Limit analysis of plates and slabs using a meshless equilibrium formulation

International Journal for Numerical Methods in Engineering

Volumn 83, Issue 13, 2010, Pages 1739-1758

  Le, Canh V ^a   Gilbert, Matthew ^a   Askes, Harm ^a  

^a UNIVERSITY OF SHEFFIELD   (United Kingdom)

Author keywords

EFG; Equilibrium model; Limit analysis; Meshless methods; Plates; Second order cone programming; Slabs

Indexed keywords

EFG; EQUILIBRIUM MODEL; LIMIT ANALYSIS; MESH-LESS METHODS; PLATES; SECOND-ORDER CONE PROGRAMMING; SLABS;

COMPUTATIONAL MECHANICS;

EID: 77956814585     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.2887     Document Type: Article

References (36)

1. Hodge Jr PhG, Belytschko T. Numerical methods for the limit analysis of plates. Transactions of ASME, Journal of Applied Mechanics 1968; 35:796-802.
2. Capsoni A, Corradi L. Limit analysis of plates-a finite element formulation. Structural Engineering and Mechanics 1999; 8:325-341.
3. Lubliner J. Plasticity Theory. Macmillan: New York, 1990.
4. Chan HSY. The collapse load of reinforced concrete plates. International Journal for Numerical Methods in Engineering 1972; 5:57-64.
5. Anderheggen E, Knopfel H. Finite element limit analysis using linear programming. International Journal of Solids and Structures 1972; 8:1413-1431.
6. Faccioli E, Vitiello E. A finite element, linear programming methods for the limit analysis of thin plates. International Journal for Numerical Methods in Engineering 1973; 5:311-325.
7. Munro J, Da Fonseca A. Yield line method by finite elements and linear programming. The Structural Engineer 1978; 56:37-44.
8. Save MA, Massonnet CE, de Saxce G. Plastic Analysis and Design of Plates, Shells and Disks. North-Holland Series in Applied Mathematics and Mechanics, vol. 43. Elsevier: Amsterdam, 1997.
9. Le CV, Gilbert M, Askes H. Limit analysis of plates using the EFG method and second-order cone programming. International Journal for Numerical Methods in Engineering 2009; 78:1532-1552.
10. Chen S, Liu Y, Cen Z. Lower-bound limit analysis by using the EFG method and non-linear programming. International Journal for Numerical Methods in Engineering 2008; 74:391-415.
11. Krenk S, Damkilde L, Hoyer O. Limit analysis and optimal design of plates with equilibrium elements. Journal of Engineering Mechanics 1994; 120:1237-1254.
12. Krabbenhoft K, Damkilde L. Lower bound limit analysis of slabs with nonlinear yield criteria. Computers and Structures 2002; 80:2043-2057.
13. Krabbenhoft K, Damkilde L. A general nonlinear optimization algorithm for lower bound limit analysis. International Journal for Numerical Methods in Engineering 2003; 56:165-184.
14. Chen JS, Wu CT, Yoon S, You Y. A stabilized conforming nodal integration for Galerkin mesh-free methods. International Journal for Numerical Methods in Engineering 2001; 50:435-466.
15. Sze KY, Chen JS, Sheng N, Liu XH. Stabilized conforming nodal integration: exactness and variational justification. Finite Elements in Analysis and Design 2004; 41:147-171.
16. Wang D, Chen JS. Locking-free stabilized conforming nodal integration for meshfree Mindlin-Reissner plate formulation. Computer Methods in Applied Mechanics and Engineering 2004; 193:1065-1083.
17. Yoo JW, Moran B, Chen JS. Stabilized conforming nodal integration in the natural-element method. International Journal for Numerical Methods in Engineering 2004; 60:861-890.
18. Mosek. The MOSEK Optimization Toolbox for MATLAB Manual. Mosek ApS, version 5.0 edition, 2008. Available from: http://www.mosek.com.
19. Nielsen MP. Limit Analysis of Reinforced Concrete Slabs. Acta-Polytechnica: Denmark, Kobenhavn, 1964.
20. Nielsen MP. Limit Analysis and Concrete Plasticity. CRC Press: Boca Raton, 1998.
21. Wolfensberger R. Traglast und Optimale Bemessung von Platten. ETH: Zurich, Schweiz, 1964.
22. Belytschko T, Lu YY, Gu L. Element-free Galerkin methods. International Journal for Numerical Methods in Engineering 1994; 37:229-256.
23. Zienkiwicz OC, Taylor RL. The Finite Element Method, Volume 1: The Basis (5th edn). Butterworth, Heinemann: London, 2000.
24. Liu GR, Gu YT. An Introduction to Meshfree Methods and their Programming. Springer: Berlin, 2005.
25. Chen Y, Lee J, Eskandarian A. Meshless Methods in Solid Mechanics. Springer: Berlin, 2006.
26. Fraeijs de V.B. Displacement and equilibrium models in the finite element method. International Journal for Numerical Methods in Engineering 2001; 52:287-342; reprinted.
27. Fraeijs de V.B, Zienkiewicz OC. Strain-energy bounds in finite element analysis by slab analogy. Journal of Strain Analysis 1967; 2:265-271.
28. Duflot M, Nguyen-Dang H. Dual analysis by a meshless method. Communications in Numerical Methods in Engineering 2002; 18:621-631.
29. Chen JS, Wu CT, Belytschko T. Regularization of material instabilities by meshfree approximations with intrinsic length scales. International Journal for Numerical Methods in Engineering 2000; 47:1303-1322.
30. Zhu T, Atluri SN. A modified collocation method and a penalty formulation for enforcing the essential boundary conditions in the element free Galerkin method. Computational Mechanics 1998; 21:211-222.
31. Krabbenhoft K, Lyamin AV, Sloan SW. Formulation and solution of some plasticity problems as conic programs. International Journal of Solids and Structures 2007; 44:1533-1549.
32. Ciria H, Peraire J, Bonet J. Mesh adaptive computation of upper and lower bounds in limit analysis. International Journal for Numerical Methods in Engineering 2008; 75:899-944.
33. Makrodimopoulos A, Martin CM. Upper bound limit analysis using simplex strain elements and second-order cone programming. International Journal for Numerical and Analytical Methods in Geomechanics 2006; 31:835-865.
34. Braestrup MW. Yield line theory and concrete plasticity. Magazine of Concrete Research 2008; 60:549-553.
35. Fox EN. Limit analysis for plates: the exact solution for a clamped square plate of isotropic homogeneous material obeying the square yield criterion and loaded by uniform pressure. Philosophical Transactions of the Royal Society of London, Series A 1974; 277:121-155.
36. Andersen KD, Christiansen E, Overton ML. Computing limit loads by minimizing a sum of norms. SIAM Journal on Scientific Computing 1998; 19:1046-1062.