Research On Interactive Construction Of 3D Models Based On Volume Subdivision And CAD Reconstruction Of Topology Optimization Results

As a widely used digital simulation technology,finite element analysis relies on the discretization of the model.The model discretization mainly converts the triangular surface model into a tetrahedral mesh model or a hexahedral mesh model.Aiming at the difficulty of generating and constructing a hexahedral mesh at present,this paper proposes an interactive construction method of complex hexahedral mesh model based on volume subdivision and builds a modeling system,which use hexahedral mesh in the modeling stage.Hexahedral cells are constructed as a base form,eliminating the time-consuming step of converting triangular surface meshes to hexahedral meshes,and applying this method to topology optimization results in the CAD reconstruction stage to generate Bézier volumes,enhancing the manufacturability of topology optimization results and can apply the reconstructed model to isogeometric analysis,etc.The main work of the paper includes two aspects:First,the first research work in this paper is an interactive construction method for complex hexahedral mesh models based on volume subdivision.This method needs to interactively construct a model skeleton,by placing hexahedral cells at the nodes of the skeleton structure,and performing interactive operations on the node hexahedron such as rotation,translation,scaling,etc.;The initial hexahedral control mesh;further,hexahedral meshes with different resolutions are generated by the Catmull-Clark interpolation volume subdivision method;finally,the degenerate elements at the boundary are eliminated and the quality of the hexahedral mesh elements is improved by adding a padding layer,so as to obtain the final hexahedral mesh model.The experimental results show that the method can generate hexahedral meshes interactively and conveniently and efficiently.The method can realize the interactive and direct construction of hexahedral mesh model,omits the intermediate step of generating volume mesh from surface mesh,and has application value in finite element analysis,isogeometric analysis,animation modeling and other fields.Secondly,the second research work of this paper is a CAD reconstruction method based on the topology optimization results expanded from the first research work.This method needs to perform hexahedral smoothing operation on the hexahedral mesh generated by the topology optimization results;then extract the surface mesh and convert it into a surface triangular mesh model;use the mean curvature flow method to extract the skeleton information of the triangular mesh;use the B-spline curve fitting method to fit the extracted skeleton in segments to generate a smooth skeleton line;use the bisection method to simplify the skeleton;finally,the rotation angle of the node is updated by the rotation minimization method;the angle and position of the node are adjusted by the interactive method;Map the constructed skeleton model to the surface mesh;convert the mapped mesh into a Bézier volume model.The experimental results show that this method can easily and efficiently convert the discrete hexahedral mesh model generated by topology optimization into a Bézier volume model,which eliminated the aliasing phenomenon of discrete models and the number of Bézier blocks is less than before,which has application value in the field of topology optimization post-processing.