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

We outline a numerical procedure for limit analysis of reinforced concrete slabs.A cell-based curvature smoothing HCT element is described.Accurate upper bound solutions are obtained with minimal computational cost.Second-order cone programming ensures solutions are obtained rapidly. 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.

[1]  A. Makrodimopoulos,et al.  Remarks on some properties of conic yield restrictions in limit analysis , 2010 .

[2]  Joost Meyboom,et al.  Limit analysis of reinforced concrete slabs , 2002 .

[3]  J. Bleyer,et al.  On the performance of non‐conforming finite elements for the upper bound limit analysis of plates , 2013 .

[4]  Mitchell Gohnert,et al.  Collapse load analysis of yield-line elements , 2000 .

[5]  Jiun-Shyan Chen,et al.  A stabilized conforming nodal integration for Galerkin mesh-free methods , 2001 .

[6]  Erling D. Andersen,et al.  On implementing a primal-dual interior-point method for conic quadratic optimization , 2003, Math. Program..

[7]  Matthew Gilbert,et al.  Automatic yield-line analysis of slabs using discontinuity layout optimization , 2014, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[8]  G. R. Liu,et al.  On Smoothed Finite Element Methods , 2010 .

[9]  Hung Nguyen-Xuan,et al.  COMPUTATION OF LIMIT LOAD USING EDGE-BASED SMOOTHED FINITE ELEMENT METHOD AND SECOND-ORDER CONE PROGRAMMING , 2013 .

[10]  Mogens Peter Nielsen,et al.  Limit Analysis and Concrete Plasticity , 2010 .

[11]  Michael L. Overton,et al.  An Efficient Primal-Dual Interior-Point Method for Minimizing a Sum of Euclidean Norms , 2000, SIAM J. Sci. Comput..

[12]  Hung Nguyen-Xuan,et al.  Upper and lower bound limit analysis of plates using FEM and second-order cone programming , 2010 .

[13]  E. A. W. Maunder,et al.  Equilibrium models for lower bound limit analyses of reinforced concrete slabs , 2012 .

[14]  H. Chan,et al.  The collapse load of reinforced concrete plate , 1972 .

[15]  Michael L. Overton,et al.  Computing Limit Loads by Minimizing a Sum of Norms , 1998, SIAM J. Sci. Comput..

[16]  D. C. Drucker,et al.  Plastic and Elastic Design of Slabs and Plates , 1963 .

[17]  Antonio Huerta,et al.  Upper and lower bounds in limit analysis: Adaptive meshing strategies and discontinuous loading , 2009 .

[18]  Knud Winstrup Johansen.  Yield-line theory , 1962 .

[19]  M. Gilbert,et al.  A locking-free stabilized kinematic EFG model for plane strain limit analysis , 2012 .

[20]  Jaime Peraire,et al.  Mesh adaptive computation of upper and lower bounds in limit analysis , 2008 .

[21]  Antonio Capsoni,et al.  Limit analysis of plates-a finite element formulation , 1999 .

[22]  Matthew Gilbert,et al.  Limit analysis of plates and slabs using a meshless equilibrium formulation , 2010 .

[23]  Kristian Krabbenhoft,et al.  A general non‐linear optimization algorithm for lower bound limit analysis , 2003 .

[24]  Mark A. Bradford,et al.  Limit analysis of local failure in shallow spherical concrete caps subjected to uniform radial pressure , 2010 .

[25]  Ted Belytschko,et al.  Numerical Methods for the Limit Analysis of Plates , 1968 .

[26]  Kristian Krabbenhoft,et al.  Lower bound limit analysis of slabs with nonlinear yield criteria , 2002 .

[27]  Rudolf Wolfensberger.  Traglast und optimale Bemessung von Platten , 1964 .

[28]  Matthew Gilbert,et al.  Limit analysis of plates using the EFG method and second‐order cone programming , 2009 .

[29]  J Munro,et al.  YIELD LINE METHOD BY FINITE ELEMENTS AND LINEAR PROGRAMMING , 1978 .

[30]  E. N. Fox.  Limit analysis for plates: the exact solution for a clamped square plate of isotropic homogeneous material obeying the square yield criteron and loaded by uniform pressure , 1974, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.