Implementation of Space-Time Finite Element Formulation in Elastodynamics.

摘要

Elastodynamics is an academic field that is involved in solving problems related to the field of the wave propagation in continuous solid medium. Finite element methods have long been an accepted way of solving elastodynamics problems in the spatial dimension. Considerable thought has been given to the ways of implementing finite element discretization in the temporal dimension as well. A particular method of finite element solving called space-time finite element formulation is explored in this thesis, which is a relatively recent technique for discretization in spatial and temporal dimensions. The present thesis explores the implementation of space-time finite element formulation in solving classical elastodynamics examples such as the mass-on-spring for a single degree of freedom and for an axially vibrating bar with multiple degrees of freedom. The space-time formulation is compared with existing finite difference techniques such as the central difference method for computational expenditure and accuracy. In the mass-on-spring case, the central difference method and linear time finite elements yield relatively similar results, whereas quadratic time finite elements are more accurate but take more time computationally. In the axially vibrating bar case, central difference is computationally more efficient than Space-Time finite element method. The final section concludes our findings and critiques the numerical effectiveness of the space-time finite element formulation.