Wewnętrzna stateczność sprężystego walca kołowego przy odkształceniach skończonych

The problem of stability of a full circular cylinder made of a hyperelastic homogeneous material with the most general physical characteristics is discussed. The finite deformation's are produced by normal loading on the frontal surfaces of the cylinder. The points of lateral surface of the cylinder cannot be freely displaced in the radial direction. The condition of stability loss results from the assumption of existence of non-zero solutions for small admissible deformations superposed on initial finite deformations. Two cases of the boundary conditions determined on the frontal surfaces of the cylinder are discussed: the boundary conditions given in displacements and those of the ''mixed'' type. It is shown that for the both cases the boundary eigenvalue problems are self-adjoint and thus the obtained stability conditions are correct when the most general kinematic criterion of stability is applied.