SONG Yan-qi, HAO Liang-jun, LI Xiang-shang. Numerical Analysis of Geometrically Nonlinear Problems Based on the S-R Decomposition Theorem[J]. Applied Mathematics and Mechanics, 2017, 38(9): 1029-1040. doi: 10.21656/1000-0887.370229
 Citation: SONG Yan-qi, HAO Liang-jun, LI Xiang-shang. Numerical Analysis of Geometrically Nonlinear Problems Based on the S-R Decomposition Theorem[J]. Applied Mathematics and Mechanics, 2017, 38(9): 1029-1040.

# Numerical Analysis of Geometrically Nonlinear Problems Based on the S-R Decomposition Theorem

##### doi: 10.21656/1000-0887.370229
Funds:  The National Natural Science Foundation of China (41430640)
• Received Date: 2016-07-22
• Rev Recd Date: 2016-09-01
• Publish Date: 2017-09-15
• To explore the numerical solution method for geometrically nonlinear problems, the theoretical derivation, the MATLAB programming and the finite element simulation were used together. Based on the S-R decomposition theorem, the interpolated element-free Galerkin method was applied to deduce the incremental variational equations through the updated co-moving coordinate formulation, which were solved with the 4-point Gauss integration method and the fixed point iteration method. Finally, the large deformations of exemplary elastic and elastoplastic planar cantilever beams were calculated and the results agreed well with those from the ANSYS simulation. The examples illustrate the correctness and rationality of the proposed geometrically nonlinear mechanics theory and the present numerical calculation method. The work provides a new basis for the solutions to geometrically nonlinear problems.
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