Piecewise shear deformation theory and finite element formulation for vibration analysis of laminated composite and sandwich plates in thermal environments

In this paper, a piecewise shear deformation theory for laminated composite and sandwich plates is presented by integrating the advantages of the layerwise theory and equivalent single layer theory. A C⁰ continuous four-noded quadrilateral isoparametric plate element based on this theory is developed for free and forced vibration analysis of laminated composite and sandwich plates in thermal environments. The accuracy and effectiveness of piecewise shear deformation theory and finite element formulation are validated by comparing the numerical results obtained by the present finite element formulation with the analytical and exact results available in literatures as well as the numerical results computed by MSC.Nastran software. It is demonstrated that the piecewise shear deformation theory and finite element formulation are suitable for the vibration analysis of thin and thick laminated composite and sandwich plates. As compared with the layerwise theory, high-order zigzag theory and high-order equivalent single layer theory, the piecewise shear deformation theory is able to produce a sufficiently accurate result at a very low computational cost. The work reported in this paper provides an efficient modeling approach for thermal vibration analysis of laminated composite and sandwich plates in practical engineering.