Research On Isogeometric Analysis Method Based On T-spline

Under the influence of the concept of "Industry 4.0" and "Intelligent Manufacturing",people are increasingly concerned about how to maximize industrial production efficiency than before.Combing Computer Aided Analysis(CAA)with Computer Aided Design(CAD)is one of the approaches to improving efficiency.Due to the incompatibility of the traditional FEM's shape function and the basis function in the CAD system,the description of the geometry in the CAA system is only a geometrical approximation rather than a geometrical accuracy,and the original CAD model cannot be completely reproduced,which greatly hinders the interaction between each other and extends the product design cycle.This dissertation is aimed at the integration of CAA and CAD that,based on the theory of isogeometric analysis,taking the CAD geometric description as the center,changing the element shape function in CAA system to the basis function of CAD geometrical description.Discretization and analysis of thin-plate systems using isogeometric finite elements based on T-spline basis functions as shape functions,ie T-spline based isogeometric thin-plate elements.To establish a kinematic model of thin plate elements based on T-spline surface isogeometry.Use a T-spline blending function to eatablish the element shape function amd use coordinates of control points to be element's node vector.In order to express the bending deformation,the stretching derfoamation and the shear deformation of the flexible body represented by the Cauchy-Lagrangian strain tensor,the first derivatives and the second derivatives of the element shape function need to be solved.Reference the absolute node coordinate formula(ANCF),element generalized force vector,mass matrix,elastic force,and tangential stiffness matrix are derived.Using this element,the system is discretized,static analysis and dynamics analysis are performed.Newton-Raphson iteration method and generalized-? method are used to solve the system static equations and dynamics equations respectively.The numerical examples show that the accuracy of isogeometric thin plate element in the solution of flexible body deformation and the convergence of the element.Compared with the ANCF,it also can ensure high accuracy.Therefore,this element can be used to solve the problem of large deformation flexible multibody system.With the above all theory and modeling methods,the T-spline based isogeometric thin plate element is applied to solve practical engineering problems.Use T-spline to model a thin plate with a rectangular hole,and to study the stress concentration when the plate is subjected to in-plane tension.Using the T-spline plate element to locally refine the hazardous area around the rectangular hole can obtain the maximum stress of the system with fewer elements,and then obtain a more accurate stress concentration factor,whicn reflects the element's advantages in integrating CAD and CAA.