Evaluation and verification of an HSDT-Layerwise generalized finite element formulation for adaptive piezoelectric laminated plates

A formulation for the bending analysis of composite laminated plates with piezoelectric layers is implemented using the generalized finite element method. This formulation is derived from a mechanical description based on Higher-Order Shear Deformation Theory which allows for the use of C0 continuous approximation functions on the domain. On the other hand, a Layerwise Theory is employed for interpolation of electric potential across the thickness of piezoelectric layers, in such a way that the kinematical hypotheses result in a mixed model. The paper presents an analysis of the approximation capability of the proposed numerical model for static analysis, using C0 continuous Partition of Unity and polynomial enrichments to span the approximation spaces, by assessment of convergence. Analytical solutions obtained from the same kinematical hypotheses are used as references. Results for relative error in the energy norm considering p- and h-refinements for regular and distorted meshes, in addition to a pointwise evaluation of the stresses and electric field, are presented. The evaluations show that the numerical methodology is a very effective tool for improving the solution through the enrichment, even for pointwise values across the thickness, and is robust to mesh distortions. Moreover, the results furnish insight about the physical modeling for both active and sensory modes, for thick and thin plates.