Application Of Hermite-type Dual Interpolation Boundary Face Method In Automatic CAE Analysis

CAE automatic analysis has always been an important topic in the field of engineering and scientific computing.The key issue is the automatic generation of meshes.The finite element method which based on continuous mesh has a low degree of automation.The boundary element method based on the boundary integral equation has no requirement for the continuity of the trial function,so it can use discontinuous meshes to calculate and analyze,thereby reducing the difficulty of mesh generation.The boundary face method inherits all the advantages of the boundary element method,and uses the B-Rep data structure in the CAD solid modeling system to directly perform CAE analysis based on the CAD model,which truly realizes the integration of CAD/CAE.The dual interpolation boundary face method combines the dual interpolation method and the boundary face method.The method unifies continuous and discontinuous elements,combines element interpolation and meshless interpolation,and greatly improves the accuracy and efficiency of the boundary face method.However,the traditional dual interpolation boundary face method uses the MLS interpolation method as the second-layer interpolation.The interpolation method needs to be implemented in the parameter space of the curve or surface,and the domain of influence of the virtual point is limited to a single edge or a single surface,so that the traditional dual interpolation boundary face method is limited when dealing with the thin-wall structures and structures with small features.Furthermore,the traditional dual interpolation boundary face method still uses the continuous meshes to calculate and analyse,which does not fully utilize the advantages of non-continuity requirements for the trial function.In this paper,the second-layer interpolation method and the use of discontinuous meshes for CAE analysis will be carried out,and the new method will be applied to solve the potential problems and elasticity problems of thin-wall structures and structures with small features.Moreover,the new singular dual interpolation element will be developed and be used to solve the three-dimensional crack and V-notch problems.The main research contents of this paper are as follows:(1)The Hermite-type dual interpolation boundary face method for the two-dimensional potential problem.The Hermite-type interpolation of the 2D potential problem is deduced.The method directly uses Cartesian coordinates,and the domain of influence of the virtual point is not limited.The Hermite-type interpolation is used to replace the MLS interpolation method in the traditional dual interpolation boundary face method,and it is used to solve the 2D homogeneous and non-homogeneous potential problems.Numerical examples show that compared with the traditional boundary face method and the dual reciprocity boundary face method,the new algorithm has higher accuracy and efficiency.Compared with the traditional dual interpolation boundary face method,the new algorithm naturally satisfies the continuity requirement of the potential and its derivative and is more suitable for solving thin-wall structures,and it is convenient to develop the unified programming.(2)The Hermite-type dual interpolation boundary face method for the three-dimensional potential problem.The Hermite-type interpolation of the 3D potential problem is proposed for the first time,and then combines the dual interpolation boundary face method to solve the 3D potential problem.Numerical examples show that compared with the traditional 3D boundary face method,the new algorithm has higher accuracy and efficiency.Compared with the traditional 3D dual interpolation boundary face method,the new algorithm is more suitable for solving engineering structures with small features and thin walls.(3)The Hermite-type dual interpolation boundary face method for two-dimensional elasticity problems.The Hermite-type interpolation method for 2D elasticity problems is proposed for the first time,and combines the dual interpolation boundary face method to solve 2D elasticity problems.Numerical examples show that compared with the traditional boundary face method,the new algorithm has higher accuracy and efficiency.Compared with the traditional dual interpolation boundary face method,the new algorithm naturally satisfies the continuity requirements of displacement and stress,and is more suitable for solving thin-wall structures,even the aspect ratio reaches 1000:1,the accuracy can still reach 10^-4.The new algorithm can simulate the stress concentration problem with high precision when solving the practical engineering structure with small features.(4)The Hermite-type dual interpolation boundary face method of three-dimensional elasticity problem based on the binary-tree meshes.The Hermite-type interpolation method for the 3D elasticity problem is proposed for the first time.Then,the method is applied to the second-layer interpolation of the dual interpolation boundary face method,and firstly combines with the binary-tree meshes to solve the 3D elasticity problem.The new algorithm not only realizes the integration of CAD/CAE,but also further realizes the use of discontinuous meshes for CAE analysis,thereby reducing the difficulty of mesh generation and laying a solid foundation for CAE automatic analysis.Numerical examples show that compared with the traditional boundary face method,this new algorithm has higher accuracy and efficiency.This new algorithm is suitable for solving thin-wall structures,and it does not need to make any geometry repair and model simplification,just retain all geometry flaws and small features when solving practical engineering structures with geometry flaws and small features,and it can achieve high accuracy just by using a little source points.(5)The Hermite-type dual interpolation boundary face method based on the binary-tree meshes is used to solve the three-dimensional crack and V-notch problems.Two new types of singular dual interpolation elements and special dual interpolation methods for 3D crack and V-notch problems are firstly proposed,and then combine with the Hermite-type dual interpolation boundary face method to solve the stress singularity problems of 3D crack and V-notch.Moreover,the relative displacement formula is derived and used to solve the stress intensity factor.Numerical examples show that the new algorithm realizes the use of discontinuous meshes to solve crack and V-notch problems,and its accuracy can satisfy the engineering requirements,thereby promoting the development of CAE automatic analysis of stress singularity problems.