An Analysis Method of Symplectic Dual System for Decagonal Quasicrystal Plane Elasticity and Application

Abstract

The symplectic solution system of decagonal quasicrystal elastic mechanics is considered. Hamiltonian dual equations together with the boundary conditions are investigated by utilizing the principle of minimum potential energy. Then the symplectic eigenvectors are given on the basis of the variable separation method. As application, analytical solution for decagonal quasicrystal cantilever beam with concentrated load is discussed. The analytical expressions of the stresses and displacements of the phonon field and phason field are obtained. The present method allows for the exploration of new analytic solutions of quasicrystal elasticity that are difficult to obtain by other analytic methods