Exact Mathematical Model and its Numerical Solution of a Two-Layer Beam Subjected to Non-Uniform Temperature Rise
Based on accurately considering the axial extension, geometrically nonlinear governing equations for a two-layer beam subjected to thermal load were formulated. By using a shooting method, the strongly nonlinear ordinary differential equations with two-point boundary conditions were solved and numerical solution for thermal post-buckling and bending deformation of a two-layer beam with pinned-pinned ends and subjected to transversely non-uniform temperature rising were obtained. As an example, equilibrium paths and configuration for a beam laminated by brass and steel are presented and characteristic curves of the nonlinear deformation changing with the thermal load were plotted. Effects of the geometric and material parameters on the deformation of the beam were discussed and analyzed in detail. The theoretical analysis and numerical results show that the bending deformation and the stretching-bending coupling terms of beam subjected to uniform or non-uniform temperature rising can be produced because of the non-homogenous distribution of the material properties. The bending deformation resulted from transversely temperature rise is primary deformation when values of average temperature rise parameter is under critical temperature, however, the curves become the thermal post-buckling equilibrium paths with the increment of average temperature rise when values of average temperature rise parameter exceed critical temperature.
X. P. Chang et al., "Exact Mathematical Model and its Numerical Solution of a Two-Layer Beam Subjected to Non-Uniform Temperature Rise", Applied Mechanics and Materials, Vols. 130-134, pp. 3163-3168, 2012