Mixed finite element model for laminated composite beams

A novel, 6-node, two-dimensional mixed finite element (FE) model has been developed to<br />analyze laminated composite beams by using the minimum potential energy principle. The model has<br />been formulated by considering four degrees of freedom (two displacement components u, w and two<br />transverse stress components sz, txz) per node. The transverse stress components have been invoked as<br />nodal degrees of freedom by using the fundamental elasticity equations. Thus, the present mixed finite<br />element model not only ensures the continuity of transverse stress and displacement fields through the<br />thickness of the laminated beams but also maintains the fundamental elasticity relationship between the<br />components of stress, strain and displacement fields throughout the elastic continuum. This is an<br />important feature of the present formulation, which has not been observed in various mixed formulations<br />available in the literature. Results obtained from the model have been shown to be in excellent agreement<br />with the elasticity solutions for thin as well as thick laminated composite beams. A few results for a<br />cross-ply beam under fixed support conditions are also presented.