A thermomechanical finite element for the analysis of rectangular laminated beams

A new three-noded thermomechanical beam finite element is derived for the analysis of laminated beams. The mechanical part is based on a refined model. The representation of the transverse shear strain by cosine function allows avoiding shear correction factors. This kinematics accounts for the interlaminar continuity conditions at the interfaces between the layers, and the boundary conditions at the upper and lower surfaces of the beam. A conforming FE approach is carried out using Lagrange and Hermite interpolations. Concerning the thermal part, a layerwise approach through the thickness is used. Moreover, the continuity of the transverse component of the thermal flux is constrained between the layers. It presents the advantage of reducing the number of temperature unknowns, and improve the results at the interface between two adjacent layers. Mechanical, thermal and thermomechanical tests are presented in order to evaluate the capability of this new finite element to give accurate results with respect to elasticity or finite element reference solutions. Both convergence velocity and accuracy are discussed.