A time domain finite element approach based on time series estimation

Abstract

This paper details the use of time series for solving finite element equations. It was aimed at eliminating the discretization of time intervals to reduce calculation time and to obtain accurate results using time-dependent variables. For this purpose, the matrix form of the time series finite element formulation for both continuous and discontinuous time functions were extracted using Taylor and Fourier series for estimating time-dependent functions. Based on the extracted formulation, for solving elastodynamic problems, a computer code and algorithm was introduced. The efficiency and accuracy of the formulation was evaluated by solving different analytical examples. To reveal the power of time series for modeling real problems three practical examples such as settlement, flood protector structures and temporary cofferdams were modeled using time series approach and the results of analyses were presented. The results showed that having removed time discretization procedure, the time series based finite element method can be efficiently applied to decrease the calculation time and computational efforts. In addition, time-continuous responses resulting from this method, help reduce the calculation steps which is vital in many engineering problems.