Continuous stress distribution following transverse direction for FEM orthotropic laminated plates and shells

•Laminated plate and shells by the finite element based on positions.•Continuous transverse stress assessment not increasing the number of degrees of freedom.•Large displacements and rotations.•Symmetric and Asymmetric orthotropic ply arrangements.

In this paper the strain field achieved from a basic solid-like kinematics with a quadratic displacement enhancement along the transverse direction will be improved to satisfy the continuity of the shear and normal stresses fields regarding transverse direction. This improvement is done almost keeping unchanged the total strain energy potential along the transverse line of the shell or plate. As a consequence, the good results achieved in previous studies for overall displacements and normal stresses (parallel to the reference surface) are not missed. Moreover, no additional degrees of freedom are introduced and the continuous shear stress distribution is achieved from simple equilibrium considerations in analytical related analysis. Numerical examples are employed to demonstrate the potential of the proposed methodology comparing the achieved stress fields in various situations.