Nonlinear aerodynamic analysis of functional graded plates using an HSDT-based isogeometric approach

Abstract

In this paper, a nonlinear FGM plate analysis model is presented based on IGA, which suppresses shear locking and is applicable to plates with a wide range of thickness-to-length ratios. Furthermore, the nonlinear aerodynamic characteristics of FGM plate subjected to the combined effect of transverse load, in-plane load, and supersonic flow are investigated. HSDT is used to construct a displacement field suitable for nonlinear vibration analysis of FGM plates with a wide range of thickness-to-length ratios. For the problem that shear locking cannot be avoided entirely in the nonlinear analysis of plates, the first derivative of transverse displacement is adopted as the first term of HSDT, which weakens the effect of shear strain. Therefore, the shear locking is effectively restrained. The nonlinear FGM plate analysis model is derived using NURBS, which meets the C1 continuity requirement of HSDT. The computational efficiency, accuracy and the suppressing capacity to shear locking are verified in three aspects: static displacement, eigenfrequency, and nonlinear frequency ratio. The Bathe method is used to obtain the displacement response of an FGM plate subjected to supersonic flow, in-plane load, and transverse load. The dynamic characteristics of the FGM plate are studied using time history, bifurcation diagrams, PSD curves, phase diagrams, and Poincaré maps.