Notice of RetractionAnalysis of an orthotropic adaptive shallow spherical shell on elastic foundation

Notice of Retraction

After careful and considered review of the content of this paper by a duly constituted expert committee, this paper has been found to be in violation of IEEE´s Publication Principles.

We hereby retract the content of this paper. Reasonable effort should be made to remove all past references to this paper.

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The aim of this paper is to explore the usefulness and economical applicability of piezoelectric layer on shallow spherical shell. Since the adaptive materials are a class of smart materials, and with growth and emergence in the field of adaptive materials, the need arises to study their applications in the field of structural, aerodynamic, aerospace and other fields. These materials can be used as sensors, transducers and actuators. Although their basic constitutive relations are already developed, but there is still a great deal of scope left in the field of applications. With this aim, a nonlinear static analysis of orthotropic piezoelectric shallow spherical shell on Pasternak foundation is investigated in the present work. The methodology and basic formulation of the problem is based on the Von-Karman nonlinear strain displacement relations and strain energy concept. Use of the principle of the minimum potential has been made in the analysis. The governing differential equations are obtained by using Euler´s variational principle. Galerkin error minimization technique has been used to solve the governing differential equations. The results are presented for simply supported immovable edge boundary condition. Influences of shell geometry, foundation parameter, and piezoelectric properties on load-deflection characteristics for different radius-to-thickness ratios are studied. Numerical results have been obtained for different values of geometrical parameters in terms of load and displacement. Geometrical par- meters are represented through non-dimensional entities η = R²/R₀h, λ = KR⁴/D₁, and μ = GR²/D₁. The results are compared with nonlinear static analysis of an orthotropic shallow spherical shell without piezoelectric layer on Pasternak foundation. It is observed that an increase in the value of piezoelectric constant and other parameters decreases the deflection of the- shallow spherical shell under the identical values. Hence, it is concluded that the application of piezoelectric layer on the shallow spherical shell will be useful, but with little economy.