Abstract
A new formulation of membrane elements with drilling degrees of freedom is presented. The Lagrange multiplier method is employed to obtain the modified functional. Since the independent rotational field is used, the present formulation is applicable to any shape of elements. The resulting stiffness matrix has negative diagonals associated with drilling rotations. This deficiency is remedied by introducing a positive parameter. It is shown that the numerical results are not affected by the value of the parameter. The present element has no zero-energy mode, and no locking phenomena are observed. Numerical results demonstrate an excellent performance of the membrane elements with drilling rotations.
