横观各向同性热弹性多孔介质板的精化理论

研究了孔隙水压力作用下横观各向同性热弹性多孔介质板的精化理论。在不做任何预先假设的情况下,利用Lur’e方法和横观各向同性热弹性多孔介质的通解,得到了横观各向同性热弹性多孔介质板的精化理论。首先,根据调和函数的sin算子函数表达式,得到了用5个二维待定函数表示的位移场和应力场;其次,在非齐次边界条件下,利用基本的数学算法,得到了在孔隙水压力载荷作用下热弹性多孔介质板的精化方程;最后,通过舍弃高阶项,得到了位移场和应力场的近似解。     

轴对称横观各向同性热弹性圆柱的分解

为了得到精确的应力场、位移场、温度场,将扭转圆轴的精化理论研究方法推广到轴对称横观各向同性热弹性圆柱。利用Bessel函数以及轴对称横观各向同性热弹性圆柱的通解,给出了轴对称横观各向同性热弹性圆柱的分解定理。根据柱面齐次边界条件获得了精确的精化方程,精化方程可以分解为一阶方程、超越方程、温度方程,从而将横观各向同性热弹性圆柱的轴对称问题分解为轴向拉压问题、超越问题、热-应力耦合问题。超越部分对应端部自平衡情况,可以清晰地了解到端部应力分布对内部应力场的影响,热-应力耦合部分对应无外加应力场时圆柱内部因温度变化引起的热应力。     

横观各向同性板的弹性精化理论

本文从横观各向同性体三维弹性力学的胡海昌解出发,推导出横观各向同性板弯曲的基本方程,由此建立了板的弹性精化理论.基本方程由一个双调和方程和一个剪切方程组成;前者对应于修正的经典板理论,而后者则表征了横向剪切变形的影响。推导过程中,没有引入板理论所采用的种种假定。所得到的板的基本方程同三维弹性力学方程相协调;即满足板方程的介一定满足三维的弹性力学的所有方程.因此,相对于三维弹性力学,本文建立的板精化理论的近似性仅在于其边界条件是由应力合力(或中面位移)描述的。     

表板不等厚钢板混凝土梁的静力计算与分析

本文将由不等厚钢板和混凝土组合而成的梁化为一等效横观各向同性构件,应用弹性理论进行分析,给出了基本静力方程和等效组合弹性常数,求得了这类梁在横向静荷载作用下的解析解。文中对这类构件的力学特性及计算特点作了分析,其结果可用于这类梁的各种静力计算与设计。     

柱面受温度载荷的轴对称横观各向同性压电热弹性圆柱的精化理论

将精化理论的研究方法推广到轴对称横观各向同性压电热弹性圆柱的研究中,利用压电热弹性问题的轴对称通解以及准调和函数的Bessel算子函数表示方法,获得了该圆柱在柱面受温度载荷作用下的精确耦合场;当柱面受到随轴向Z增大而逐渐减小的轴对称量纲为一的温度载荷时,绘制出圆柱在半径r分别为0.2、0.4、0.6、0.8、1.0时的位移分量、电势、温度增量沿轴向z的分布。结果表明:圆柱在同一高度的情况下,径向位移和轴向位移随半径增大而增大,电势的绝对值也随半径的增大而增大,而温度增量随半径的变化则不明显。此外,本文还通过算例验证了该精化理论应用的正确性。     

定常温度热弹性梁中精化理论和分解定理的等价性

根据分解定理,把自由表面热弹性梁内的应力状态分解为三部分:内应力状态、热应力状态和Papkovich-Fadle应力状态(简称P-F应力状态)。随后给出了定常温度热弹性Biot通解的一种新的简化形式。不作预先假设,从热弹性理论出发,利用热弹性通解和Lur'e算子方法构造了梁的精化理论,得出了自由表面热弹性梁的三个精确方程:四阶方程、温度方程和超越方程。最后分别证明了分解定理的三个应力状态与精化理论的三个方程一一等价。     

横观各向同性弹性半空间地基上正交异性矩形中厚板弯曲解析解

对横观各向同性体通解进行双重傅里叶变换,获得了直角坐标系下横观各向同性弹性半空间地基受任意竖向荷载作用下的位移积分变换解;在此基础上建立了板与地基的变形协调方程,并与三个广义位移变量描述的弹性地基上四边自由正交各向异性矩形中厚板的弯曲控制方程相结合,用三角级数法,得出横观各向同性弹性半空间地基上四边自由正交异性矩形中厚板受任意竖向荷载作用的弯曲解析解。相关算例分析表明,本文方法是有效的。     

横观各向同性三维热弹性力学通解及其势理论法

通过引入两个位移函数，对用位移表达的运动平衡方程作了简化．利用算子理论，严格地导出了横观各向同性非耦合热弹性动力学问题的通解．对于静力学问题，通解的形式可进一步简化成用4个准调和函数来表示．具体考察了横观各向同性体内平面裂纹上下表面有对称分布温度作用的问题，推广了势理论方法，导出了一个积分方程和一个微分-积分方程．针对币状裂纹表面受均布温度作用情形，给出了具体的解。     

横观各向同性饱和多孔半平面与梁的动力相互作用

以Biot理论为基础,通过引入一个函数Φ,将横观各向同性饱和多孔半平面的基本方程组简化为一个6阶控制方程.利用Fourier变换,分析了横观各向同性饱和多孔半平面体的动力响应.利用Fourier变换或正弦级数,研究了该介质上梁的简谐振动问题,将原先极为复杂的问题转化为数值积分问题.文末还对横观各向同性饱和多孔半平面与梁的相互作用问题进行了数值计算.     

横观各向同性中厚度圆柱形壳体的十阶微分方程式及其分解

本文在Reissner型修正理论的基础上,建立了一个横观各向同性圆柱形壳体考虑横向剪切变形的精化理论,导出了十阶基本微分方程式.该微分方程可以分解成一个二阶和两个四阶的共轭微分方程式;在力学上,前者代表剪切变形的修正项,后者对应于经典薄壳理论的结果.当壳体的横向剪切刚度很大时,证明了本文提出的精化理论同经典理论的一致性.略去一些次要项,两个四阶共轭微分方程可以退化为各向同性圆柱形薄壳的Mororley、Norozhilov和Donnell方程.     

Fundamental solution for transversely isotropic thermoelastic materials

We use the compact harmonic general solutions of transversely isotropic thermoelastic materials to construct the three-dimensional fundamental solutions for a steady point heat source in an infinite transversely isotropic thermoelastic material and a steady point heat source on the surface of a semi-infinite transversely isotropic thermoelastic material by three newly introduced harmonic functions, respectively. All components of coupled field are expressed in terms of elementary functions and are convenient to use. Numerical results for hexagonal zinc are given graphically by contours.     

Refined theories may be needed for vibration analysis of structures with overhang

The effect of shear deformation and rotary inertia terms on the free vibration of a beam with overhang was investigated. A recently proposed modified Timoshenko-type equations of motion were used to analyze the vibration of the structure. Two different sets of boundary conditions, with either a fixed or hinged end support, were studied. The results were compared with those obtained for the classical Bernoulli–Euler beam theory. The comparison shows that for a hinged end beam with very long overhang, where the span between the supports is less than one tenth of the overall beam length, the classical theory significantly overestimates the values of the fundamental natural frequencies, even for isotropic shear rigidity. On the other hand, the span effect is reversed for the clamped end beam, for which a relatively significant difference between the classical theory and shear theory results may occur only for a long span. For transversely isotropic beams, the refined theory predictions of the fundamental natural frequencies may be much smaller than those obtained through the rigid shear theory, especially for short span hinged end beams and long span clamped end beams.     

Wave propagation in dual-phase-lag anisotropic thermoelasticity

The present paper is concerned with the propagation of plane waves in a transversely isotropic dual-phase-lag generalized thermoelastic solid half-space. The governing equations are solved in x–z plane to show the existence of three plane waves. Reflection of these plane waves from thermally insulated as well as isothermal stress-free surfaces is studied to obtain a system of three non-homogeneous equations in reflection coefficients of reflected waves. For numerical computations of speeds and reflection coefficients, a particular material is modeled as transversely isotropic dual-phase-lag generalized thermoelastic solid half-space. The speeds of plane waves are computed numerically for a certain range of the angle of propagation and are shown graphically against the angle of propagation for the cases of dual-phase-lag (DPL) thermoelasticity, coupled thermoelasticity and Lord–Shulman generalized thermoelasticity. Reflection coefficients of various reflected plane waves are computed numerically for thermally insulated as well as isothermal cases and are shown graphically against the angle of incidence for the cases of DPL thermoelasticity, coupled thermoelasticity and Lord–Shulman generalized thermoelasticity.     

Theory and refined theory of elasticity for transversely isotropic plates and a new theory for tnick plates

A theory of elasticity for the bending of transversely isotropic plates has been developed from the basic equations of elasticity in terms of displacements for transversely isotropic bodies, which takes into account the loads distributed over the surfaces of the plates. Based on this theory, a refined theory of plates which can satisfy three boundary conditions along each edge of the plates and a new theory of thick plates are established. The solution of the refined theory for simply supported polygonal plates has been obtained; and its numerical result is very close to the exact solution of the three-dimensional theory of elasticity. A systematic comparison with the former theories of thick plates shows that the present theory of thick plates is closest to the result of the theory of elasticity.     

Three-dimensional Green’s functions for transversely isotropic thermoelastic bimaterials

Green’s functions for transversely isotropic thermoelastic biomaterials are established in the paper. We first express the compact general solutions of transversely isotropic thermoelastic material in terms of harmonic functions and introduce six new harmonic functions. The three-dimensional Green’s function having a concentrated heat source in steady state is completely solved using these new harmonic functions. The analytical results show some new phenomena of temperature and stress distributions at the interface. The temperature contours are normal to the interface for the isotropic material but not for the orthotropic one. The normal stress contours are parallel to the interface at the boundary in the isotropic region only and shear failure is most likely at the heat source due to the highly degenerated direction of shear stress contours.     

Propagation of Rayleigh waves on free surface of transversely isotropic generalized thermoelastic diffusion

The present paper is devoted to the study of Rayleigh wave propagation in a homogeneous, transversely isotropic, thermoelastic diffusive half-space, subject to stress free, thermally insulated/isothermal, and chemical potential boundary conditions in the context of the generalized thermoelastic diffusion theory. The Green-Lindsay（GL） theory is used in the study. In this theory, thermodiffusion and thermodiffusion mechanical relaxations are governed by four different time constants. Secular equations for surface wave propagation in the considered media are derived. Anisotropy and diffusion effects on the phase velocity, attenuation coefficient are graphically presented in order to present the analytical results and make comparison. Some special cases of frequency equations are derived from the present investigation.     

Wave propagation in thermally conducting linear fibre-reinforced composite materials

The propagation of plane waves in a fibre-reinforced, anisotropic, generalized thermoelastic media is discussed. The governing equations in x–y plane are solved to obtain a cubic equation in phase velocity. Three coupled waves, namely quasi-P, quasi-SV and quasi-thermal waves are shown to exist. The propagation of Rayleigh waves in stress free thermally insulated and transversely isotropic fibre-reinforced thermoelastic solid half-space is also investigated. The frequency equation is obtained for these waves. The velocities of the plane waves are shown graphically with the angle of propagation. The numerical results are also compared to those without thermal disturbances and anisotropy parameters.     

Transient thermoelastic waves in an anisotropic hollow cylinder due to localized heating

This paper presents a theoretical study of transient ultrasonic guided waves generated by concentrated heating of the outer surface of an infinite anisotropic hollow circular cylinder. Generalized thermoelastic theory proposed by Lord and Shulman is adopted to model the dynamic thermoelastic behavior of the cylinder. The concentrated heat source model used is to represent heating due to a pulsed laser beam, which is focused on the outer surface of the cylinder. A semi-analytical finite element (SAFE) method is employed to evaluate guided wave modes in the cylinder. Using integral transform techniques, the modal wave forms are obtained in frequency and wave number domains. Time histories of the propagating modes are then calculated by applying inverse Fourier transformation in the time domain. Numerical results showing the dispersion curves for the group velocities of the propagating modes and transient radial displacements are presented. For this purpose it is assumed that the cylinder is made of transversely isotropic silicon nitride (Si₃N₄). Attention is focused on the propagation characteristics of longitudinal and flexural modes separately.     

Effect of relaxation times on circular crested waves in thermoelastic diffusive plate

The propagation of circularly crested thermoelastic diffusive waves in an infinite homogeneous transversely isotropic plate subjected to stress free, isothermal/insulated and chemical potential conditions is investigated in the framework of different thermo- elastic diffusion theories. The dispersion equations of thermoelastic diffusive Lamb type waves are derived. Some special cases of the dispersion equations are also deduced.