Investigation of the Analytic Solution of Orthotropic Beams under Thermal-Mechanical Coupling Loading

The symplectic method was applied in the orthotropic beams under the thermal mechanical coupling in the present paper. With Hamiltonian variational principle and Legendre's transformation, Hamiltonian canonical equations are obtained, together with side boundary conditions. So the analytic solution with different boundary conditions can be converted into determination of eigensolution with separation of variables and symplectic expansion. The results showed that the present solution have better convergence and precision, which provides a basic theory for studying the plane beam under thermal-mechanical coupling.