Temporal finite elements in the dynamic analysis of structures

Abstract

This thesis demonstrates that the use of finite elements need not be confined to space alone, but that they may also be used in the time domain, It is shown that finite element methods may be used successfully to obtain the response of systems to applied forces, including, for example, the accelerations in a tall structure subjected to an earthquake shock. It is further demonstrated that at least one of these methods may be considered to be a practical alternative to more usual methods of solution. A detailed investigation of the accuracy and stability of finite element solutions is included, and methods of applications to both single- and multi-degree of freedom systems are described. Solutions using two different temporal finite elements are compared with those obtained by conventional methods, and a comparison of computation times for the different methods is given. The application of finite element methods to distributed systems is described, using both separate discretizations in space and time, and a combined space-time discretization. The inclusion of both viscous and hysteretic damping is shown to add little to the difficulty of the solution. Temporal finite elements are also seen to be of considerable interest when applied to non-linear systems, both when the system parameters are time-dependent and also when they are functions of displacement. Solutions are given for many different examples, and the computer programs used for the finite element methods are included in an Appendix.