The creep and stress concentration of a viscoelastic circular cylinder under its own weight

摘要

The classical problem of a viscoelastic circular cylinder under its own weight is analysed using the Hamiltonian system method. By introducing dual variables of stresses, the method of separation of variables can be applied. Hence the general solutions of the governing equations in the Hamiltonian system are obtained. The solutions are divided into two groups, zero eigensolutions and nonzero eigensolutions. Actually, zero eigensolutions correspond with various classical Saint-Venant problems. Nonzero eigensolutions are local effect solutions, decaying rapidly with the distance from the boundary. Since the adjoint symplectic relationships in the time domain are constructed, the Hamiltonian system method can be applied by expanding the general solutions to satisfy the boundary conditions in the time domain directly. Numerical results show the stress concentration near the end due to the displacement constraints and the creep of radial displacement.