矩形地基厚板的有限变形动力学方程

Finite deformation dynamic equations of a thick rectangular plate-on-foundation

以有限变形连续体的最小加速度原理为基础 ,导出了在任意横向动力载荷作用下各类典型工程边界条件下放置于地基上的矩形厚板的有限变形运动方程 ,该方程反映了横向剪切效应、膜力效应和转动惯性效应 ;其退化形式符合公认的结果。所采用方法具有推导过程直接、简便、结果正确的特点。所得到的运动方程与几何方程、本构方程等构成地基厚板的有限变形动力控制方程 ,从而对于分析板的大变形冲击动力学问题具有意义。

In this paper, the finite deformation equations of motion of a thick rectangular plate-on-foundation, which is subjected to normal loads, are derived by using the minimum principle in dynamics of elastic-plastic continua at finite deformation. The effects of shear deformation, membrane force and the rotatory inertia are reflected in the equation. It can be shown that the course of educing the equation is direct and straightforward, the method is valid. The equations of motion and the geometry and constitutive equation make up of the governing equations of finite deformation dynamic of the plate. It is fitting to represent the impact dynamic problem of finite deformation structure.