Extension of the fixed grid finite element method to eigenvalue problems

This paper details the development of the fixed grid FEA (FGFEA) method to the solution of eigenvalue (natural frequency and buckling) problems, using a 4 node 20 degree of freedom shell element. The formulation of the FG element stiffness, buckling and natural frequency equations is presented. The first natural frequency and buckling load are determined for the simply supported plate with a central circular void. The void is then offset to three further locations to asses the applicability of FGFEA eigenvalue analysis at reduced symmetry. A correlation trend is formed by comparison with traditional FEA results at nine increasingly refined mesh densities for each example. In addition to this, a relationship between the FGFEA error and the boundary element intersection angle with the void is formed.