Analysis of functionally graded piezoelectric Timoshenko smart beams using a multiquadric radial basis function method

In the present work, a global interpolation scheme is proposed to describe the electro-mechanical static response of piezoelectric smart beams considering applied mechanical loads and electric potential. First, bimorph and three-layered Timoshenko smart beams are investigated and the model is validated for both actuator and sensor capabilities. Lastly, a functionally graded piezoelectric (FGP) bimorph beam is studied in its actuator configuration. The governing equations of motion are derived by the application of Hamilton's principle considering an equivalent-single-layer first-order-shear-deformation theory (ESL-FSDT) with layerwise electric potential. The equations are subsequently solved using a grid free method based on Kansa's asymmetric collocation using multiquadric radial basis functions (RBFs). The method relies on the Euclidean distance between nodes and on a shape parameter which must be warily selected to avoid matrix ill-conditioning. Accurate results are obtained while maintaining a very low computational cost.