Thermoelastic buckling analysis of pre-twisted functionally graded beams with temperature-dependent material properties

As a first endeavor, the thermal buckling behavior of pre-twisted functionally graded (FG) beams with temperature-dependent material properties is investigated. The governing stability equations are derived based on the third-order shear deformation theory (TSDT) in conjunction with the adjacent equilibrium state criterion under the von Kármán's nonlinear kinematic assumptions using the Chebyshev-Ritz method. The Chebyshev polynomials multiplied with some suitable boundary functions are used as the basis functions, which allow one to analyze the beams with different boundary conditions. The extracted system of nonlinear algebraic eigenvalue equations is solved iteratively to obtain the critical temperature rise. The convergence behavior together with accuracy of the solution method and the correctness of formulation are demonstrated through different examples. Then, the influences of the linear and nonlinear variation of the angle of twist along the beam axis, the value of twist angle, length-to-thickness ratio, thickness-to-width ratio, material gradient index and temperature dependence of material properties on the critical temperature rise of the pre-twisted FG beams under different boundary conditions are investigated. It is shown that the pre-twist angle increases the thermal buckling resistance of the pre-twisted FG beams, but the temperature dependence of material properties reduces it.