Development And Application In Vehicle Dynamic Analysis Of New Element Based On The Absolute Nodal Coordinate Formulation

The traditiaoal multibody system dynamic modeling method,which is based on the little deformation and rotation assumption,cannot exactly describe the behavior of the coupling high speed and large deformation of the components which are widely used in the aerospace,robotics,vehicles and mechanism energineerings.Absolute nodal coordinate formulation,on the other hand,employs the absolute positon and gradient vectors as its nodal coordinates,results in the system motion equation which is non-incremental,has constact mass matrix and doesn't have the Coriolis and centrifugal force.All these features make it suitable for solving large rotation and deformation problems.It promotes the integration of the finite element and multibody system dynamics theory.Furthermore,the geometry description of the traditional finite elements which utilize the displacement and rotation as nodal coordinates is not consistent with the NURBS method,which is widely used in the computer-aid design software.This fact makes it difficult to convert a geometry model developed in the computer-aid design software to a finite element mesh.However,the absolute nodal coordinate formulation finite elements are consistent with NURBS geometry,which gives them the potential to integrate computer-aid design and analysis.That's why the absolute nodal coordinate formulation has been the most popular research area of the multibody system dynamics since it was born.The scope of this investigation is the relationship between the absolute nodal coordinate formulation and the NURBS geometry,developing new elements and the application in vehicle dynamic simulation.The rational ANCF cable element is proposed.The element shape function is derivative.The knot inserting algorithm is used to present the convertion between the new elements and NURBS curves.It is proved that the third order contintuity condition on a interface node will fully eliminate the coordinates on this node,results in a new element defiend on a larger domain.It can be seen as a demonstration of the equivalency of two methods utilized by ANCF elements and B-spline curves.The concept of piecewise ANCF element is proposed.The method that constructe a piecewise ANCF cable element which contains two segments is firstly given.The higher continuity condition is required,the less nodal vectors should be preserved at the inner nodes.The recursive algorithm of developin g a piecewise ANCF cable element which contains arbitrary inner nodes and segments is then presented.The relationship between the new element and B-spline curves is given.In order to avoid singular reference,only the position vector should be preserved as nodal vector instead of the gradient vector at the inner nodes under second order continuity condition.The properties of the element shape function are discussed.The element shape function should at least have the same continuity condition as the element at an inner node.The mixed-coordinate ANCF thin plate element is proposed and the element shape function is derivatived.The new element chose to not use the curvature vector as nodal coordinates at four conner nodes,but four inner nodes which only have the position vectors.It makes the new element more convenience to use when modeling complex geometries.The continuity control methods of the ANCF thin plate element and B-spline surface are compared.Redundant constraints will be introduced when B-spline is trying to change the knot multiplicity because of its fixed recursive definition.ANCF,compared with B-spline,uses linear constraints to eliminate independent coordinates to achieve a certain order of continuity,which is more efficient.The rational ANCF thin plate element is developed and its relationship with the rational Bézier surface is investigated.The comparison of the computated mass moment of inertia with the analytical results shows that the exact description of the conic geometry ca n be achieved by using only a few of the rational ANCF elements.The key technology of the leaf spring dynamic simulation is investigated.The inverse of the position vector gradient evaluated in the undeformed configuration is introduced into the formulation of the elastic force based on the general continuum mechanics so that the pre-stress of the leaf spring can be described.The method of modeling the contact between the leaves is proposed.A local coordinate frame is settled on each leaf to introduce the element number into the dimensionless coordinates in order to search for the normal direction of the contact surface.The three exsiting ANCF thin plate elements are used to build the tire model.The exsisting formulation of the thin plate elastic forc e is improved to describe the dynamic behavior of the model with initially curved reference configuration.The new concept of ANCF reference node is used to integrate other components into the leaf spring model and finally express the entire vehicle model by using one sigle element mesh.The numerical results are presented to demonstrate the feasibility of the method presented in this investigation.