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

• 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
• ISSN: 0001-5970; 1619-6937
• DOI: 10.1007/s00707-021-03086-2

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.