Polynomial Stress Functions for Piezoelectric Problems and Their Application in ATF Method

Abstract eng:
In this paper, the analytical trial fimction method for the 8-node hybrid element (ATF-Q8) is generalized to piezoelectric plane problems. Based on generalized Lekhnitskii’s formalism, systematic schemes are given to determine all the n—th independent polynomial stress functions for piezoelectric problems, and the results can be degenerated to the case of anisotropic problem and isotropic problem. Complete polynomial stress fimctions are introduced as the trial fimctions of the generalized ATF method for analysis of piezoelectric problems. Unlike the isotropic case, the trail polynomials are related to the material constants. In the end, the new explicit polynomial stress fimctions are implemented in the ATF-Q8 element method to solve some numerical cases to test the accuracy of this approach.

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