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New deformable element with arbitrary polygon shape for continuous modeling of limit analysis
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DOI：10.1016/j.ijsolstr.2025.113745.png)
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Abstract
En 中文
This paper proposes two alternatives for the polygon discretization in the finite element limit analysis. The construction of the upper bound limit analysis for the constant-strain polygon element is first presented. However, when implementing it to analyze the strip footing problems, a severe locking effect is observed in the results, which stems from the constant-strain assumption. Further sensitivity analysis demonstrates that such a locking issue becomes significant when using polygons with complex or concave shapes. The volumetric incompressible effect will also appear in both polygon and triangular meshes in the zero-friction case, and this is more remarkable in the polygon case because of the severe interlocking among the elements. The corresponding optimization problem will become unsolvable. An approximated solution can still be obtained by including spurious interfacial friction though. Finally, to theoretically resolve the locking problem, another type of polygon element with piecewise-constant strain is developed. Reproducing the previously considered strip footing problems through the new element, the results indicate that the polygon locking is largely released after introducing the strain variation in the elements. The analysis gives an accurate load prediction within an acceptable computational cost, presenting a great edge in precision and robustness against the established triangular elements. Nonetheless, the constant-strain polygon can remain employed in some scenarios where the locking effect is not obvious, taking merit from its great efficiency.
Keywords:
Finite element limit analysis
Upper bound theorem
Polygon element
Constant strain
Piecewise-constant strain
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