Geometrically nonlinear and coupled thermopiezomechanical modeling and analysis of smart FGM plates and shells

Schmidt, Rüdiger; Schröder, Kai‐Uwe; Mekala, Narasimha Rao

doi:10.1201/9781315641645-68

Cited by 2 publications

(1 citation statement)

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“…These elements are typically defined by two layers of nodes on the outer surfaces of the shell with three displacement degrees of freedom (DOF) and are known as isoparametric six‐parameter piezoelectric solid‐shell elements. However, the six‐parameter solid‐shell element formulation based on the complete constitutive equations of thermopiezoelectricity 47,48 is deficient because thickness locking occurs. This is due to the fact that the linear displacement field in the thickness direction results in a constant transverse normal strain, which causes artificial stiffening of the shell element in the case of nonzero Poisson's ratios.…”

Section: Introductionmentioning

confidence: 99%

Coupled thermoelectroelastic analysis of thick and thin laminated piezoelectric structures by exact geometry solid‐shell elements based on the sampling surfaces method

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2021

Numerical Meth Engineering

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A hybrid‐mixed exact geometry four‐node thermopiezoelectric solid‐shell element through the sampling surfaces (SaS) formulation is proposed. The SaS formulation is based on the choice of an arbitrary number of SaS within layers parallel to the middle surface and located at Chebyshev polynomial nodes in order to introduce the temperatures, displacements and electric potentials of these surfaces as basic shell unknowns. Due to the variational formulation, the outer surfaces and interfaces are also included into a set of SaS. Such choice of unknowns with the use of Lagrange polynomials in the through‐thickness approximations of temperatures, temperature gradient, displacements, strains, electric potential, and electric field leads to a very compact higher‐order thermopiezoelectric shell formulation. To implement efficient analytical integration throughout the solid‐shell element, the extended assumed natural strain method is employed for all components of the temperature gradient, strain tensor, and electric field vector. The developed hybrid‐mixed four‐node thermopiezoelectric solid‐shell element is based on the Hu–Washizu variational principle and shows a superior performance in the case of coarse meshes. It can be useful for the three‐dimensional thermoelectroelastic analysis of thick and thin doubly curved laminated piezoelectric shells under thermal loading, since the SaS formulation allows one to obtain the numerical solutions with a prescribed accuracy, which asymptotically approach exact solutions of the theory of thermopiezoelectricity as a number of SaS tends to infinity.

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Section: Introductionmentioning

confidence: 99%