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A smoothed finite element method using second-order cone programming
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DOI：10.1016/j.compgeo.2020.103547.png)
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In this paper, a new approach abbreviated as SOCP-SFEM is developed for analysing geomechanical problems in elastoplasticity. The SOCP-SFEM combines a strain smoothing technique with the finite element method (FEM) in second-order cone programming (SOCP) and thereby inherits the advantages of both the smoothed finite element method (SFEM) and the SOCP-FEM. Specifically, the low-order mixed element can be used in the SOCP-SFEM without volumetric locking issues and the singularity associated with some typical constitutive models (e.g. the Mohr-Coulomb model and the Drucker-Prager model) is no longer a problem. In addition, the frictional and the cohesive-frictional interfaces can be implemented straightforward in the developed SOCP-SFEM owing to the adopted mixed variational principle and the smoothing technique. Furthermore, the multiple contact constraints, such as a cohesive interface with tension cut-off which is commonly used for analysing the bearing capacity of a pipeline buried in clays, can be simulated with little extra effort. To verify the correctness and robustness of the developed formulation for SOCP-SFEM, a series of benchmarks are considered where the simulation results are in good agreements with the analytical solutions and the reported numerical results.
Keyword:
Smoothed finite element method
Convex programming
Strain smoothing technique
Second-order cone programming
Contact problems
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