Assumed strain stabilization procedure for the 9-node Lagrange shell element

An assumed strain (strain interpolation) method is used to construct a stabilization matrix for the 9-node shell element. The stabilization procedure can be justified based on the Hellinger–Reissner variational method. It involves a projection vector which is orthogonal to both linear and quadratic fields in the local co-ordinate system of each quadrature point. All terms in the development involve 2 × 2 quadrature in the 9-node element. Example problems show good accuracy and an almost optimal rate of convergence.

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