关于弹性力学半无限问题的注记

根据两个合理的判断依据，对弹性力学中的楔形体、半平面体、圆锥体和半空间体等经典解答进行了比较分析，发现了半无限平面应变问题和半空间体问题解答之间的关系；通过对解答之间的关系进行研究分析指出，弹性力学中的半无限平面体的符拉芒解答和半空间体的布希涅斯克解答存在局限性。对半无限地基、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分析，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些。

Note on elasticity’s semi-infinite problem

According to two logical judgements, the relation of the semi-infinite plane strain problem and semi-infinite spatial problem is found through analyzing the classical answer of wedge, semi-infinite plane, cone and semi-infinite spatial etc. The Flament answer of semi-infinite plane strain problem and the Boussinesq answer of semi-infinite spatial problem are confinable from the relation. 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.