GDQ computation for thermal vibration of thick FGM plates by using third-order shear deformation theory

The third-order shear deformation theory (TSDT) effects on the thick functionally graded material (FGM) plates under thermal vibration are investigated by using the generalized differential quadrature (GDQ) method. The nonlinear coefficient term of displacement field of TSDT is used to derive the equations of motion for thermal vibration of thick FGM plates. The simpler form stiffness of FGM plates under linear temperature rise is considered in the thermo-elastic stress-strain relations. The dynamic equilibrium differential equations of FGM plates in terms of partial derivatives of displacements and shear rotations subjected to partial derivatives of thermal loads, mechanical loads and inertia terms are derived. Two parametric: environment temperature and FGM power law index effects on the thermal stress and center deflection of FGM thick plates are investigated.

Automated summary

The effects of the third-order shear deformation theory (TSDT) on thick functionally graded material (FGM) plates under thermal vibration are investigated using the generalized differential quadrature (GDQ) method. The equations of motion for thermal vibration of thick FGM plates are derived using the nonlinear coefficient term of the displacement field of TSDT. The dynamic equilibrium differential equations of FGM plates, considering the simplified stiffness under linear temperature rise, are derived in terms of partial derivatives of displacements, shear rotations, thermal loads, mechanical loads, and inertia terms. The effects of two parameters, environment temperature and FGM power law index, on the thermal stress and center deflection of FGM thick plates are investigated.