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The complex variable element-free Galerkin method based on the conjugate basis function for 3D elastoplastic problems
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DOI：10.1016/j.enganabound.2025.106425.png)
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Abstract
En 中文
This study proposes 3D complex variable element-free Galerkin (CVEFG) method for analyzing elastoplastic problem. The shape functions are constructed through the 3D complex variable moving least squares (CVMLS) approximation based on conjugate basis functions, which is then incorporated into the discrete equations derived from the Galerkin weak form for 3D elastoplastic problem, ultimately establishing the CVEFG method formulation for 3D elastoplastic analysis. To verify the validity of the derived equations, we present four numerical examples for analyzing the effects of nodal distribution, penalty factors, scaling parameters, and load steps on the computational accuracy of numerical solutions. These numerical examples conclusively demonstrate that the proposed CVEFG method not only exhibits convergence properties but also outperforms traditional EFG method in computational accuracy for 3D elastoplastic analyses. This superiority stems from the fact that the complex-variable formulation in the CVMLS shape functions incorporates more sophisticated mathematical principles than standard MLS approximations. This theoretical advancement makes the CVEFG method particularly suitable for addressing complex nonlinear problems.
Keywords:
3D elastoplastic analysis
complex variable moving least squares
element-free Galerkin method
shape function construction
numerical accuracy
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