Finite element method

Pure mathematics

Mathematics

Structural engineering

Evolutionary biology

Biology

Mathematical optimization

Engineering

Mathematical analysis

Weight function

Function (biology)

Composite material

Galerkin method

Materials science

Deformation (meteorology)

Numerical analysis

Moving least squares

Penalty method

Applied mathematics

Invertible matrix

International Journal of Applied Mechanics

In this study, based on a nonsingular weight function, the improved element-free Galerkin (IEFG) method is presented for solving elastoplastic large deformation problems. By using the improved interpolating moving least-squares (IMLS) method to form the approximation function, and using Galerkin weak form based on total Lagrange formulation of elastoplastic large deformation problems to form the discretilized equations, which is solved with the Newton–Raphson iteration method, we obtain the formulae of the IEFG method for elastoplastic large deformation problems. In numerical examples, the influences of the penalty factor, scale parameter of influence domain and weight functions on the computational accuracy are analyzed, and the numerical solutions show that the IEFG method for elastoplastic large deformation problems has higher computational efficiency and accuracy.

A Meshless Method Based on the Nonsingular Weight Functions for Elastoplastic Large Deformation Problems