Science Letters： Analytical solutions for a uniformly loaded circular plate with clamped edges

A bi-harmonic potential function was constructed in this study. Love solution was employed to obtain analytical solutions of uniformly loaded plates with two different types of clamped edges. The treatment of clamped boundary conditions was the same as that adopted by Timoshenko and Goodier （1970）. The analytical solution for the first type of clamped boundary condition is identical with that obtained by Luo et al.（2004）, and the solutions for both types were compared with the FEM results and the calculations of thin plate theory.     

深埋圆形富水隧道应力与位移的弹塑性解

研究目的：推导获得深埋圆形富水隧道应力场与位移场分布的弹塑性解析解。创新要点：皋于弹性力学厚壁圆筒受均布压力的拉姆解答和Mohr—Coulomb屈服条件,推导了考虑渗流作用和应力释放时含衬砌深埋隧道的弹塑性解,并采用FLAC3D有限差分程序验证了其正确性。研究方法：通过理论分析建立考虑渗流作用和应力释放的含衬砌深埋圆形隧道的解析模型（图1）,然后推导了基于Mohr-Coulomb屈服准则的隧道同岩与衬砌渗流场、位移场和应力场计算的弹塑性解析公式,并通过数值模拟程序（图2）验证了推导公式的正确性。重要结论：基于前人研究皋础,推导获得了深埋富水隧道应力与位移场分布的理论解析解,并通过数值模拟方法验证了其正确性。该解析解一方面可以用于深埋高水头隧道的预设计,如预测隧道周围的水压力、应力场和位移场分布规律,另一方面可用于校核大型复杂数值模型的正确性。