Exact solutions for coupled analysis of thin-walled functionally graded beams with non-symmetric single- and double-cells

In the present work, the exact solutions for coupled analysis for bending and torsional case thin-walled functionally graded (FG) beams with non-symmetric single- and double-cells are presented for the first time. For this purpose, an accurate and efficient method is proposed to obtain the FG member stiffness matrix based on the series expansions of displacement components. Three types of material distributions are considered and the beam mechanical properties are graded along the wall thickness according to a power law of the volume fraction. The present beam model is on the basis of the Euler-Bernoulli beam theory and the Vlasov one for bending and torsional problems, respectively. The explicit expressions for displacement parameters are derived using the power series approach from the four coupled equilibrium equations. Finally, the FG member stiffness matrix is determined from the seven force-displacement relations. In order to show the accuracy and super convergence of the thin-walled FG beam element developed by this study, the numerical solutions are presented and compared with results obtained from the finite beam element based on the approximate interpolation polynomials and other available results. Especially, the effects of various structural parameters such as material distribution type, volume fraction index, boundary condition, and material ratio on the spatially coupled responses of FG box beams with non-symmetric single- and double-cells are parametrically investigated.