A modified lower-order theory for FG beam with circular cross-section - Duan, T. C.; Li, X. Y.; Xiao, Y.; Zhang, L.; Chen, C.; Li, Z. J. (Frontiers in Materials, 2022)
The modified uncoupled lower-order beam theory (LBT) based on the third-order shear deformation model was established for functionally graded (FG) beams with circular cross-section in this paper. Based on the shear stress free condition on the boundary of the circular cross-section, the bidirectional warping function of the axial displacement is mathematically derived for the first time. The power-law form in the radial direction is adopted to describe continuous variation of material properties. Generalized stresses are defined through the orthogonal form of the axial displacement and then expressed in the decoupling form, in which the shear correction factor and three relatively small coefficients are involved. The frame independent uncoupled equilibrium equations and the corresponding boundary conditions are obtained via the asymptotic principle of virtual work. The present LBT is validated through the pure bending of a Clamped-Clamped FG beam by comparing the obtained deflections with the published results. Accordingly, the effects of shear, warping and stress mitigation acting on the cross-section influenced by the power-law exponent have been described graphically and discussed.