Abstract:

The meshfree methods can avoid grid distortion problems because it does not need to be meshed, which make them widely used in large deformations and other complicated problems. Radial basis collocation method (RBCM) is a typical strong form meshfree method. This method has the advantages of no need for any mesh, simple solution process, high precision, good convergence and easy expansion to high-dimensional problems. Since the global shape function is used, this method has the disadvantages of low precision and poor representation to local characteristics when solving high gradient problems. To resolve this issue, this paper introduces finite subdomain radial basis collocation method to solve the large deformation problem with local high gradients. Based on the total Lagrangian formulation, the Newton iteration method is used to establish the incremental solution scheme of the FSRBCM in large deformation analysis. This method partitions the solution domain into several subdomains according to its geometric characteristics, then constructs radial basis function interpolation in the subdomains, and imposes all the interface continuous conditions on the interfaces, which results in a block sparse matrix for the numerical solution. The proposed method has super convergence and transforms the original full matrix into a sparse matrix, which reduces the storage space and improves the computational efficiency. Compared to the traditional RBCM and finite element method (FEM), this method can better reflect local characteristics and solve high gradient problems. Numerical simulations show that the method can effectively solve the large deformation problems with local high gradients.

Key words: meshfree, finite subdomain radial basis collocation method, large deformation, high gradient, Newton iteration method