Analysis-suitable Parameterization For Isogeometric Analysis Of Spacial Beam

The automobile industry is one of the national pillar industries and plays an important role in the national economic development.Beam structures are widely used in automobiles,such as frame body structures,car bumpers and shock absorbers.Therefore,the beam structure plays a very important role in the conceptual simulation of automobile.The isogeometric analysis method unifies the geometric description of CAD and CAE,which can integrate product design and analysis.It can shorten the product development cycle,improve the simulation accuracy and simplify the product development process.The CAD model is determined by the basis function and control point of B Spline or NURBS(Non-uniform Rational B Spline).The parametric quality of CAD model in geometric simulation analysis is similar to that in finite element analysis,which will directly affect the simulation results.Therefore,it is very important to study the parameterization of geometric models.Improving the parameterization quality of geometric models can directly improve the simulation accuracy.In this paper,Based on the beam theory,the stiffness matrix and the mass matrix of the symmetrical section and the asymmetric section space beam structure are derived.the influence of interpolation and approximation fitting on the fitting result of curved beam geometric model is studied,and the fitting geometric model is taken into the equivalent geometric analysis for calculation,and the influence of the fitting result on the accuracy of equivalent geometric analysis is studied.The specific contents are as follows:(1)Taking Timoshenko beam as the research object,the coordinate system representation and the basic equation of elasticity of 3D beam are studied,the D matrix and B matrix of symmetric and asymmetric beam structures are given,and the stiffness matrix K is derived.According to the Hamiltonian principle,the dynamic characteristic equation of the continuum with uniform mass distribution is derived,and on this basis,the mass matrix of symmetric beam structure and asymmetric beam structure is obtained.(2)Starting from a set of given data points,this paper calculates the parameter expression of the curve through fitting method,and discusses two basic fitting methods,namely approximation method and interpolation method.Three kinds of sampling point parameterization strategies are studied,namely equidistant method,chord length method and centripetal method.The results show that the results of the interpolation method are stable,and the accuracy and stability of the interpolation method are optimal.(3)There are many methods of parameter expression for the same geometric model,the fitting geometric model is brought into the geometric analysis for calculation,and the influence of the fitting result on the accuracy of the equivalent geometric analysis is studied.With the increase of the number of sampling points,the simulation precision of approximation method and interpolation method can be greatly improved,and the accuracy of the interpolation method is higher than that of the approximation method.The fitting geometric model is combined with the classical refinement method for simulation calculation,the results show that the accuracy and efficiency of the two methods are higher than that of the fitting method with the same order and control points.