直角坐标系下层状地基力学计算中的传递矩阵技术

给出了在直角坐标系下计算层状地基力学问题的传递矩阵技术,改变了过去只能在柱坐标系下求解层状地基力学问题的状况,大大地简化了任意荷载作用下层状地基力学问题的计算。从直角坐标系下弹性问题的基本方程出发,通过改变坐标系的常规位置,成功地利用Laplace变换及其微分性质,首次推导出直角坐标系下的状态控制方程和对应的传递矩阵,并给出了利用该方法的求解过程。     

横观各向同性饱和层状地基的三维稳态动力响应

首先引入状态向量,将直角坐标系下横观各向同性饱和土的Biot波动方程转化为一组状态方程,然后基于双重Fourier变换,求解了状态方程并得到传递矩阵。进而利用传递矩阵,并结合饱和地基的边界条件、排水条件及层间接触和连续条件,求解了横观各向同性饱和层状地基的稳态动力响应问题。数值算例表明采用各向同性饱和介质的动力学模型,不能准确描述具有明显各向异性特性的饱和土地基的动力特性。     

层状横观各向同性地基性质对刚性条基摇摆振动的影响

分析了土体的横观各向同性及层状性质对刚性条形基础摇摆振动的影响。首先利用解析层元法得出层状横观各向同性地基的总刚度矩阵。再根据刚性条形基础与地基相互作用的混合边值条件,建立了一组对偶积分方程,并借助Jacobi正交多项式求解了该对偶积分方程,从而得到地基动力柔度系数。计算结果与已有文献的结果吻合较好。同时,算例结果表明:土的水平向与竖向弹性模量比的减小、竖向的剪切模量与弹性模量比的增大,以及水平向泊松比与竖向泊松比比值的增大,都将导致地基动力柔度系数增大;而且,层状地基中上层土的弹性模量的减小使得地基动力柔度系数也增大。     

饱和弹性半空间地基与中厚圆板的动力相互作用

利用Fourier-Bessel级数,对横观各向同性饱和弹性半空间地基与中厚圆板的动力相互作用问题进行了系统地分析。板的位移函数、荷载、地基反力及板下地基表面的沉降均被展开为二重Fourier-Bessel级数,这些级数中的待定系数由板的边界条件、板的控制方程及板-地基的相容条件加以确定,从而将饱和弹性半空间地基与中厚圆板的动力相互作用问题转化为数值积分和代数方程组的求解问题。数值计算表明,该级数解答具有较快的收敛速度。可以将该方法推广到弹性半空间与梁、矩形板相互作用问题的分析。     

横观各向同性土体三维比奥固结有限层解法

建立了三维横观各向同性土体固结的有限层求解方法,并编制了相应的计算程序;通过2个算例的分析对比,验证了计算方法和程序的正确性;探讨了横观各向同性地基参数对三维地基固结的影响,给出了对工程有价值的相关计算图表和结论.     

轴对称横观各向同性土体中桩的扭转振动响应研究

基于单相弹性土体的运动方程以及横观各向同性材料的本构关系,研究了轴对称条件下端承桩在横观各向同性土体中的耦合扭转振动响应问题.在柱坐标下推导得到横观各向同性土体受谐和扭转荷载作用的动力控制方程,并采用分离变量法求得了土体扭转振动位移形式解.依据桩土接触面上的衔接条件,求解了桩身的动力平衡方程,并在频域内得到了桩身转角、扭矩和桩顶复刚度的解析解.最后分析了横观各向同性土体的力学参数对动力响应的影响.结果表明,横观各向同性土体的力学参数对桩顶复刚度、桩身转角和扭矩沿深度方向的变化均有着显著影响.     

横观各向同性层合压电矩形板稳定问题的三维精确分析

从横观各向同性压电弹性力学的三维基本方程出发,通过引入位移函数和应力函数,构造了两类相互独立的状态空间方程,使原方程解耦成两个低阶方程,有利于具体问题的求解。对于四边简支压电层合矩形板面内双向均匀受压的稳定问题,建立了层合板上下表面状态变量间的关系式,利用边界条件进一步导出特征方程。发现存在两类彼此无关的稳定形式:第一类对应板的纯面内稳定,而第二类则是一般意义上的板的弯曲稳定。给出了数值结果,并考察了相关参数的影响。     

运动简谐振子作用下地基梁体系振动特性的半解析研究

该文研究了地基梁体系在运动简谐振子作用下的振动特性。其中,地基梁体系由均质各向同性的欧拉梁以及弹簧和阻尼器组成的粘弹性地基模型组成。而移动的简谐振子则通过单自由度体系来描述。推导地基梁体系-简谐振子的耦合振动控制方程,并通过引入中间变量建立该耦合振动控制方法状态空间方程,给出该状态空间的方程的逐步求解方法。最后,通过简单算例,研究地基的基本特性、简谐振子的基本特性对梁的振动的影响。     

用传递矩阵法求解多层地基的轴对称问题

本文应用Hankel积分变换,求解单层弹性地基表面在轴对称荷载作用下位移和应力的初始函数解答,然后,利用矩阵传递方法求出多层地基位移和应力的一般表达式,不论弹性层数目多少,都不必求解任何联立方程。根据本文导出的公式编制了微型计算机程序。给出的算例说明了提供方法的正确性。     

层状TI饱和半空间均布斜线荷载及孔隙水压动力格林函数

基于Biot流体饱和多孔介质模型,采用动力刚度矩阵方法结合傅里叶变换,给出了层状横观各向同性(TI)饱和半空间中均布斜线荷载及孔隙水压的动力格林函数。方法首先将荷载作用层固定,在波数域内求得层内响应和固端反力,进而由刚度矩阵方法求得反加固端反力于整个层状半空间而产生的响应,最后叠加层内解和固端反力解经由傅里叶逆变换求得空间域内解。所给出的层状TI饱和半空间格林函数为建立相应边界元方法进而求解层状TI饱和介质相关波动问题提供了一组完备基本解。通过与已发表的各向同性饱和结果和TI弹性结果进行对比,验证了方法的正确性。进而给出了数值计算结果并进行了参数分析。结果表明:TI饱和介质与各向同性饱和介质对应的动力响应差异显著,且介质的各向异性参数对动力响应有着重要影响。此外,荷载埋深越小,地表位移和孔压波动更剧烈;介质渗透系数起到类似阻尼的作用,减小渗透系数可降低动力响应;随着频率的增大,位移、应力和孔压的波动也更为剧烈。     

Axisymmetrically loaded thin circular plate in adhesive contact with an elastic half-space

The interaction problem of adhesive contact between an axisymmetrically loaded thin circular plate and an isotropic or transversely isotropic elastic half-space is reduced to a problem of solving a pair of coupled integral equations for the unknown normal and shearing interfacial tractions. The system of integral equations is solved numerically and some results are presented.     

Axisymmetric elasticity solutions for a uniformly loaded annular plate of transversely isotropic functionally graded materials

Summary The axisymmetric problem of a functionally graded, transversely isotropic, annular plate subject to a uniform transverse load is considered. A direct displacement method is developed that the non-zero displacement components are expressed in terms of suitable combinations of power and logarithmic functions of r, the radial coordinate, with coefficients being undetermined functions of z, the axial coordinate. The governing equations as well as the corresponding boundary conditions for the undetermined functions are deduced from the equilibrium equations and the boundary conditions of the annular plate, respectively. Through a step-by-step integration scheme along with the consideration of boundary conditions at the upper and lower surfaces, the z-dependent functions are determined in explicit form, and certain integral constants are then determined completely from the remaining boundary conditions. Thus, analytical elasticity solutions for the plate with different cylindrical boundary conditions are presented. As a promising feature, the developed method is applicable when the five material constants of a transversely isotropic material vary along the thickness arbitrarily and independently. A numerical example is finally given to show the effect of the material inhomogeneity on the elastic field in the annular plate.     

Normal point force and point electric charge in a piezoelectric transversely isotropic functionally graded half-space

Normal point force and point electric charge acting on surface of a transversely isotropic piezoelectric half-space with a functionally graded transversely isotropic piezoelectric coating are considered. Elastic moduli, piezoelectric constants and dielectric permeabilities of the coating vary with depth according to arbitrary functions. Analytical expressions for the elastic displacements and potential of the electrostatic field are derived for a fixed value of the depth coordinate. Asymptotical analysis of these formulas is derived for small and big values of a radial coordinate. An equilibrium of the half-space under the action of axisymmetric mechanical (normal and tangential) and electric loading is studied and a scheme of reducing the solutions of mixed boundary value problems to integral equations is obtained. As an illustration of the obtained solution, the PZT-5H piezoceramics with typical examples of functionally graded and homogeneous coatings are considered. The results include computations of the profiles of displacements and electric potential for different types of variation of electro-elastic properties in the coating.     

Analytical layer-element approach for wave propagation of transversely isotropic pavement

Asphalt pavements have been recognised as transversely isotropic multi-layered structures. In this paper, an analytical layer-element approach is utlised to solve the wave propagation of transversely isotropic multi-layered pavement structures under the falling weight deflectometer impact load. After the application of Fourier–Hankel transform, the Navier's equation for transversely isotropic layer by impulsive force are solved analytically. The global stiffness matrix equation of multilayered structures is further obtained by assembling the interrelated layer-elements, and the actual solution is achieved by numerical inversion of the Fourier–Hankel transform after the solution in the transformed domain is obtained. The layer-element of a single layer and the global stiffness matrix only contain negative exponential functions, which leads to a considerable improvement in computation ef?ciency and stability. Numerical examples are presented to demonstrate the accuracy of this method and to inversitgate the influence of the properties of transversely isotropic elastic materials on the load-displacement responses.     

Three-dimensional analytical solution for functionally graded magneto–electro-elastic circular plates subjected to uniform load

The problem of a functionally graded, transversely isotropic, magneto–electro-elastic circular plate acted on by a uniform load is considered. The displacements and electric potential are represented by appropriate polynomials in the radial coordinate, of which the coefficients depends on the thickness coordinate, and are called the generalized displacement functions. The governing equations as well as the boundary conditions for these generalized displacement functions are derived from the original equations of equilibrium for axisymmetric problems and the boundary conditions on the upper and lower surfaces of the plate. Explicit expressions are then obtained through a step-by-step integration scheme, with five integral constants determinable from the boundary conditions at the cylindrical surface in the Saint Venant’s sense. The analytical solution is suited to arbitrary variations of material properties along the thickness direction, and can be readily degenerated into those for homogeneous plates. A particular circular plate, with some material constants being the exponential functions of the thickness coordinate, is finally considered for illustration.     

Annular crack surrounding an elastic fibre in transversely isotropic elasticity

The axisymmetric problem of an infinitely long transversely isotropic elastic fibre perfectly bonded to a dissimilar transversely isotropic elastic matrix containing an annular crack is considered. The annular crack, surrounding the fibre, is subjected to prescribed longitudinal tension. A potential function approach is used to find the solution of the basic equations. The mixed boundary value problem is reduced to the solution of a singular integral equation, which is further reduced, by using Chebyshev polynomials, to a system of algebraic equations.     

A refined theory of transversely isotropic piezoelectric plates

Summary. A refined theory for transversely isotropic piezoelectric plates is derived from the general solution of three-dimensional transversely isotropic piezoelasticity by means of Lure operator method. As a special case, the governing differential equations for transversely isotropic elastic plates are obtained directly.