无限均布压力作用下弹性地基的应力和位移

Study on elastic foundation under infinite uniform pressure

通过两个典型的半无限体实例,对水平表面作用无限均布压力下弹性地基的应力和位移解答进行研究,结果表明:对边界条件不明确的无限边界仅采用解答的必要非充分条件——平衡条件来等效处理,其应力解答不是唯一的,因为此时该边值问题不是一个适定的数学问题.对弹性地基梁板中的半无限大地基、底部完全位移约束的有限深地基和底部光滑刚性支承的有限深地基在水平表面作用无限均布压力时的应力和位移分量进行了比较,认为底部完全位移约束的有限深地基模型较其他两种地基模型更合理.

Case study was performed on two typical semi-infinite bodies to investigate the stress and displacement of elastic foundation under infinite uniform pressures on horizontal surface. The result showed that, if only the necessary but insufficient condition, the equilibrium condition, was adopted to deal with the infinite uncertain boundary condition, the solution to the stress was non-unique due to the fact that the boundary problem here was a mal posed mathematic problem. Based on a comparison of stress and displacement components of the semi-infinite elastic foundation, the elastic finite depth foundation with rigid constraint at the bottom, and the elastic finite depth foundation with smooth rigid supporting constraint at the bottom under infinite uniform pressure on horizontal surface, it is concluded that the elastic finite deep foundation model with rigid constraint at the bottom is more rational than other two models.