Multi-variable Method For Three Demensional Contact/Impact Dynamics And Research On Contact Model

In the engineering field, there are a lot of discontinuous dynamicsproblems such as contact/impact between flexible bodies. Flexiblemulti-body contact/impact dynamics has always been plagued by twoproblems: one is how to ensure the accuracy of contact position andimprove the efficiency of the global simulation at the same time, thisrelates to what kinematics variables are used to describe the flexiblebodies; the other is the two typical contact models——appendedconstraint method and penalty function method, they treat contact asconstraint and force element respectively, in the numerical simulationwhich model is better? In this paper the problem of3-D contact dynamicsis studied and multi-variable method (MVM) is used to describe flexiblebody with both modal coordinates and nodal coordinates, so bothsimulation accuracy and efficiency are considered. The problem ofvariable selection of MVM is studied leading to the maximum reduction of degrees of freedom. The last is the comparative study on the simulationdifferences between the appended contact constraint method (ACCM) andpenalty function method under the effect of different factors. The concreteresearch contents are as follows:The first part studies the MVM on3-D contact/impact problem.Based on the appended contact constraint method, the dynamics equationof flexible multi-body discretized by3-D solid element is derived.3-Dcontact problems are much more complex than the2-D ones, includingaspects such as the finite element modeling, the contact constraintequation and contact detection. Then the MVM is extended to3-Dcontact/impact problem, and through some numerical examples, MVM iscompared with complete finite element method (FEM), the softwareLs-Dyna and the experiment, and the results show both the accuracy andefficiency of MVM.The second part is the study on variable selection problem of MVM.The center thought of MVM lies in that the body is divided to regionsdescribed by different coordinates, to reduce the degrees of freedom of thesystem Obviously, how to divide the contact region and non-contactregion directly determines the degrees of freedom of system, that is to sayhow many nodes are used to describe the contact region and how many modes are applied to the non-contact region, and at the same time theaccuracy is guaranteed. But the current variable selection methods rely onartificial and random regulation. Based on the experimental example oflongitudinal contact between two rods, the influences on result accuracy ofnode position, modal orders and material parameter are studied, theoptimal multi-variable selection is realized which reduces the DOFs to themaximum extent and also achieves accuracy in the same time.The third part is a comparative research on the appended constraintmethod and the penalty function method. The penalty function methoduses penetration depth and velocity as parameters to calculate the contactforce, which depends on the penalty factor. However, the appendedconstraint method accords with the actual physical contact without mutualpenetration, and there is no need to set any parameters. We find that theresults of penalty function method rely on factors such as the penaltyfactor, the impact velocity, but the appended constraint method is hardlyaffected by these factors.