Polar Decomposition and Finite Rotation Vector in First — Order Finite Elastic Strain Shell Theory

Abstract

While large strain membrane theories are well established in literature since more than three decades, there exist considerably less papers which deal with large elastic strain shell theory incorporating also the bending effects into the nonlinear analysis. Recently, however, this topic has gained considerable interest. Important contributions have been given by CHERNYKH [1,2] , LIBAI and SIMMONDS [5,6] , and SIMMONDS [20] , where also additional references on related works may be found. The aforementioned authors agree that such a theory should be based on a refined Kirchhoff-Love type model which admits at least changes in shell thickness. Due to bending this thickness change is in general asymmetric about the undeformed midsurface so that its deformed configuration is no longer the geometrical midsurface of the deformed shell. This requires a representation of the position vector of the deformed shell space which incorporates at least quadratic terms with respect to the thickness coordinate.