An Introduction to the Composite Element Method Applied to the Vibration Analysis of Trusses

Abstract

This paper introduces a new type of Finite Element Method (FEM), called Composite Element Method (CEM). The CEM was developed by combining the versatility of the FEM and the high accuracy of closed form solutions from the classical analytical theory. Analytical solutions, which fulfil some special boundary conditions, are added to FEM shape functions forming a new group of shape functions. CEM results can be improved using two types of approach: h-version and c-version. The h-version, as in FEM, is the refinement of the element mesh. On the other hand, in the c-version there is an increase of degrees of freedom related to the classical theory (c-dof). The application of CEM in vibration analysis is thus investigated and a rod element is developed. Some samples which present frequencies and vibration mode shapes obtained by CEM are compared to those obtained by FEM and by the classical theory. The numerical results show that CEM is more accurate than FEM for the same number of total degrees of freedom employed. It is observed in the examples that the c-version of CEM leads to a super convergent solution.