Finite element model of smart beams with distributed piezoelectric actuators

In the present work, the static and the dynamic analysis of intelligent advanced beams structures with piezoelectric actuators have been studied. The structure substrate is made of isotropic and/or anisotropic materials, subjected to axial and transverse mechanical loads as well as electrical load. The actuators layers are made of piezoelectric material of PZT type. The model is able to solve the structure with piezoelectric actuators either patches or completely covers the structure; in the upper or lower surface or impeded in the structure. The classical laminate theory is used to represent the deformation of the lamination for each considered structure. The ID isoperimetric Hermit cubic shape functions and the Lagrange interpolation functions are used to formulate the finite element model for the distributed coupled electromechanical behavior. The equations of motion of each structure system is obtained by using the principle of total potential energy considering the Euler-Bernoulli beam assumptions. A Matlab code is prepared to perform the analysis of such beams. The results of the proposed finite element model for each structure are compared to the available finite element and analytical results of other investigators, good agreement is generally obtained.