## Limit analysis of plates and slabs using a meshless equilibrium formulation.(English)Zbl 1202.74019

Summary: A meshless Element-Free Galerkin (EFG) equilibrium formulation is proposed to compute the limit loads which can be sustained by plates and slabs. In the formulation pure moment fields are approximated using a moving least-squares technique, which means that the resulting fields are smooth over the entire problem domain. There is therefore no need to enforce continuity conditions at interfaces within the problem domain, which would be a key part of a comparable finite element formulation. The collocation method is used to enforce the strong form of the equilibrium equations and a stabilized conforming nodal integration scheme is introduced to eliminate numerical instability problems. The combination of the collocation method and the smoothing technique means that equilibrium only needs to be enforced at the nodes, and stable and accurate solutions can be obtained with minimal computational effort. The von Mises and Nielsen yield criteria which are used in the analysis of plates and slabs, respectively, are enforced by introducing second-order cone constraints, ensuring that the resulting optimization problem can be solved using efficient interior-point solvers. Finally, the efficacy of the procedure is demonstrated by applying it to various benchmark plate and slab problems.

### MSC:

 74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials) 74K10 Rods (beams, columns, shafts, arches, rings, etc.) 74S30 Other numerical methods in solid mechanics (MSC2010)
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