Contact Dynamics Of Thin Beams Subject To Overall Motions And Large Deformations

During the deployment of large deployable space structures composed of trusses and meshes under microgravity,flexible cables composing the reflector networks and tension networks of these structures not only will be subject to overall motions and large deformations but also will contact,wrap and even knot between each other,which will lead to failure of the in-orbit deployment of these structures.To avoid such accidents,it is essential to numerically simulate and analyse the above complicated dynamic behaviors of flexible cables during the design phases of space structures.The thin beam model is commonly adopted to investigate the dynamic problem of flexible cables.The beam element based on the Absolute Nodal Coordinate Formulation(ANCF)can accurately describe the coupled dynamics of both large overall momtions and large deformations of beams,but it is few using this element to study contact dynamics of thin beams.The study on contact of beams at present is only limited to contact between two beams or self-contact of one single beam.The point-wise contact model is mostly used to detect contact points,which can't describe the contact problems of beams with multiple contact zones.Besides,there will exist frictions between rough surfaces of cables during contact and wrap,and plastic deformations of cables will happen if strains are larger than the yield strains,both of which have not been studied deep at present.They are of great scientific significance and engineering value to study the contact dynamics of thin beams subject to large overall motions and large deformations,with the consideration of both contact friction and local plasticity.This dissertation focuses on contact dynamics problems of thin beams with large overall motions and large deformations based on the absolute nodal coordinate formulation.The specific research contents are shown as follows.(1)The frictional single-zone contact model of thin beams is proposed based on the minimal distance criterion and the master-slave algorithm.The normal contact force and its jacobian matrix are derived by using the penalty method,while the tangential ones are efficiently computed via the regularized Coulomb friction model(R-Coulomb model).A new local coordinate system is introduced into the spatial thin beam element of absolute nodal coordinate formulation for efficient contact detection in the contact dynamics simulation.The generalized-? integration method is adopted to solve contact dynamic problems of thin beams with large overall motions and large deformations.Numerical examples validate the correctness and feasibility of the model in dealing with the above contact problems.(2)The frictional multi-zone contact model of thin beams is proposed based on the above single-zone contact model of thin beams.In the model the mutual penetration of two thin beams with multiple contact zones of large size is a multi-peak function of the local coordinate of the slave beam.Each contact zone contains at least one local minimal mutual penetration point pair.By checking all the local minima of the function,the contact zones of two thin beams can be efficiently located.The simulation results show that the model can be successfully applied in both the static and dynamic contact problems and that the model exhibits good effectiveness to even more tough problems about the frictional contact dynamics of thin beams with multiple contact zones of large size.(3)To adopt the LuGre friction model to describe the friction force during the contact of thin beams more correctly and efficiently,a piecewise analytic expression of the LuGre friction model(LuGre-PAE model)is proposed under reasonable assumptions.The performances of the model,the ordinary differential equation expression of the LuGre friction model(LuGre-ODE model)and the regularized Coulomb model(R-Coulomb model)are compared via numerical examples and indicate that LuGre-PAE model not only exhibits the Stribeck effect and frictional stick,but also captures the friction-induced hysteresis very well.(4)Results of numerical examples show that the friction forces based on both the R-Coulomb model and the LuGre-PAE model not only limit the relative slip of contacting thin beams effectively,but also decrease the oscillations of thin beams significantly.Moreover,with larger friction coefficient,these effects are more obvious.(5)The Spatial elasto-plastic thin beam element based on the absolute nodal coordinate formulation is proposed under the assumption of the plastic strain of the thin beam element depending only on its longitudinal deformation.The influence of the plasticity on the dynamic response of thin beam contact systems is investigated.The simulation results offer the convergence and validation of the proposed element.A smaller initial yield stress gives rise to a larger plastic deformation and correspondingly,a larger total energy dissipation of the thin beam.The thin beams may undergo plastic deformations when there are contacts.Moreover,the plastic deformations will reduce the beam oscillations after the dynamic contacts,and this phenomenon becomes obvious if the beam material has small initial yield stress.(6)An experiment system of wrapping three-line pendulum is designed to validate the correctness of the multi-zone frictional contact model of thin beams proposed in this dissertation.The experimental results show that the maximum and minimum values of the angular velocity of the disk approach the steady angular velocity of the motor,and that the period of the disk angular velocity decreases slightly with time.By determing the parameters of the experiment system,the system is numerically simulated with the multi-zone frictional contact model of thin beams.The numerical results indicate that the above phenomena are mainly given rise to the air resistance acted on the disk.