A higher-order shear deformable mixed beam element model for accurate analysis of functionally graded sandwich beams

In this paper, a new higher-order shear deformation beam theory is developed by introducing the stress equilibrium condition. On the basis of the new shear deformation theory, novel shear deformable mixed beam elements with independent internal force fields and displacement fields are developed for accurate analysis of the functionally graded sandwich beams. Furthermore, a shear deformable beam element with additional interpolated axial displacement is also constructed in order to get reliable reference solutions. Two examples are presented to investigate the solution accuracy of different beam elements. Numerical results indicate that the present mixed beam elements can accurately predict the stress distributions over the cross section and ultimately give accurate displacement solutions. Moreover, the characteristics of axial displacement distributions and transverse shear strain distributions for functionally graded sandwich beams are discussed and the difficulty of getting accurate solutions by introducing a single form higher-order displacement function is pointed out. In these cases, the equilibrium-based beam theory and the corresponding mixed beam elements are more effective and reliable to obtain accurate solutions. Finally, the numerical stability for different beam elements is investigated and the results indicate the present higher-order shear deformable mixed beam element has excellent numerical stability.