Finite Element Method applied to the single-layer equivalent theory for laminated beams

Resumo

Over the last decades, laminated beams have been widely used as a structural element in
several areas of knowledge, such as in civil, naval, mechanical and aeronautical engineering. Having
advanced the knowledge and development of composite materials, theoretical modeling to describe the
mechanical behavior of laminated beams has become of great importance. Among the various theories,
we have the refined (or high order) theories that have emerged to heal the limitations present in classical
theories. This limitation is represented by the failure to consider the shear strain field or by incorrect
consideration of such deformations, without respecting the nullity of the shear stress at the edges of the
beam. Thus, the present work seeks to present the development of a finite element model applied to the
Equivalent Layer (ESL) theories for laminated beams. Therefore, a unified displacement field will be
used that allows the simultaneous development and comparison of several refined theories found in the
literature. After obtaining the governing equations, the finite element model is constructed using the
Hermite and Lagrange polynomial functions. Finally, to show the good efficiency of the theories and
the finite element model, numerical results for static and dynamics analysis are shown and compared
with the exact solution of the elasticity.