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Smart Structures and Systems Volume 18, Number 1, July 2016 , pages 155-181 DOI: https://doi.org/10.12989/sss.2016.18.1.155 |
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Nonlinear modelling and analysis of thin piezoelectric plates: Buckling and post-buckling behaviour |
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Michael Krommer, Yury Vetyukov and Elisabeth Staudigl
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| Abstract | ||
| In the present paper we discuss the stability and the post-buckling behaviour of thin piezoelastic plates. The first part of the paper is concerned with the modelling of such plates. We discuss the constitutive modelling, starting with the three-dimensional constitutive relations within Voigt\'s linearized theory of piezoelasticity. Assuming a plane state of stress and a linear distribution of the strains with respect to the thickness of the thin plate, two-dimensional constitutive relations are obtained. The specific form of the linear thickness distribution of the strain is first derived within a fully geometrically nonlinear formulation, for which a Finite Element implementation is introduced. Then, a simplified theory based on the von Karman and Tsien kinematic assumption and the Berger approximation is introduced for simply supported plates with polygonal planform. The governing equations of this theory are solved using a Galerkin procedure and cast into a non-dimensional formulation. In the second part of the paper we discuss the stability and the post-buckling behaviour for single term and multi term solutions of the non-dimensional equations. Finally, numerical results are presented using the Finite Element implementation for the fully geometrically nonlinear theory. The results from the simplified von Karman and Tsien theory are then verified by a comparison with the numerical solutions. | ||
| Key Words | ||
| piezoelastic plates; geometrical nonlinearity; buckling and post-buckling behaviour; nonlinear Finite Elements | ||
| Address | ||
| Michael Krommer, Yury Vetyukov and Elisabeth Staudigl: Institute of Mechanics and Mechatronics, Vienna University of Technology,Getreidemarkt 9, A-1060 Vienna, Austria | ||