Elasticity solutions of clamped laminated arches with temperature-dependent material properties under thermo-mechanical loading

The mechanical behaviors of the clamped laminated arch with temperature-dependent material properties under the thermal and mechanical loadings are studied in this paper. An analytical method based on the theory of thermoelasticity is proposed for predicting the exact solutions of stresses and displacements in the arch with arbitrary thickness and layer numbers. The clamped support is equivalent to a simply support with a support reaction with the unit pulse function and the Dirac function. The space state method is utilized to establish the state equation by employing the displacements and stresses as the state variables. A slice model is introduced to simplify the coefficient matrix. Based on the continuities at the interfaces, the displacement and stress relationships between the internal and external surfaces of the laminated arch are derived with the transfer matrix method. Exact solutions for the displacements and stresses can be obtained according to the stress boundary conditions on the surfaces of the laminated arch. Finally, convergence and comparison studies demonstrate the excellent efficiency and accuracy of the present method. The influences of material dependency with temperature, thermal load, and thickness-to-radius ratio on the distributions of displacements and stresses are discussed in detail.