The quasi-static analysis for the viscoelastic hollow circular cylinder using the symplectic system method

The symplectic system method is introduced into the quasi-static analysis for axial symmetric problems of the viscoelastic hollow circular cylinder, with the emphasis on the local effects. By employing the method of separation of variables, all the fundamental eigenvectors of the governing equations are obtained directly. The combinations of the eigenvectors can describe the classical Saint-Venant problems and the local effects near the boundary. After constructing the adjoint symplectic relationships between the eigenvectors, the symplectic system method can be applied to solve quasi-static viscoelastic problems by expanding the eigenvectors to satisfy the given boundary conditions. Numerical results show the local effects due to the displacement constraints and the creep phenomenon of the time dependent material under certain boundary conditions. The results obtained by the approach are accurate, because all the given lateral boundary conditions and end conditions of the cylinder can be satisfied.