Convergence of curved shell elements based on assumed covariant strain interpolations

Abstract

Abstract A C 0 9‐node shell element based on assumed interpolations of covariant strain components defined with respect to the element natural co‐ordinate system has recently been proposed. In this formulation, the covariant strains are obtained directly from the Cartesian strains by tensor transformation without any need to compute laminar co‐ordinate based strains. In the present work, the interpolated covariant strains used in this element are analysed to determine their satisfaction of the basic requirements for successful strain interpolation. These basic requirements are stated as invariance to rigid body motions and ability to represent constant and linear strain states. In the finite element formulation, the weak form of momentum balance is expressed in terms of covariant strains and contravariant stresses. The corresponding elasticity tensor is a function of the components of the metric tensor associated with the element natural co‐ordinate system. The invariance properties of the metric tensor in the context of the finite element approximation are also discussed.