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The Hamiltonian system in quasi-static problems of 3D viscoelastic solids has been introduced in this paper.
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 the analytical fundamental eigensolutions and their
corresponding Jordan forms are derived. After the establishment of symplectic adjoint relation, the final solution is expressed
by linear combinations of the general eigensolutions, and the combinations are determined by the given boundary
conditions. For its applications, problems of various boundary conditions and the inhomogeneous governing equations are