The exact theory of piezoelectric beams

Without requirement of any ad hoc assumptions concerning the deformation or the stress state, various equations and solutions for piezoelectric beams are deduced systematically. A method for the exact solution of two-dimensional equations is presented under non-homogeneous boundary conditions. The equations and solutions are used to construct the exact theory of deep beams for symmetrical deformation. With this method, the exact theory can now be explicitly established from the general solution of piezoelectricity and the Lur´e method. In an illustrative example of piezoelectric beams, it is shown that explicit expressions of analytical solutions can be obtained by using the exact theory.