水管冷却混凝土温度场计算的三维p型有限元法

3D p-version hierarchical finite element method for calculation of concrete cooling pipe temperature field

引入阶谱与自适应技术,将p型有限元法应用于水管冷却混凝土温度场的仿真计算,通过对单元升阶谱,以扩大容许函数空间来提高数值解精度,并编制了p型自适应有限元计算程序。针对同一计算模型,分别采用不同网格密度的常规有限元法和p型有限元法进行了水管冷却混凝土温度场的计算分析和对比研究。结果表明,p型有限元法的计算结果在网格稀疏的情况下仍然能够达到较高的精度,特征点温度时程线和温度场等值线与精细算法值吻合得较好,而常规有限元法则误差相对较大。同时,采用p型有限元法进行水管冷却混凝土温度场模拟,可以在保证计算精度的前提下减少单元数量,从而降低前处理的难度、工作量以及计算的时间成本。

Introducing hierarchical and adaptive technique, increasing the order of hierarchical and expand-ing the space of basis function to improve the numerical precision,the 3D p-version hierarchical finite ele-ment method（FEM） and corresponding finite element program of concrete cooling pipe temperature field are proposed and compiled. For a same calculation model, the different mesh density of the traditional FEM and p-version hierarchical FEM is used for analysis and comparative study of concrete cooling pipe tempera-ture field. The comparison of the calculation results shows that the p-version hierarchical finite element method brings better precision with a coarse grid in unsteady cooling pipe temperature field analysis. At the same time, under the condition of the same computational precision, the element number can be re-duced,so that the time consumption for preprocess and computation is obviously reduced.