Exact geometry SaS-based solid–shell element for coupled thermoelectroelastic analysis of smart structures with temperature-dependent material properties

An exact geometry hybrid-mixed four-node laminated piezoelectric solid–shell element with temperature-dependent material properties using the sampling surfaces (SaS) method is proposed. The SaS method is based on the choice of an arbitrary number of SaS located at Chebyshev polynomial nodes inside t...

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Bibliographic Details
Published in:Acta mechanica 2023-01, Vol.234 (1), p.163-189
Main Authors: Kulikov, G. M., Plotnikova, S. V.
Format: Article
Language:English
Subjects:
Chebyshev approximation
Classical and Continuum Physics
Control
Dynamical Systems
Electric fields
Engineering
Engineering Fluid Dynamics
Engineering Thermodynamics
Exact solutions
Heat and Mass Transfer
Laminates
Material properties
Original Paper
Piezoelectricity
Polynomials
Shells
Smart structures
Solid Mechanics
Temperature
Temperature dependence
Theoretical and Applied Mechanics
Three dimensional analysis
Vibration
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Summary:An exact geometry hybrid-mixed four-node laminated piezoelectric solid–shell element with temperature-dependent material properties using the sampling surfaces (SaS) method is proposed. The SaS method is based on the choice of an arbitrary number of SaS located at Chebyshev polynomial nodes inside the layers and interfaces to introduce temperatures, displacements and electric potentials of these surfaces as fundamental shell unknowns. This choice of unknowns with the use of Lagrange polynomials in the through-thickness approximations of temperature, temperature gradient, displacements, strains, electric potential, electric field and material properties leads to a compact and effective higher-order thermopiezoelectric shell formulation with temperature-dependent material properties. The developed hybrid-mixed piezoelectric solid–shell element is based on the Hu–Washizu variational principle and three-dimensional (3D) analytical integration, which provides excellent performance for coarse meshes. It can be useful for the 3D thermoelectroelastic analysis of thick and thin laminated piezoelectric shells under thermo-electro-mechanical loading, since the SaS shell formulation makes it possible to obtain the numerical solutions with a prescribed accuracy, which asymptotically approach exact solutions of the theory of thermopiezoelectricity as the number of SaS goes to infinity.
ISSN:0001-5970
1619-6937
DOI:10.1007/s00707-021-03086-2