On Geometrically Non-Linear Theories for Thin Elastic Shells

Abstract

The present paper deals with geometrically non-linear first approximation Kirchhoff-Love type theories for thin elastic shells undergoing small strains accompanied by moderate, large or unrestricted rotations. All theories will be given in an entirely Lagrangian description. We shall start our considerations with a general theory valid for small strains and arbitrary, unrestricted rotations. Then, this general theory will be simplified for shell problems in which the shell material elements undergo large rotations according to the classification scheme given below. Three variants will be derived which admit large rotations about tangents to the shell middle surface and either large, moderate or small rotations about the normal. Finally, the general shell equations will be simplified for shells undergoing moderate rotations about tangents to the shell middle surface and either moderate or small rotations about the normal. All theories presented here are derivable from variational principles.