The thick shell element of Ahmad, Irons and Zienkiewicz (Ref. 1) has been used in the study of plate and shell buckling and vibration problems.
A concise tensor based theory for finite elements, in general, and the shell element, above, in particular is developed in this study. Using this theory, expressions for the geometric stiffness and mass matrix of the above element are developed.
The subspace iteration method of Bathe and Wilson (Ref, 13) has been used for determining buckling loads and natural frequencies of vibration, A modified iteration method is developed, which allows use of the method for certain examples which previously were not solvable using the standard method. These examples are characterized by having as a solution set, pairs of eigenvalues, equal in magnitude, but opposite in sign. This modified method has been incorporated in the program with the basic standard method. Examples in the buckling field which exhibit this behaviour include the shear buckling of flat plates and the lateral buckling of beams. Both these cases have been investigated in this study.