Formulation for Non-axisymmetric Stability Loss

The formulation for the non-axisymmetric stability loss problem is given. The geometry of the considered element, the considered coordinate systems, the assumptions for the initial imperfection, and the details of the applied loading are given. Subsequently, the field equations of TDLTS (e.g., equilibrium equations, non-symmetric Kirchhoff stress tensor, displacement vector) are provided. The basic constitutive relations for viscoelastic materials are also provided to build the ground for formulating the final form of these relations using well-known equations for composite materials. The operators defining time-dependent strain are also mentioned herein. Finally, the boundary conditions at the ends and at the internal and external surfaces of the considered cylinder are also derived.