On the mixed formulation of a 9-node Lagrange shell element

Abstract A 9-node Lagrange shell element is examined using a strain-based mixed method. Starting from a modified Hellinger-Reissner principle, finite element equations are derived by assuming both the displacement and strain fields independently. The strain functions are carefully chosen in conjunction with several considerations discussed in the paper. The resulting element is free from shear and membrane locking, hence it can be used for modeling of either thin or moderately thick shells. All kinematic deformation modes have been systematically suppressed. Further, a Jacobian transformation for the strain functions is employed between the natural and lamina coordinates to reduce the element sensitivity to geometric distortions. Six examples are given to illustrate the numerical performance of the proposed element.

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