Research On Simulating Algorithms In Nonsmooth Contact Dynamics Of Multibody Systems

The research on simulation algorithm in nonsmooth dynamics of multibody systems has wide application prospects,for example,it has important guiding role and practical value in vehicle engineering,aerospace and other related fields.Based on the bi-potential method,this Ph.D work forms a set of numerical algorithms for effectively solving the nonsmooth contact dynamics of rigid multibody systems,flexible multibody systems and rigid-flexible multibody systems,which makes the bi-potential method more universally applicable.In the rigid multibody systems,the dynamic equation based on the velocity-impulse is established by the Lagrange model,and the implicit Moreau midpoint method is used to solve the particle displacements.The bi-potential method is applied to the collision solution of rigid multibody systems,and a general calculating model of the bi-potential coefficient is proposed.The FER/Mech-BI algorithm is developed,which combines the Moreau collision model with the Newton restitutive coefficient,so that the numerical results meet the law of energy conservation/dissipation and ensure the numerical stability.The comparisons with the analytical solution and other numerical methods that fully prove the correctness and accuracy of the FER/Mech-BI algorithm.Finally,the bi-potential method is extended from the collision solution of discrete granules to that of rigid multibody coupling systems.The effects of friction coefficient and normal restitutive coefficient on the numerical simulation results are discussed,and the energy consistency is also compared.The results show that the proposed algorithm agrees well with the analytical solution in the discrete granular collision problems,and has no difference with the Linear Complementarity Problem(LCP)method in the accuracy range.In the collision problems of the rigid multibody coupling systems,the FER/Mech-BI algorithm has more advantages than the LCP method.Because the numerical solution of the FER/Mech-BI algorithm is closer to the theoretical solution,and its numerical stability is also better.In the verification of energy consistency,the proposed algorithm satisfies the law of energy conservation/dissipation without any energy overflow.Both the friction coefficient and normal restitutive coefficient have obvious effects on displacements.Besides,the larger the normal restitutive coefficient,the smaller the value of the stability factor and the smaller the value of the bi-potential coefficient.In the flexible multibody systems,the complexity of collision solution is overcome by separating the nonlinear factors,the collision force on the nodes is solved by using the bipotential method.Then,the form of external load other than the contact force is assigned to the dynamic equation through the transformation matrix.The Tamma-Namburu integral scheme and the Newton-Raphson iterative method are combined to solve the nonlinear problems.The FER/View-F algorithm is verified by the collision models of a linear elastomer and a hyperelastomer,and then the proposed algorithm is applied to the analysis of the cushioning performance of composites.The research shows that the FER/View-F algorithm neither needs to change the global stiffness matrix nor increases the degree of freedom of the system,and the solution process is more stable.When the deformation of the collision bodies is not explored,the results obtained by the FER/Mech-BI algorithm are the closest to the analytical solution,and the computing efficiency is very high.When it is necessary to analyze the stress and strain of the collision bodies,the solution of the FER/View-F algorithm is more accurate than that of the finite element software MSC.Marc.At the same time,the proposed algorithm meets the law of energy conservation/dissipation,and the stability of its solution is better.In the example of the cushioning performance of the composite,several typical composite materials are discussed.Among them,the composite materials with the carbon black filled rubber on the surface and the foam polyurethane rubber on the bottom have the best cushioning performance.In the rigid-flexible multibody systems,the collision force is solved by combining the bi-potential method and the node-point contact identification strategy.The geometric nonlinearity of the material is described by the total Lagrange formula,and the first-order integration scheme is used to solve the dynamic equation.The accuracy of the algorithm is verified by comparing with the analytical solution and MSC.Marc.In addition,the rigidflexible interaction collision model and the rigid-flexible coupling collision model are both considered.In the rigid-flexible interaction model,the symmetric collision and asymmetric multiple collision are studied respectively.In the rigid-flexible coupling model,the multibody systems with spring-damping as coupling members and the displacement constraints as coupling nodes are analyzed.The conclusions are as follows: The contact detection in the FER/View-RF algorithm is more accurate and the numerical stability is also better,which satisfies the law of energy conservation/dissipation.In the numerical applications,the proposed algorithm is in good agreement with MSC.Marc.In the coupled multibody systems with spring-damping as the connecting members,the spring member will disturb the flexible bodies,and the damping member can reduce the ability to transmit vibration.In the rigid-flexible coupled plate with node-displacement constraints,the simulation results show that the impact resistance of carbon black filled rubber material is the best,and it plays a better role in protecting the objects wrapped by the material.