Layerwise theories for composite beams with continuous and discontinuous stresses

Due to the unique characteristics of composite materials, the study of composite beams is far more complex than the study of homogeneous beams. The finite element method has proven to be a powerful approach to analyze composites subjected to the most distinctive situations. In the present work, two element solutions using cubic polynomials are considered: with continuous stresses and with discontinuous stresses along the transverse direction. Both converge to the analytical solution as the number of elements increase, i.e. with a finer mesh. Besides satisfying the boundary conditions at the surfaces and interfaces, the first solution gives better outcomes close to the center of the beam. On the other hand, the second solution gives better outcomes close to the borders of the beam, but it has a larger number of nodal parameters. The results are compared to a zig-zag element solution which has a number of nodal parameters independent of the number of layers. An element based on the Reissner mixed variational theorem is also included for additional comparisons. It is concluded that the cubic polynomials used to expand the cross section functions, must be different in each layer in order to achieve a reasonable agreement between the analytical and the calculated transverse normal stress.