基于高阶有限元法的水工混凝土结构开裂及裂缝扩展问题的数值模拟

水工混凝土建筑物（如大坝）中的开裂及裂缝扩展问题一直是国内外水利水电工程中的重要研究课题。对于混凝土开裂及裂缝扩展问题的数值模拟，目前常用的方法有无单元法、边界元法、数值流形法、有限单元法和扩展有限元法等，其中有限单元法是工程领域中广为应用的数值模拟方法，但有限单元法本质上是一种连续介质力学方法,不能直接用来分析诸如混凝土结构开裂及裂缝扩展这样的不连续问题。目前，Belytschko等提出的扩展有限元法是求解混凝土结构开裂及裂缝扩展等强不连续问题最有效的数值方法，但扩展有限元法大多使用低阶插值，收敛速度较慢，计算精度较低。本项目将运用高阶有限元法，结合扩展有限元法，通过构造新的形函数（高阶插值函数加入反映局部特性的附加函数),对水工混凝土结构开裂及裂缝扩展问题进行数值模拟分析，以期得到具有更高精度和更快收敛速度的数值计算结果。

The problems of cracking and crack propagation in the hydraulic concrete building(such as dams) have been a major topic in water conservancy and hydropower engineering in both domestic and aboard. At present, for the numerical simulation of concrete cracking and crack propagation, commonly used methods are element free method、boundary element method、numerical manifold method、finite element method and extended finite element method, etc., the finite element method is a numerical method which has been used widely in engineering field, but the finite element method is essentially a kind of continuum mechanics method, it cannot be used directly to analyse such as the discontinuous problems of concrete structure cracking and crack propagation. Currently, the extended finite element method proposed by Belytschko et al is the most effective numerical method to solve the problem of strong discontinuity of cracking and crack propagation in concrete structures, but the extended finite element method mostly uses low order interpolation, the convergence rate is slow and the accuracy is also low. This project will simulate and analyse numerically the cracking and crack propagation in hydraulic concrete structures by applying the high order finite element method, combined with the extended finite element method, and constructing new shape functions (higher order interpolation functions add additional functions that reflect local characteristics) to obtain the numerical results with higher precision and faster convergence rate.