Iterative Approach for Predicting Free Edge Stresses in Piezoelectric Laminates Upon Polynomial Assumption

This paper presents a stress function based iterative approach for predicting the free edge stresses in piezoelectric laminates upon polynomial assumption. The polynomial stress function based iterative approach is quite different from the traditional plate and shell theories, where the polynomial stress fields are adopted instead of displacement field functions. The stress boundary conditions are prescribed at the surfaces and applied at the free edges so that the stress components satisfy the boundary conditions automatically. The complementary virtual work is adopted to derive the governing equations resulting in a set of fourth order coupled differential equations. Some results are given to study the efficiency and accuracy of the proposed methodology. The proposed approach can be used as an efficient tool for analysis of free edge stresses in piezoelectric composite structures.