Composite Element Method for vibration analysis of structure, Part I:: Principle and C0 element (bar)

A series of two papers is devoted to develop a new kind of numerical method for vibration analysis of structure, called Composite Element Method (CEM), by combining the conventional finite element method and classical analytical theory, aiming at utilizing both the versatility of the traditional FEM and the closed analytical solution of classical theory. First of all, two sets of coordinate systems are defined to describe the displacement field of discretization element: the nodal DOF system (same as in the conventional FEM), as well as the field DOF system of element. The goal of the former is to inherit the versatility of the conventional FEM; the latter is to obtain the higher approximate degree of accuracy. These two sets of coordinate systems are coupled and combined by means of the Rayleigh-Ritz principle. Two kinds of approaches are available to improve the GEM: (1) refining the element mesh, i.e., h-version, (2) increasing the degrees of freedom based upon the classical solution (i.e., c-DOF), called c-version. The numerical results show that c-version possesses a potential to lead to a superconvergence. This paper is the first of the series concentrating on the principle of GEM, C-0 element and the related applications. (C) 1998 Academic Press.