Generalized Particle Domain Method(GPDM) Based On CAD Data

The material point method,which combines the advantages of both the Lagrangian and Eulerian methods,has been successfully applied in many engineering problems involving large displacement and deformation.However,the generation of material points has not been a good way.For entities with complex geometric shapes,a finite element mesh generator can be used to build a mesh and use the center of the element as the material point,which is actually how many material point methods discretize the continuum.This preprocessing is undoubtedly time-consuming and labor-intensive,which severely limits the development of the material point method.In order to solve the above problems,this research develops a method to directly use CAD data to generate material points.The main research contents are:The Generalized Particle Domain Method(GPDM)is proposed in the framework of Convective Particle Domain Method(CPDI).GPDM directly uses CAD data to generate material points,and directly uses NURBS basis functions as the interpolation function for the material point domain.In that way GPDM doesn’t need other techniques to discrete continuum.At present,complex models can only be represented by multi trimmed tensor product NURBS surfaces.For complex models with trimmed patch,the TSA method proposed by Kim is used.TSA divides the irregular integration area into different regular triangle domains.The calculation of material points generated by trimmed NURBS surfaces is given.For three-dimensional problems,this research presents a method to generate NURBS entities in three-dimensional space by establishing linear equations at the Greville abscissae.Then,particles are generated through three-dimensional NURBS entities.In this research,three examples of compliant cantilever beam,impact of two elastic bodies and large deformation vertical rod are calculated to verify the correctness of the GPDM method.Among them,the compliant cantilever beam and collision between two balls is a two-dimensional problem,and the large deformation vertical bar is a three-dimensional problem.The calculation results of the GPDM method of the three examples are almost the same as the CPDI2 method.But compared with the CPDI2 method,the GPDM method does not require a preprocessing process,which saves a lot of preprocessing cost.Like the material point method,the GPDM method has great advantages in simulating large deformations.However,unlike the isogeometric analysis,the GPDM method does not have the multi-patch problem.The generalized particle domain method can provide a link to material point method and isogeometric analysis in the future.