自由边各向异性矩形板的弯曲

Bending of anisotropic rectangle plates with free edges

通过傅立叶级数法得到了有自由边的各向异性矩形板的一般解.板的挠度被展成重傅立叶级数,挠度和其导数在边界上的值被展成单傅立叶级数.利用控制微分方程和边界条件,求解被简化成求其边界值的傅立叶级数的系数.文后给出了弹性地基上的方板、角支方板、悬臂方板和两邻边固定另两边自由的方板的挠曲面图.据作者所知,这里给出的是第一个有关这类问题的精确而完美的处理.

In this paper the general solutions to anisotropic rectangle plate with freeedges on elastic foundation have been obtained by means of Fourier series. The displacement is expanded in double Fourier series andi some of its differential coefficienton boundaries in single Fourier series. Using governing equation and some boundary conditions, the solution is reduced to solve Fourier series for coefficients in the series it self or in its differential coefficients on boundaries. The deflections of rectangle plate with variant boundary conditions are presented. This represents, to the author's knowledge, the first accurate comprehensive treatment of this set of problems.