Thermal vibration of stiffened FGM plates with cutouts using Nitsche-based isogeometric approach

Abstract

Based on the integration of first-order shear deformation concept and the principle of Timoshenko’s beam theory, we develop an isogeometric analysis (IGA) framework for the study of free vibration characteristics in stiffened functionally graded material (FGM) plates, both with and without stiffeners and cutouts, under three typical thermal loads. The framework introduces a physical neutral surface for a precise description of the material properties of FGM plate along the thickness direction. Initially, the stiffened FGM plates with or without cutouts, are modeled employing non-overlapping NURBS patches. The stiffeners are strategically positioned along the shared boundaries of neighboring patches, utilizing the identical control points that define these boundaries. Subsequently, the distinct patches are seamlessly integrated through the Nitsche method. Initially, the convergence of the proposed methodology is verified by the rectangular FGM plate without any stiffener and cutout under uniform temperature field. Consequently, we present an in-depth analysis of the free vibration of rectangular, skew, and elliptical FGM plates, exploring the effects of the stiffener orientation, the number and shape of cutouts, the boundary conditions of the plates, the gradient factor, temperature rise, and the type of thermal load on the free vibration characteristics. Through comparative analysis, the computed results are highly consistent with the data in existing literature, further validating the robustness of the proposed method.