New orthogonality relationship of plane elasticity in sectorial region and its variational principle

In the plane elasticity sectorial region problem, an off-diagonal Hamiltonian operator is obtained by constructing new dual vectors and using virtual circumferential coordinate in spatial domain to mathematically analogize the time variable in temporal domain of Hamiltonian system. The operator possesses some structural characteristics that the elements of main diagonal are zero and skew diagonal entries are symmetric operators. Two independent and symmetrical orthogonality sub-relationships are discovered. By selecting dual vectors appropriately, the new orthogonality relationships in the rectangular coordinates are generalized into the polar coordinates for isotropic plane elasticity problems. By using integral form, a variational principle which is relative to differential form is derived, and moreover, a complete functional expression is proposed.