A curvature smoothing Hsieh-Clough-Tocher element for yield design of reinforced concrete slabs

This paper describes a numerical kinematic formulation for yield design of reinforced concrete slabs governed by Nielsen yield criterion. A cell-based smoothing technique is introduced to original Hsieh-Clough-Tocher (HCT) element, ensuring that only first derivatives of shape functions are needed to establish stabilized curvatures. The size of the resulting optimization problem is reduced significantly due to the fact that only one integration point is needed per sub-element. The discrete optimization problem was solved using a highly efficient primal-dual interior point algorithm. The proposed numerical procedure is applied to various reinforced concrete slab problems with arbitrary geometries and different boundary conditions.