比奥固结有限元分析中位能的研究

Potential energy in Biot consolidation FEM

对虚位移有限元法和伽辽金有限元法推导的Biot固结有限元方程进行了研究,详细讨论了位置高度z引起的荷载项(即位能),发现分别采用上述两种方法得到的位置高度z引起的荷载项不相等.采用伽辽金有限元法推导的Biot固结有限元方程的位能的物理力学概念明确,其位能项为浮力;而采用虚位移有限元法计算的位能的物理力学含义不明确,这在进行饱和土体的固结沉降分析时值得注意.

Based on analysis of virtual displacement FEM and Galerkin FEM for Biot consolidation, the load arisen by the altitude z is discussed. The load arisen by the altitude z is not equal using the two method above. The potential energy deduced by the Galerkin FEM is more rational; and potential energy is buoyant force. While the potential energy deduced by the virtual displacement FEM doesn＇t have physics concept. It must be noticed when analyzing saturated soil consolidation.