Direct modification for non-conforming elements with drilling DOF

A uni ed approach to eliminate the undesirable lockings in distorted meshes for both non-conforming quadrilateral membrane and hexahedral elements with drilling (or rotational) degrees of freedom is presented. The direct modi cation scheme is utilized in the formulation of non-conforming modes to improve the general behaviour of isoparametric-based elements. It is shown that the direct modi cation is very e ective in eliminating the locking and this improvement of element behaviour may be doubled if the selective integration scheme is used simultaneously. To verify the validity of elements formulated by the proposed schemes and to evaluate their e ectiveness, several numerical tests are carried out. The combined use of additional non-conforming modes with the direct modi cation method and the selective integration technique plays an important role to improve the behaviour of elements, especially for distorted mesh cases. Test results also show that the results for both non-conforming quadrilateral membrane and hexahedral elements obtained by the proposed schemes are equally satisfactory