Nonlinear modelling and analysis of thin piezoelectric plates: Buckling and post-buckling behaviour

• Journal title : Smart Structures and Systems
• Volume 18, Issue 1,  2016, pp.155-181
• Publisher : Techno-Press
• DOI : 10.12989/sss.2016.18.1.155
Title & Authors
Nonlinear modelling and analysis of thin piezoelectric plates: Buckling and post-buckling behaviour
Krommer, Michael; Vetyukova, Yury; Staudigl, Elisabeth;
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.
Keywords
piezoelastic plates;geometrical nonlinearity;buckling and post-buckling behaviour;nonlinear Finite Elements;
Language
English
Cited by
1.
Hybrid asymptotic–direct approach to finite deformations of electromechanically coupled piezoelectric shells, Acta Mechanica, 2017
2.
Finite deformations of thin plates made of dielectric elastomers: Modeling, numerics, and stability, Journal of Intelligent Material Systems and Structures, 2017, 1045389X1773305
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