用强化假定不连续应变实体单元分析弹性地基薄板

用强化假定不连续应变(EAS)实体单元离散弹性地基薄板,假设板上的荷载按分布力形式传递到地基中,根据半无限空间上任一点节点力与任一点处的位移关系用高斯积分法建立了地基表面分布力与节点位移关系表达式,在此基础上根据地基与板间的位移协调及静力平衡条件,建立了以板上的节点位移为未知量的有限元方程.算例分析表明,采用强化假定不连续应变实体单元分析薄板类问题是合理的,进行弹性地基薄板受力分析时考虑地基分布反力是必要的.

Enhanced assumed strain (EAS) element-based analysis of thin plates on elastic foundations

The EAS element method is used to discretize the thin plate on the elastic foundation. Under the assumption that the contact forces on the interface of the plate and foundation are in the distributive form, the relationship between the distributed force on the surface of foundations and nodal displacement is established according to the theoretical solution of the displacement at nodes in the semi-infinite space subjected to vertical and horizontal forces. Then, based on the conditions of compatibility of displacement and static force equilibrium between the plate and the foundation, FEM equations are formulated with displacements at nodes on the middle surface of the plate taken as unknown variables. An example is given to verify the rationality of the EAS element for analysis of thin plates and to show the necessity of taking the distributed force on the interface between plates and foundations into account.