【摘要】 本文利用富氏变换研究了带体力的垂向不均匀横观各向同性弹性体静力学问题基本方程,得到了分层均匀多层问题的通解。通过炮阵传递、富氏逆变换,可得到本问题在一般定解条件下的解。它们的格林函数可表成零阶和一阶汉克尔变换形式。本解可退化到前人用镜像法和积分变换等给出的类似问题解,其中包括Boussinesq问题和Mindlin问题的解。 作为算例,给出了二层弹性半空间在矩形区域内受抛物形分布的垂直载荷作用下的位移和应力。更多还原

【Abstract】 The paper investigates the foundamental equations (1, 2) with body forces of a vertically inhomogeneous and transversely isotropic elastic medium by the twodimensi-onal Fourier tranform. The basic equations are then written into two sets of ordinary differential equations In z, eq. (3). Using Laplace transform, we can obtain the simple general solution for a homogeneous single layer in terms of boundary stresses (σz,σxz,τyz) and displacements (u, v, w) at its top surface which is given in (5). For N layers, with the matrix transfer equations (7), one gets the general solution in Fourier transforms of the j-th layer (9)-for fully connected interface between layers. The out boundary stresses and displacements at z=0 and at z=H(n-th layer is a finite thick layer) or only at z= 0 (n-th layer is a half-space), will then yield a set of linear algebraic equations in Fourier transform space. Finally, under general condition and by two-dimensional inverse Fourier transform, we can obtain a closed form solution for the stress and displacement in the body (13). In the final solution, the Green functions can be expressed in terms of Hankel transforms of order zero and unity (14) and become rather neat. These solutions can be reduced to those of Boussinesq and Mindlia’s problems. Therefore, we may consider them as a general Boussinesq and Mindlin’s solution in N-layered systems.A numerical example is worked out for a 2-layer medium. The stress and displacement distribution are given in fig. 1-4. Since this is a closed-form solution, it is easy to vary the parameters and boundary conditions to get a optimum distribution. Thus it is useful in the dessign of composites and layered road construction.更多还原