The Sublaminate Generalized Unified Formulation (SGUF) is a variable kinematics plate modeling approach and is here extended to composite plates including piezoelectric plies. The two-dimensional plate equations are obtained upon defining a priori the through-thickness distribution of the generalized displacements, i.e., the displacement field and the electric potential. According to SGUF, independent approximations can be adopted for the four components of the generalized displacements, which encompass: an Equivalent Single Layer (ESL) or Layer- Wise (LW) description over an arbitrary group of physical plies constituting the composite plate (the sublaminate) and the polynomial order that is employed in each sublaminate. The solution of the two-dimensional piezoelectric plate equations is subsequently sought in weak form by means of a Ritz method. Boundary functions are thus used in conjunction with the domain approximation, whose orthogonal basis may be spanned by trigonometric functions, Chebyshev polynomials or Legendre polynomials. Free-vibration problems as well as static problems involving actuator and sensor configurations are addressed. Three validation case studies are first presented, which demonstrate the high accuracy of the proposed Ritz method in conjunction with high order models. A model assessment is then proposed for showcasing to which extent the flexible SGUF approach allows a reduction of the number of unknowns with a controlled impact on the accuracy of the response.

Extension to Piezoelectric Plates of the Ritz Sublaminate Generalized Unified Formulation Approach

DOZIO, LORENZO;VESCOVINI, RICCARDO;
2017-01-01

Abstract

The Sublaminate Generalized Unified Formulation (SGUF) is a variable kinematics plate modeling approach and is here extended to composite plates including piezoelectric plies. The two-dimensional plate equations are obtained upon defining a priori the through-thickness distribution of the generalized displacements, i.e., the displacement field and the electric potential. According to SGUF, independent approximations can be adopted for the four components of the generalized displacements, which encompass: an Equivalent Single Layer (ESL) or Layer- Wise (LW) description over an arbitrary group of physical plies constituting the composite plate (the sublaminate) and the polynomial order that is employed in each sublaminate. The solution of the two-dimensional piezoelectric plate equations is subsequently sought in weak form by means of a Ritz method. Boundary functions are thus used in conjunction with the domain approximation, whose orthogonal basis may be spanned by trigonometric functions, Chebyshev polynomials or Legendre polynomials. Free-vibration problems as well as static problems involving actuator and sensor configurations are addressed. Three validation case studies are first presented, which demonstrate the high accuracy of the proposed Ritz method in conjunction with high order models. A model assessment is then proposed for showcasing to which extent the flexible SGUF approach allows a reduction of the number of unknowns with a controlled impact on the accuracy of the response.
2017
SMART 2017
978-84-946909-3-8
Piezoelectric Composites, Variable Kinematics Model, Ritz Method, Unified Formulation
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1028067
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