| Contact-impact dynamics is a main research topic in the area of aeronautics,astronautics and mechanical engineering.In the multibody dynamics considering contact-impact,the frequently changed topology of system,the strong impact acting on the local region in short time and the elastic wave propagation of high frequency bring big challenges to the dynamic modelling and the numerical solution of the system.Considering the large overall motions of the system,the methods to describe the contact-impact behavior in fast time scale as well as the efficient modelling of the system become the major issues in engineering.For this point,this dissertation presents the following research work for the dynamic problems of the flexible multibody systems with contact-impact:Firstly,a multi-variable dynamic model for the flexible multibody systems considering contact-impact is presented based on the idea of the component mode synthesis method and the sub-regional modelling method.In many engineering problems,the contact-impact always takes place in the fixed positions.With the consideration of ensuring the accuracy of the impact force as well as the dynamic response and improving the efficiency of the numerical solution,fixed-interface component mode synthesis method is employed to reduce the system degrees of freedom.Finite element method is used for discretization.The flexible body involving contact can be divided into the contact region and the un-contact region.The nodes in the contact region are defined as the boundary nodes of the substructure,and the nodes in the non-contact region are defined as the inner nodes of the substructure.The free vibration equations of the fixed-interface substructure are established by fixing the boundary nodes,and then the dominant modal vectors can be obtained by solving the generalized eigenvalue problem.Releasing the nodal degrees of freedom of the boundary nodes one by one,the constraint modal matrices are obtained.Based on the low-order modal coordinates and the nodal deformation coordinates of the boundary nodes,a combined vector of multi-variable coordinates is given to describe the deformation of the whole flexible body,which significantly decreases the degrees of the freedom.Moreover,the dynamic model of the flexible multibody systems is presented based on the hybrid coordinate formulation considering the large overall motions.The advantage of the multi-variable method proposed in this dissertation is that by leading into the constraint modal matrices,the equal displacement condition of the common nodes of the divided regions is naturally taken into account without the need of imposing displacement constraint equations,as the previous multi-variable methods did.Based on the multi-variable method,the contact detection strategy is proposed.The normal node-surface contact model is established based on the penalty method and the Lagrange multiplier method,respectively.Afterwards the generalized force vector associated with the normal contact force is derived.For the contact-impact problems involving friction,the friction behavior is divided into stick period and slip period based on the Coulomb friction law.The friction model is established based on the penalty method and the Lagrange multiplier method,respectively,and then the generalized force vector associated with the frictional force is obtained.Finally,the numerical solution of the differential-algebraic equations corresponding to the penalty method and the Lagrange multiplier method is proposed.In the process of finite element discretization,sufficient elements are needed to satisfy the accuracy demand.However excessive refinement may lead to the waste of elements and extremely small time step.Based on the sub-region mesh method,the criterion of allowed maximum element sizes within the contact area,the local contact region and the wave propagation region is proposed for the contact-impact of flexible bodies according to the description of the contact surface,stress distribution of the local contact area and the propagation of the high-frequency elastic wave,respectively.By using the sub-region mesh method,the flexible bodies involving contact can be meshed with minimal elements and optimal distribution of element size.Furthermore,the normal contact and the oblique contact problems between a flexible rod and a plate are investigated experimentally.The accuracy of the theoretical model proposed in this dissertation is validated by the strain measurement of the feature points obtained by the strain gauges,and then the digital image correlation(DIC)technique is used for the first time for the measurement of the strain field and the velocity field of the plate in the contact duration.By the comparison with the traditional experiment technique,the measurement of DIC in contact problems is proved to be reliable.For some specialized material,elasto-plastic deformation may occur during the contact-impact.With the consideration of the material nonlinear effect,the dynamic model of elasto-plastic multibody system made of isotropic hardening material is established based on the nonlinear relationship between the stress and the strain in the incremental form.Simulations of the contact-impact between the steel rod and the aluminum rod as well as the contact-impact between the steel rod and the aluminum plate show the influence of the elasto-plasticity within the local contact region on the dynamic response of the system.The accuracy of the dynamic model is validated by the elasto-plastic experiments.Finally,the multi-variable modeling method and the sub-region mesh method are applied to solve the contact-impact problems in engineering.The step impact problem in the control rod drive mechanism which is very important to the nuclear reactor is investigated numerically.The influence of the local contact on the dynamic response of the system is analyzed.By the comparison of the dynamic response in different working conditions,it is concluded that the contact between the latch and the drive rod will have the largest effect on the velocity response of the drive rod when the drive rod is lifted to the maximum height. |
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