Layerwise solution of free vibrations and buckling of laminated composite and sandwich plates with embedded delaminations

Layerwise plate theory of Reddy, extended for the analysis of delaminations, has served as a basis for development of enriched finite elements. The proposed model assumes layerwise linear variation of in-plane displacements and constant transverse displacement through the plate thickness. Jump discontinuities in displacement field in three orthogonal directions are incorporated using Heaviside step functions, depending on delamination position through the plate thickness. Equations of motion are derived using Hamilton’s principle. Using the proposed model laminated composite and sandwich plates were analyzed. All numerical solutions are obtained using originally coded MATLAB programs. Proposed model is verified using existing results from the literature. Results for natural frequencies, mode shapes and critical buckling loads for intact and damaged plates are compared. Effects of plate geometry, lamination scheme, degree of orthotropy and delamination size or position on dynamic characteristics of the plate are presented. Excellent agreement is obtained and a family of new results is presented as a benchmark for future investigations.