Nonlinear static analysis of orthotropic piezoelectric shallow cylindrical shell on elastic foundation

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 cylindrical shell on Pasternak foundation is investigated in the present work. Basic formulation of the problem is based on strain energy concept, and 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, displacement, and electric potential. Geometrical parameters are represented through non-dimensional entities η=a²/Rh, λ = Ka⁴/D₁₁, and μ̄ = Ga²/D₁₁. The results are compared with nonlinear static analysis of an orthotropic shallow cylindrical shell without piezoelectric layer on Pasternak foundation. It is observed that an increase in the value of piezoelectric constant decreases the deflection of the shallow cylindrical shell under the identical values.