SECOND ORDER FINITE ELEMENT SCHEMES FOR ELASTODYNAMICS

Abstract

This thesis is concerned with second order time integration schemes for linear elastodynamics equations. In addition to those existing algorithms, we proposed two new schemes derived from the traditional DBF2 method. We analysed accuracy and stability properties of both schemes, proved that they are both second-order accurate. Moreover, we theoretically compared these two schemes with the Newmark Algorithm which is one of the most popular methods among engineers. At last, with the help of Finite Element Method, we did accuracy check to constructed elastodynamics problems with known analytic solutions, and applied them to practical problems.