Free-vibration analysis of thin/thick laminated structures by layer-wise shell models

The objective of this contribution is the free-vibration analysis of thick/thin shell structures by means of finite element (FE) models permitting the consideration of arbitrary complex through thickness distribution of transversal shear deformations as well as thickness stretching in any desired accuracy order and presenting therefore an alternative to 3D FE formulation. The development basis is a refined shell kinematics, where the displacement field is approximated by a quadratic polynomial. Numerically attractive aspect of this approach is the multiplicative decomposition of the first-order term and inclusion of a quadratic stretching parameter. This formulation is then extended to a layer-wise model to develop in a further step, an isoparametric four-node element by means of assumed strain concept. A large number of examples are investigated, showing the performance of the element proposed particularly in dealing with thick structures. The influence of transverse strains on the response is also discussed by adequate examples.