Symplectic approach for the plane elasticity problem of quasicrystals with point group 10 mm

The symplectic approach is introduced into the plane elasticity problem of quasicrystals with point group 10 mm. The basic equations of the problem are equivalently written as the Hamiltonian dual equations. It is shown that the generalized eigenvector system of the corresponding Hamiltonian operator matrix is complete in the Cauchy Principal Value (CPV) sense. The analytical solution and related numerical results of the problem are then given.