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

• Published in: Engineering computations Vol. 33; no. 5; pp. 1310 - 1326
• Main Authors: Zhang, Qingdong, Zhang, Boyang, Lu, Xingfu
• Format: Journal Article
• Language: English
• Published: Bradford Emerald Group Publishing Limited 04.07.2016
• Subjects: Aerospace engineering; Approximation; Axisymmetric; Computer simulation; Computing time; Deformation; Energy consumption; Engineering; Extrusion; Extrusion dies; Finite element analysis; Finite element method; Flow stability; Galerkin method; Galerkin methods; Mathematical analysis; Mathematical models; Meshless methods; Metal forming; Metal working; Methods; Numerical methods; Partial differential equations; Plastic deformation; Queuing theory; Velocity; EFG method; Flow function; Plane stress; Element free Galerkin; Axisymmetric pipe extrusion; Plane strain
• ISSN: 0264-4401; 1758-7077
• DOI: 10.1108/EC-04-2015-0097

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.