Equations of motion for growing shells

摘要

The theory of elastic shells growing in the transverse direction is considered. Growing shells are treated as a special case of growing solids, i.e., inhomogeneous laminated bodies whose inhomogeneity is due to the junction of incompatible deformed parts. The constitutive equations and equations of motion are obtained. It is proposed to supplement the statement of the boundary value problem with an equation for the implant field. A geometric interpretation of the implant field as the generator of a non-Euclidean material connection is given.