Koziy I. Finite-element analysis of stability of shells amenable to shear and compression

The thesis research relates to the study of stability in shells amenable to shear and compression. On the basis of correlations of non-linear geometric theory of thin shells amenable to shear and compression (a six-modal variant), the key equations for the determination of initial post-critical state by the finite element method have been noted; appropriate variational problem has been stated. Theorem on continuity and symmetry of the forms of this variational problem for the possibility of further application of iteration methods has been proven. The correlation for detecting proper frequencies of free vibrations within the considered shells has been noted. Numerical schemes for finite element method applying biquadratic isoparametric approximations for solving the problems of stability, vibrations and linear and nonlinear deformation of shell amenable to shear and compression have been constructed. A number of test problems was studied, which testify the authenticity of the results obtained based on the suggested method having applied self-developed set of programs. The order of the rate of convergence of finite element method has been researched.