Trigonometric series solution for analysis of composite laminated plates

Koç, Samet
In this study, static bending and free vibrations of symmetric rectangular laminated composite plates are examined by using a new trigonometric series expansion technique and finite element analysis. Kirchhoff (Classical Laminated Plate) plate theory is applied in the analytical formulation of both bending and free vibration problems. Mid-plane displacement is expanded into a series of trigonometric shape functions, which allow exact satisfaction of the boundary conditions. In the case of static bending, application of the Rayleigh-Ritz method leads to a linear system for the coefficients of the trigonometric series. For free vibrations, minimization of the energy functional in conjunction with the Rayleigh-Ritz approach results in an eigenvalue problem. Finite element models for both bending and free vibrations are constructed by means of plate elements that incorporate first-order shear deformation theory. Numerical results are generated for simply-supported and fully-clamped composite plates as well as for a composite plate with a single free and three clamped edges. The trigonometric series technique developed is verified by comparisons to the outcomes of the finite element analyses. Presented numerical results illustrate the effects of geometrical parameters, boundary conditions, and composite plate stacking sequence on deflection, transverse stresses, natural frequencies, and mode shapes. The proposed method leads to rapid convergence, possesses computational efficiency, and could be useful in design and optimization studies involving laminated composite structures.


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Citation Formats
S. Koç, “Trigonometric series solution for analysis of composite laminated plates,” M.S. - Master of Science, Middle East Technical University, 2023.