The Open Cybernetics & Systemics Journal

2015, 9 : 1606-1610
Published online 2015 September 30. DOI: 10.2174/1874110X01509011606
Publisher ID: TOCSJ-9-1606

A Hamiltonian System Method for Three-Dimensional Viscoelastic Solids

W.X. Zhang and Y. Bai
School of Civil Engineering and Architecture, Henan University of Technology, Zhengzhou, Henan, P.R. China.

ABSTRACT

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 discussed.

Keywords:

Eigensolution, Quasi-static, Viscoelastic, Hamiltonian system, Boundary Conditions, Eigensolutions.