Static bending analysis of functionally graded sandwich beams using a novel mixed beam element based on first-order shear deformation theory

In this paper, the static bending behavior of the functionally graded sandwich beams is investigated using a novel mixed beam element based on the first-order shear deformation theory. The proposed beam element consists of two nodes and three degrees of freedom per node as the traditional Timoshenko beam element. By introducing a special process, selective or reduced integration are not required to calculate the element stiffness matrix and nodal force vector. The efficiency and accuracy of the proposed element are verified via some comparison studies. Then the proposed element is applied to study the bending behavior of the functionally graded sandwich beams with various boundary conditions. The influences of some parameters such as the power-law index, the slender ratio and the boundary conditions are studied carefully. The comparison studies and numerical results present that the new beam element is compatible with the static bending analysis of the functionally graded sandwich beams with a very coarse mesh. Besides, the numerical results show that the stress concentration may occur on the separated surface of the core layer and two face sheets, which should be noticed in practical applications of the FG sandwich beams.