A simplified Kirchhoff–Love large deformation model for elastic shells and its effective isogeometric formulation

Isogeometric Kirchhoff–Love elements have received an increasing attention in geometrically nonlinear analysis of elastic shells. Nevertheless, some difficulties still remain. Among the others, the highly nonlinear expression of the strain measure, which leads to a complicated and costly computation of the discrete operators, and the existence of locking, which prevents the use of coarse meshes for slender shells and low order NURBS, are key issues that need to be addressed. In this work, exploiting the hypothesis of small membrane strains, we propose a simplified strain measure with a third order polynomial dependence on the displacement variables which allows an efficient evaluation of the discrete quantities. Numerical results show practically no difference to the original model, even for very large displacements and composite structures. Patch-wise reduced integrations are then investigated to deal with membrane locking in large deformation problems. An optimal integration scheme for third order C2 NURBS, in terms of accuracy and efficiency, is identified. Finally, the recently proposed Newton method with mixed integration points is used for the solution of the discrete nonlinear equations with a great reduction of the iterative burden with respect to the standard Newton scheme.