A pseudo-equilibrium finite element for limit analysis of Reissner-Mindlin plates

•Finite element for yield design (limit analysis) of Reissner-Mindlin plates.•Computational procedure generates small SOCP problem with remarkable performance.•Special attention given to the effect of boundary layer in the collapse load. A new finite element is developed for the yield design of Reis...

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Bibliographic Details
Published in:Applied Mathematical Modelling 2021-08, Vol.96, p.336-354
Main Authors: Cavalcante, E.L.B., Neto, E. Lucena
Format: Article
Language:English
Subjects:
Algorithms
Boundary conditions
Boundary layer
Boundary layers
Collapse load
Computational geometry
Convexity
Equilibrium
Equilibrium equations
Finite element
Finite element method
Limit analysis
Lower bounds
Mindlin plates
Optimization
Reissner-Mindlin plate
Second-order cone programming
Shear locking
Static theorem
Yield criteria
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Summary:•Finite element for yield design (limit analysis) of Reissner-Mindlin plates.•Computational procedure generates small SOCP problem with remarkable performance.•Special attention given to the effect of boundary layer in the collapse load. A new finite element is developed for the yield design of Reissner-Mindlin plates based on the static theorem of limit analysis. This three-node triangular element satisfies the equilibrium equations and the mechanical boundary conditions on average, and, as such, it is not expected lower bounds on the collapse load from the computed results. The yield criterion is, however, exactly satisfied throughout the element. The relatively small nonlinear convex optimization problem posed here is treated as second-order cone programming and solved with a primal-dual interior-point algorithm implemented in the MOSEK optimization package. The proposed procedure exhibits excellent performance on a series of numerical tests, demonstrating that not satisfying the equilibrium equations and the mechanical boundary conditions rigorously is far from being a handicap. It is also observed that the solution may develop boundary layer along certain types of edges. This real physical phenomenon, likely to be manifested in Reissner-Mindlin plate solutions and that nearly no attention has been paid in the framework of yield design, is a source of convergence delay.
ISSN:0307-904X
1088-8691
0307-904X
DOI:10.1016/j.apm.2021.03.004