Derivation of a linearly elastic elliptic membrane shell theory in the framework of magnetoelasticity

Abstract

Starting from a three-dimensional model of linearized magnetoelasticity, we investigate the asymptotic behavior of a thin shell as its thickness approaches zero. Our analysis focuses on a family of linearly elastic elliptic membrane shells. Using $\Gamma$-convergence, we rigorously derive a two-dimensional linear magnetoelastic shell model and establish its relationship to the original three-dimensional model in terms of the convergence of minimizers.