Generalized viscoelastic model for laminated beams using hierarchical finite elements

The formulation of an enriched hierarchical one-dimensional finite element suitable to analyze the rheological behavior of thick arbitrarily laminated beams is presented. The formulation is based on the Equivalent Single Layer (ESL) theory and was developed to allow the use of any high-order beam shear deformation theory (HBST) in a unified approach. A generalized Maxwell model was implemented to analyze the time-dependent behavior of the composite. The finite element employs local Lagrange and Hermitian support functions enriched with orthogonal Gram-Schmidt polynomials and is free of shear locking. The enriched macro elements can be used with very coarse meshes and the precision can be controlled without generating a new mesh. The formulation has been validated with numerical examples of symmetric and non-symmetric laminated beams using the three-dimensional finite element program PLCD.