and too much constraints deliver bad results. An a-priory estimation of the optimal distribution and number of subareas cannot be given yet. Figure 3: Contour plot of relative errors of mode based computation with respect to reference computation Figure 4 contains on the left hand side an exemplarily gap distribution with 20 considered JIM and 64 subareas (=constraints). On the right hand side the distribution of the absolute error with respect to the reference computation, depicted in figure 2, is given. Note, that even the difference in the gap distribution is small, a lot of DOF could have been saved. The reference computation needed 1025 nodal DOF and 512 non penetration constraints which are, in fact, a kind of internal DOF for the quadratic programming problem. The modal based computation, on the other hand, needed 35 modal DOF and 64 constraint equations which is much less. The difference in the CPU time for the ‘qpsolve’ routine of Scilab was about a factor of 113 which was measured with the ‘timer’ routine of Scilab. 5. Conclusion It has been shown that computational contact mechanics based on non penetration constraints in the framework of modal analysis is not straight forward as it would be when a penalty approach is used. In this contribution non penetration constraints based on subareas instead of FE nodes, is discussed. It has been shown that accurate displacement results can be obtained even if the considered number of DOF and constraint equations is significantly smaller as by the node based FEM. An obvious drawback of the presented method is the absence of an a-priory estimation of an optimal distribution of subareas with respect to selected mode base. Even the approach was very intuitive, it indicates a potential for future work to save a lot of computational effort for joint contact computations with non penetration constraints in the framework of modally reduced systems. 34
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