An isogeometric framework for thermally induced vibration of skew FGM plates on Winkler–Pasternak foundations

Abstract

This paper presents an isogeometric analysis (IGA) framework for the thermally induced vibration of skew functionally graded material (FGM) plates resting on a two-parameter (Winkler–Pasternak) elastic foundation, with temperature-dependent properties. The plate kinematics are described by the third-order shear deformation theory (TSDT). Material properties vary continuously through the thickness by a power law and depend on the local temperature. The nonlinear one-dimensional transient heat conduction equation through the thickness is solved using the finite difference method coupled with the Crank–Nicolson scheme, and the resulting temperature history is mapped onto the mechanical model at each time step. NURBS-based IGA is used to discretize the skew plate domain and satisfy the higher-order continuity required by TSDT, and the coupled thermo-mechanical equations of motion are integrated in time using the Newmark method. Numerical examples validate the proposed formulation against benchmark solutions, and parametric studies examine the effects of skew angle, power-law index, foundation parameters, and thermal boundary conditions on the transient thermally induced vibration response of skew FGM plates.