Abstract
A numerical model for the two-dimensional nonlinear elastic–plastic problem is proposed based on the improved interpolating complex variable element free Galerkin (IICVEFG) method and the incremental tangent stiffness matrix method. The viability of the proposed model is verified through three elastic–plastic examples. The numerical analyses show that the IICVEFG method has good convergence. The solutions using the IICVEFG method are consistent with the solutions obtained from the finite element method using the ABAQUS program. Moreover, the IICVEFG method shows greater computing precision and efficiency than the non-interpolating meshless methods.
Highlights
In the science and engineering fields, nonlinear elastic–plastic problems are very common, and are complicated due to the nonlinearity of the plastic state
Since there are no analytical solutions for nonlinear elastic–plastic problems, the ABAQUS program is used as a reference in this paper
Through numerical analyses we found that, in the interpolating complex variable element free Galerkin (IICVEFG) method, the variance is smaller as the number of total nodes increases
Summary
In the science and engineering fields, nonlinear elastic–plastic problems are very common, and are complicated due to the nonlinearity of the plastic state. Based on these novel basis functions, a new interpolating shape function and interpolating trial function are derived This new method was named the improved interpolating complex variable moving least squares (IICVMLS) method [30]. Combining the IICVMLS method with the integral weak forms of diverse problems, the corresponding improved interpolating complex variable element free Galerkin (IICVEFG) methods were presented. The derived final discrete system is more concise, which leads to greater computing efficiency and accuracy, in contrast to other non-interpolating complex variable meshless methods. The intention of this paper is to build a more efficient and accurate numerical model for the two-dimensional nonlinear elastic–plastic problem based on the IICVEFG method, and to verify the viability of the proposed model. The computational advantages of the IICVEFG method are demonstrated, in comparison with the ABAQUS program and other non-interpolating meshless methods
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