International Scientific Journals
of Scientific Technical Union of Mechanical Engineering "Industry 4.0"

In this paper a new algorithm and numerical approach which gives two-sided approximations of eigenvalues for second-order problem is presented. Conforming finite element methods are used in combination with an appropriate nonconforming interpolation. Numerical Aspects are discussed and also experiments which demonstrate the proposed algorithm are given.

The paper deals with a shaft subjected to an axial pressure with force P and relatively high moment of rotation M. In order to determne the lines of deflection we propose various approaches. The assessment of critical values of P and M is also discussed when loss of stability is available. Thus two fourth-order eigenvalue problems are considered and their mixed variational models are proposed. Finally, some numerical experimental results are presented.