Two dimensional element free Galerkin coupled flow function method and its application

Abstract

Purpose

The purpose of this paper is to propose a hybridization numerical method to solve the plastic deformation of metal working based on the flow function method and meshless method.

Design/methodology/approach

The proposed method is named as flow function-element free Galerkin (F-EFG) method. It uses the flow function as the basic unknown quantity to get the basic control equation, the compactly supported approximate function to establish a local approximate flow function by means of moving least square approximation, and the element free Galerkin (EFG) method to solve variational equation. The F-EFG method takes the upper limit method essence of flow function method, and the convergence, stability, and error characteristics of EFG method.

Findings

The steady extrusion process of the axisymmetric extrusion problems as well as the extrusion deformation law and main field variables are subjects in the modeling and simulation analysis using F-EFG method. The results show that the F-EFG method has good computational efficiency and accuracy.

Originality/value

The F-EFG method proposed in this paper has the advantages of high-solution precision of flow function method and large deformation solution of element free method. It overcomes the difficulties in global flow function establishment in flow function method and low-solution efficiency in element free method. The method is beneficial to the development of flow function method and element free method.

Citation

Zhang, Q., Zhang, B. and Lu, X. (2016), "Two dimensional element free Galerkin coupled flow function method and its application", Engineering Computations, Vol. 33 No. 5, pp. 1310-1326. https://doi.org/10.1108/EC-04-2015-0097