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SUMMARYA uniÿed 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 modiÿcation 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 modiÿcation 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 modiÿcation 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.

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In this study, a new dynamic interaction analysis method for tilting trains and curved track is presented. Three dimensional lumped parameter vehicle elements are used to model tilting train, and the proposed analysis technique can simulate driving direction change of vehicle, the effect of track cant, wheel-rail contact angle, and tilting angle of tilting trains, etc. The proposed method passed several basic verification tests, and it is expected that the suggested method is applicable for practical problems.

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