Static and dynamic analysis of thick laminated plates using enriched macroelements

The development, computational implementation and application of polynomially-enriched plate macro-element are presented in this work. This macro-element has been formulated by the authors for thin isotropic plates using Gram–Schmidt orthogonal polynomials as enrichment functions and, in this work, the first-order shear deformation theory and the material anisotropy is incorporated. For taking into account plates of several geometrical shapes, an arbitrary quadrilateral laminate is mapped onto a square basic one, so that a unique macro-element can be constructed. The obtained formulation is applied to the static and dynamic analysis of thick composite laminated plates. Besides, it is possible to study generally coplanar plate assemblies by combining two or more macro-elements via a special connectivity matrix. Thus, hierarchically enriched global stiffness matrix, mass matrix, and loading vector of general laminated plate structure are derived. Several different boundary conditions may be arranged in the analysis. This procedure gives a matrix equation of static equilibrium and a matrix-eigenvalue problem that can be solved with optimum efficiency. Numerical obtained results show very good correlation with published results. Besides, the formulation produces stable results and it is computationally efficient.