DYNAMIC ANALYSIS BY THE P-VERSION OF THE FINITE ELEMENT METHOD

It is not until relatively recent rapid development of modern numerical analysis techniques and high speed digital computers that the Finite Element Method (FEM) has become a powerful tool for approximately solving the underlying differential equations which describe different physical phenomena. Due to its versatile applicability to deal with such a broad range of physical problems, and the ease with which it copes with complexities of such problems, the FEM enjoys widespread acceptance. Substantial research efforts for making the FEM more efficient and accurate are continually in progress. Three kinds of convergence processes are distinguished. The conventional one familiar to the typical analyst which involves using lower order elements in a fine mesh is referred to as the hversion of the FEM. The alternative is called the p-version of the FEM, where larger elements with higher polynomial order are used. The most advanced process takes advantage of the merits of both the h-version and p-versions in order to achieve optimal or quasi-optimal convergence. The research results contained in this dissertation are divided into three parts. In the first part, a literature review of the theoretical comparisons between the h-version and p-version is given. Some recent developments which, in the author's opinion, will be important to future developments of the FEM, and particularly the p-version, will be emphasized. Even though theoretical proofs are available which demonstrate that the p-version is superior to the conventional h-version, it still lacks general acceptance. It is the purpose of the second part of this dissertation to present the solutions by the p-version of several practical problems which are difficult to solve using the conventional h-version. It is shown that both efficiency and accuracy can be achieved much more easily through the use of the p-version of the FEM. Since the behavior of the p-version in static problems is generally well understood, it is the purpose of the third part of this dissertation to explore the behavior of the p-version in dynamic problems. Special emphasis is placed on eigenvalue analysis.