A Hamiltonian System Method for Three-Dimensional Viscoelastic Solids

This paper introduces the Hamiltonian system into quasi-static problems of 3D viscoelastic solids. Based on the principle of elastic-viscoelastic correspondence, the problem of solving partial differential equations is reduced to finding general eigensolutions of the dual equations, and all analytical fundamental eigensolutions and their corresponding Jordan forms are derived. After the symplectic adjoint relation being established, the final solution is expressed by linear combinations of the general eigensolutions, and the combination is always determined by the given boundary conditions. As its applications, problems of various boundary conditions and the inhomogeneous governing equations are dentally discussed.