水工混凝土带缝结构温度场问题的扩展有限元法

Temperature field analysis of harbor engineering structure with cracks based on XFEM

长期处在温度荷载等作用下运行的水工结构或多或少都会产生裂缝,有必要对其温度场进行计算分析。鉴于扩展有限元法求解不连续问题的独特优势,文章用其求解温度场;首先分析给出了裂缝结构温度场的逼近形式,随后推导了用扩展有限元法求解不连续温度场的离散方程,其中裂缝采用等温形式进行模拟,即温度连续但其一阶导数不连续,继而建立起温度场的扩展有限元法。并以带缝十字形板的算例验证了扩展有限元法求解温度—应力问题的正确性;最后,用该方法分析了某面板堆石坝面板裂缝在冬季降温期的扩展情况,其结果与实际监测成果较一致。

For the long-term exposure to temperature load, certain parts of a concrete structure have more or less cracks during its construction and operation period. It is necessary to calculate and analyze the temperature field. For the difficulty of applying classical fracture criteria to the actual hydraulic engineering and simulating the process of cracking by conditional FEM, the XFEM was introduced into the analysis of the temperature field in hydraulic structures in this paper. Firstly, the approximation form of the temperature field of cracked structure was analyzed and provided, and then the discrete equation for solving discontinuous temperature field was deduced, where the crack was simulated by isothermal form, namely, the temperature field is continuous but its first derivative is not continuous. The temperature field by XFEM was established. And a numerical example of a cross shaped plate with slit was used to verify the validity of proposed method. Finally, this method was used to analyze the expansion of the cracks in the face slab of a concrete face rock-fill dam in winter. The results are consistent with the actual monitoring results.