Modeling the Deformation of a Plate Using Piezoelectric Elements Located on its Surface

Abstract

One of the directions of using piezoelectric elements in modern technology is related to their use for controlling the shape of a structure under the influence of operational loads. The issue of a change in the shape (geometry) of a structure can be caused, for example, by the need for minimization of displacements in certain regions or, vice versa, for maximization of displacements to ensure the stability of a structural shape under operational loads. Due to the presence of the inverse piezoelectric effect in piezoelectric materials, this problem can be solved by applying a predetermined electric voltage to the electroded surfaces of piezoelectric elements. Elastic structures with elastic piezoelectric elements attached to their surfaces become electroelastic. It is necessary to first assess the abilities of piezoelectric elements to have an effect on deformations caused by external actions of different types in order to use different strategies of control over their mechanical behavior. This means that piezoelectric elements must provide a controlled form change depending not only on the characteristics of the elements themselves (the size, physico-mechanical properties of the material, and position) but also on the parameters of the structure (its geometry, size, boundary conditions, and physico-mechanical characteristics) and acting loads. The influences of different factors on the deformation of an electroelastic structure under the action of an electric voltage applied to the piezoelectric elements in this work was established numerically based on mathematical modeling by solving the static problem of electroelasticity. The numerical implementation was carried out by the finite-element method in the ANSYS software package. The possibilities for using piezoelectric elements for changing the shape of a structure for different numbers of elements and different options of their layout on the surface are demonstrated based on the example of a cantilevered fixed plate.