Thermomechanical analysis of functionally graded material (FGM) plates using element-free Galerkin method

A meshfree model is presented for the active shape control as well as the dynamic response repression of the functionally graded material (FGM) plate containing distributed piezoelectric sensors and actuators. The FGM plate is assumed to be made of ceramics and metals whose volume fractions vary continuously in the thickness direction according to a power law. The element-free Galerkin method is used to derive the shape functions using the moving least squares (MLS) method with C1 consistency. The weak form formulation is established based on the first-order shear deformation theory (FSDT) and variational principle accounting for thermo-electro-mechanical coupling. A constant displacement and velocity feedback control algorithm is introduced to realize the static deflection and vibration control through a closed control loop. Several numerical examples are studied. The effects of the volume fraction exponent, loading type and control gain are also discussed in detail.