考虑地基水平变形的弹性基础板有限元分析

Finite element analysis of elastic foundation plate concerning horizontal deformation of foundation

用任意四边形板单元离散弹性基础板,将基础板按平面问题加薄板弯曲问题进行描述.假设 地基与板之间在板单元中心处通过链杆连接,且各链杆作用在地基表面上的力均匀分布在与板相 对应的地基表面单元上.用高斯积分法建立了各链杆处的位移与所有地基反力(包括垂直方向和 水平方向)之间的关系式,并对该式求逆获得了地基的柔度矩阵.在此基础上根据板与地基之间的 位移协调条件和静力平衡条件建立了考虑板与地基相互作用以板的节点位移为未知量的有限元方 程.通过算例说明了考虑地基水平变形对地基反力的影响,并验证了计算方法的正确性.

Mesh of elastic foundation plate is generated with arbitrary quadrilateral elements, which is described according to theories of both plane problem and bending problem. Two assumptions are made: one is that foundation and plate are linked by linking-rods on the center of plate elements; the other is that forces exerting on the surface elements of foundation linked to the plate are distributed uniformly. Therefore, calculation formulas between displacement of every link-rod and all foundation action (including horizontal forces and vertical forces) are built by Gaussian integral. Flexibility matrixes are also obtained by matrix inversion. Based on the condition of compatible displacement and static force equilibrium, FEM equations are built with nodal displacements as unknown variables by considering the action between plate and foundation. By using several examples the feasibility of the method is proved.