p-VERSION FINITE ELEMENTS IN STRUCTURAL DYNAMICS AND STABILITY

The performance of the finite element method (FEM) may be improved in three ways. The first is by the h-version to refine the finite element mesh and the second is by the p-version to increase the order of polynomial shape functions for a fixed mesh. The third is simultaneously to refine the mesh and increase the degrees of elements uniformly or selectively, called the h-p version, which is a combination of the first two methods. The advantages of the p-version elements over the h-version are: (i) they have better conditioned matrices; (ii) they do not require a change in the mesh and can be easily used in the adaptive analysis; (iii) just one element can predict accurate solutions for a simple structure; (iv) they tend to give the same accurate results with far fewer degrees of freedom (DOF); and (v) they can overcome some locking problems. The main objectives of present study are to give a wide range of application of the Fourier p-elements and polynomial p-elements to investigate the vibration problems, buckling problems and dynamic stability problems of various conservative linear structures including beam-columns, straight Timoshenko beams, pre-twisted straight beams, Mindlin plates and open thin shell panels. The natural frequencies, buckling loads and the relation of frequencies and various buckling loads are considered. Good agreement is achieved with the available results. The main work can be divided into five parts. Firstly, the numerical examples of uniform or tapered beam-columns with or without end mass are considered and compared with results of dynamic stiffness method. New results of straight beamcolumns subjected to uniformly distributed follower tension are originally