wall shear stress decreases. These results confirm the conclusions reached in other recent studies. The energy equation is solved to determine the temperature distribution in the thermal boundary layer for a range of values for both the slip parameter as well as the fluid Prandtl number. The increase in Prandtl number and/or the slip parameter reduces the dimensionless surface temperature. The actual surface temperature at any location of x is a function of the local Knudsen number, the local Reynolds number, the momentum accommodation coefficient, Prandtl number, other flow properties, and the applied heat flux.     

Wave propagation and transient response of a functionally graded material plate under a point impact load in thermal environments

In this paper, the wave propagation and transient response of an infinite functionally graded plate under a point impact load in thermal environments are studied. The thermal effects and temperature-dependent material properties are taken into account. The temperature field considered is assumed to be a uniform distribution over the plate surface and varies in the thickness direction only. Material properties are assumed to be temperature-dependent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. Considering the effects of transverse shear deformation and rotary inertia, the governing equations of the wave propagation in the functionally graded plate are derived from Hamilton’s principle. The analytic dispersion relation of the functionally graded plate is obtained by means of integral transforms and a complete discussion of dispersion for the functionally graded plate is given. Using the dispersion relation and integral transforms, exact integral solutions of the functionally graded plate under a point impact load in thermal environments are obtained. The influences of the volume fraction distributions and temperature field on the wave propagation and transient response of functionally graded plates are discussed in detail. The results carried out can be used in the ultrasonic inspection techniques and provide a theoretical basis for engineering applications.     

Effect of variable density on hydromagnetic mixed convection flow of a non-Newtonian fluid past a moving vertical plate

The effect of temperature-dependent density on MHD mixed convection flow of power-law fluid past a moving semi-infinite vertical plate for high temperature differences between the plate and the ambient fluid is studied. The fluid density is assumed to decrease exponentially with temperature. The usual Boussinesq approximations are not considered due to the large temperature differences. The surface temperature of the moving plate was assumed to vary according to a power-law form, that is, T_w(x) = T_∞ + Ax^γ. The fluid is permeated by a uniform magnetic field imposed perpendicularly to the plate on the assumption of small magnetic Reynolds number. A numerical shooting algorithm for two unknown initial conditions with fourth-order Runge–Kutta integration scheme has been used to solve the coupled non-linear boundary value problem. The effects of various parameters on the velocity and temperature profiles as well as the local skin-friction coefficient and the local Nusselt number are presented graphically and in the tabular form. The results show that application of Boussinesq approximations in a non-Newtonian fluid subjected to high temperature differences gives a significant error in the values of the skin-friction coefficient and the application of an external magnetic field reduces this error markedly in the case of shear-thickening fluid.     

The uniform heating and bending of a two-layer plate

The problem of the uniform heating of a two-layer plate is solved. The transversely isotropic layer considered (a soft plate) is in ideal contact with a rigid isotropic thin elastically deformed layer. The ends of the plate are load-free. A boundary layer of the soft plate (a thin contact layer) is introduced, which enables the boundary conditions on the ends of the plate to be formulated in such a way that the problem has a bounded smooth solution [1]. The two-layer plate, generally speaking, is bounded along the axis perpendicular to the axes directed along the length and thickness of the plate. The resultant force and the resultant moment, applied to the end transverse sections, are equal to zero. The exact solution of the temperature problem is sought using the equations of the theory of elasticity. The plane problem of the bending of a two-layer plate acted upon by a uniformly distributed pressure applied to the side surface of an anisotropic layer is solved by a similar method. The ends of the rigid isotropic layer are clamped.     

微极热弹性无限板的轴对称自由振动

研究了在应力自由和刚性固定边界条件下,无能量耗散的均匀、各向同性微极热弹性无限板的轴对称自由振动波的传播,导出了相应的对称和斜对称模态波传播的闭合式特征方程和不同区域的特征方程.对短波的情况,应力自由热绝缘和等温板中对称和斜对称模态波传播的特征方程退化为Rayleigh表面波频率方程.根据导出的特征方程得到了热弹性、微极弹性和弹性板的结果.在对称和斜对称运动中计算了板的位移分量幅值、微转动幅值和温度分布,给出了对称和斜对称模式的频散曲线,并示出了位移分量和微转动幅值和温度分布的曲线.能够发现理论分析和数值结论是非常一致的.