Kirchoff-Love Magnetoelastic Shells #

Abhishek Ghosh, Andrew McBride, Zhaowei Liu, Luca Heltai, Paul Steinmann, Prashant Saxena

11:30 Wednesday in 4Q08.

Part of the Filaments, membranes, and shells session.

Abstract #

Magnetoelastic shells are thin, lightweight structures capable of elastic deformation and magnetic responses. They are made of materials that exhibit magnetic and mechanical properties. The Kirchoff-Love shell equations are obtained for magnetoelastostatics using the derived-theory. We start with a variational form involving mechanical deformation, an independent variable representing the magnetic component (the magnetic field vector), and the indeterminate pressure due to the incompressibility constraint in the body along with the presence of body force, dead-load tractions, external pressures, and external magnetic field. The magnetostatic energy is restricted to finite volumes in Euclidean space, and the deformation map in the body is differentiated from that in the surrounding space throughout the motion in the present analysis. Moreover, the shell is considered hyperelastic implying the existence of a through-thickness stretch due to the incompressibility during deformation. As a three-dimensional body, the shell is visualized as a stack of surfaces, and thereby, the general deformation map in the body is further restated concerning a point on the deformed mid-surface with an additional term involving the through-thickness stretch and the deformed normal. This presents complex and interesting situations while deriving the strong-form equations from the first variation of the total potential energy of the system, and the present work provides an appropriate and unique overview in this regard.