Three dimensional numerical solution for the bending study of magneto-piezo-elastic spherical and cylindrical shells

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Arce M.
Bustamante D.E.
Calderon M.S.
Leiva S.
Mendoza J.E.
Oliva M.
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Elsevier Ltd
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This paper presents an exact solution for the static analysis of magneto-electro-elastic simply supported shallow shells panels. The mechanical equations are derived via equilibrium elasticity relations. The electrical and magnetic governing equations are obtained by electrostatic and magnetostatic equilibrium relations. The shell displacements, electrical and magnetic potential functions are solved analytically by the Navier closed form solutions. The governing equations formulated in terms of thickness coordinate are solved semi-analytically by using the differential quadrature method. The Lagrange polynomials are employed as basis functions. The equations are discretized per each layer by the Chebyshev-Gauss-Lobatto grid distribution. The continuity conditions in the adjacent layers for mechanical displacement, transverse dielectric displacement, electric and magnetic scalar function and transverse magnetic induction are complied. The correct load traction condition is considered at the top and bottom of the shell. Numerical results for spherical, cylindrical and rectangular panels are reported. The results are in excellent agreement with other 3D elasticity solutions reported in the literature so a new benchmark problem for shell is proposed. © 2021 Elsevier Ltd
This paper was written in the context of the project: “Desarrollo de materiales avanzados para el diseño de nuevos productos y servicios tecnológicos para la minería Peruana” founded by CONCYTEC (FONDECYT and GRUPO BANCO MUNDIAL) under the contract number N° 032-2019-FONDECYT-BM-INC.INV. The authors of this manuscript appreciate the financial support from the Peruvian Government.
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Three-dimensional solutions