Static and dynamic analysis of arch dam using 3D scaled boundary finite element method

The static and dynamic analysis of the arch dam is performed using the 3D scaled boundary finite element method (SBFEM). Only the boundaries are discretized and the solution in the radial direction is described analytically, which reduces the dimensions by one and leads to results with high precision. The previous substructure method used in arch dams depends on the partition form of substructures due to the irregular geometries and sometimes may lead to difficulty in choosing the scaling center. To solve these problems, the hexahedral elements modelled by the SBFEM are developed. The element mass matrix and stiffness matrix are given, and the elastodynamic equations using the SBFEM are established. The Newmark integration method is applied to obtain the dynamic response of the arch dam. Numerical examples are carried out to verify the accuracy and stability of the hexahedral elements modelled by 3D SBFEM. The first example is a cuboid subjected to static loads. The calculated nodal displacements are found to be identical to the analytical solution. The second example is the static and dynamic numerical simulation of an arch dam. The displacements and stresses of static and dynamic loading conditions are calculated and compared to the results of ANSYS, respectively. Good agreement is observed for the results of SBFEM and ANSYS. The good accuracy and stability of 3D SBFEM make it be an attractive alternative method for the static and dynamic analysis of arch dams.