A positional FEM approach for free vibrations of orthotropic laminated shells

Resumo

This paper presents a positional formulation of the Finite Element Method (FEM) for free vibration analysis of laminated shells with cross-ply and angle-ply fibers. The starting point of this formulation is the use of positions and generalized vectors as degrees of freedom, i.e., three coordinates and three vector components per node in the 3D space. The formulation is more general than Reissner-Mindlin by introducing an additional parameter which allows linear deformation in the three directions, avoiding locking effects. The material layers are orthotropic according to the Saint-Venant Kirchhoff law, in which the constitutive tensor regarding the shell reference axes is obtained with a second-order tensor transformation matrix. The numerical solution uses Hammer quadrature on the shell reference surface and Gauss-Legendre to integrate along the thickness, while the free vibration problem is solved as a standard eigenvalue and eigenvector problem. Two examples are discussed. The results are compared with papers in the open literature, which demonstrates good accuracy and efficiency of the present formulation.