双参数地基圆(环)形板的边界剪力及其力学响应

Boundary force and mechanical response of circular or annular plate on two-parameter foundation

针对目前考量双参数地基上圆形或环形板边界剪力中存在的一些不足,应用Hankel变换法求得双参数地基的解析解,研究了任意环状线荷载作用下双参数地基的挠度、转角及地基反力间的关系。指出双参数地基在线荷载处的转角差与表示横向联系的地基参数之乘积等于线荷载集度;环内的分布荷载仅影响环内侧转角,而环外分布荷载也仅影响环外侧转角;进而又给出了适用于双参数地基圆形或环形板的内/外边界剪力的简明表达式。最后分别给出了双参数地基上自由边界圆形薄板中点承受集中力、圆形均布荷载作用时边界剪力对板中点挠度、弯矩的影响规律;双参数地基边界剪力对板挠度、弯矩有较明显影响,尤其是板的相对半径ρ0<4或是荷载距板边界较近时这种影响更为明显。

In view of some deficiencies in the boundary force of circular or annular plates on two-parameter foundations, the Hankel transform method is applied to find the analytical solution of two-parameter foundations,and the relationship between the flexure displacement, radial rotation angle and subgrade reaction of the two-parameter foundation under any annular line load is studied.It is pointed out that the product of the radial rotation angle difference at the line load and the foundation parameters representing the horizontal contact is equal to the line load intensity, and the distributed load inside the annulus only affects the radial rotation angle inside the annulus, so does the distributed load outside of the annulus.Furthermore, a concise expression of the boundary force applied to the inner or outer boundary of circular or annular plates on two-parameter foundations is given.Finally, the influence of boundary force on the midpoint flexure displacement and bending moment of circular plates with free boundary under concentrated loads and circular uniformly distributed loads is analyzed referring that the boundary force has a significant effect on the flexure displacement and bending moment,especially when the plate is small in size or the load is close to the board boundary.