Stabilization by non-conforming modes : 9-node membrane element with drilling freedom

A simple technique of stabilizing spurious zero energy modes by non-conforming modes is presented. The non-conforming modes are derived by removing one or a number of nodes from the original element, and hence the associated stiffnesses are used to stabilize a uniform reduced integrated 9-node element. Three models were pursued to control the communicable spurious modes. The proposed model has been on the basis of including drilling freedoms and retaining much of the excellent performance of the original 9-node element with uniform reduced integration. The drilling freedoms are incorporated by constraining the true continuum mechanics definition of rotation at the reduced integration points by the penalty function method. A patch test was applied and a considerable number of problems were tested to investigate the performance of the new element.

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