A new higher order C0 mixed beam element for FGM beams analysis

This paper presents a 2-node, 4 DOF/node beam element based on higher order shear deformation theory for axial-flexural-shear functionally graded material. The theory accounts for parabolic distribution of the transverse shear strain through the thickness of the beam. A discrete constraint is used to get the stress free condition on the top and bottom surface and to avoid the C1 transverse continuous displacement. A beam element, based on a displacement formulation, is first developed. Next, the numerical treatment of the shear field is improved in a second element using a mixed formulation. Numerical examples, selected from the literature, are illustrated. A good agreement is obtained between numerical results of mixed beam element and the reference solutions. The proposed formulation gives an exact solution at the nodes even for a coarse mesh.