Upper Bound Method for Yield Design of Reinforced Concrete Slabs Using Conic Programming and an Adaptive Remeshing Strategy

Abstract

This study presents a numerical procedure for the analysis of reinforced concrete slabs (RCS) that obey Nielsen's yield criterion (slabs orthogonally reinforced). An upper bound formulation combined with finite elements was established to solve the kinematic theorem as a conic optimization problem with the aim to determine the maximum bearing capacity of RCS. Discrete Kirchhoff finite elements were implemented and adapted to establish a limit state problem for the yield design. By using Nielsen´s criterion, a kinematic criterion was established applying the flow rule of plasticity. The kinematic criterion was included in the upper bound formulation with the aim to constraint the curvatures of the slab. The upper bound formulation was organized in the standard form of a second order cone programming (SOCP) problem since the kinematic criterion was formulated in conic form. Numerical examples were proposed to test the accuracy of the method including the adaptive remeshing strategy.