A new meshless method based on 2D-EFG for the analysis of piezoelectric laminated Timoshenko beam

Piezoelectric laminated beams are common piezoelectric structure. It has been applied in many fields, such as the driving element of the bimorph and unimorph piezoelectric actuators bending. For static and dynamic, linear and nonlinear, analytical method and numerical method, the mechanical behaviors of this structure (including bending, vibration, buckling and control, etc.) have very comprehensive research. In these studies, most of the research is to use of laminated beam theory simplified into 1D control equation. However, this paper will adopt a new approximate method based on 2D element free Galerkin (2D-EFG) for the numerical simulation of piezoelectric laminated Timoshenko beam bending. This new meshless method can overcome the material discontinuity between layer and thickness lock phenomenon. This new method is suitable for thin beam and thick beam. It can be generalized to the numerical calculation of laminated curved beam, laminated plate and shell structures. Numerical examples verify the validity and precision of the proposed method.