Bending and Vibration Analysis of Trigonometric Varying Functionally Graded Material via a Novel Third-Order Shear Deformation Theory

Given the significant potential of multi-directional functionally graded materials (MFGMs) for customizable performance, it is crucial to develop versatile material models to enhance design optimization in engineering applications. This paper introduces a material model for an MFGM plate described by trigonometric functions, equipped with four parameters to control diverse material distributions effectively. The bending and vibration analysis of MFGM rectangular and cutout plates is carried out utilizing isogeometric analysis, which is based on a novel third-order shear deformation theory (TSDT) to account for transverse shear deformation. The present TSDT, founded on rigorous kinematics of displacements, is demonstrated to surpass other preceding theories. It is derived from an elasticity formulation, rather than relying on the hypothesis of displacements. The effectiveness of the proposed method is verified by comparing its numerical results with those of other methods reported in the relevant literature. Numerical results indicate that the structure, boundary conditions, and gradient parameters of the MFGM plate significantly influence its deflection, stress, and vibration frequency. As the periodic parameter exceeds four, the model complexity increases, causing result fluctuations. Additionally, MFGM cutout plates, when clamped on all sides, display almost identical first four vibration frequencies.