Lower-bound limit analysis by using the EFG method and non-linear programming

International Journal for Numerical Methods in Engineering

Volumn 74, Issue 3, 2008, Pages 391-415

  Chen, Shenshen ^a   Liu, Yinghua ^a   Cen, Zhangzhi ^a  

^a TSINGHUA UNIVERSITY   (China)

Author keywords

Complex method; EFG method; Limit analysis; Non linear programming; Self equilibrium stress

Indexed keywords

BOUNDARY ELEMENT METHOD; ELASTOPLASTICITY; FINITE ELEMENT METHOD; GALERKIN METHODS; ITERATIVE METHODS; NONLINEAR PROGRAMMING; STRESS ANALYSIS;

ELASTO-PLASTIC INCREMENTAL ANALYSIS; LIMIT ANALYSIS; SELF-EQUILIBRIUM STRESS;

LOAD LIMITS;

BOUNDARY ELEMENT METHOD; ELASTOPLASTICITY; FINITE ELEMENT METHOD; GALERKIN METHODS; ITERATIVE METHODS; LOAD LIMITS; NONLINEAR PROGRAMMING; STRESS ANALYSIS;

EID: 42049094182     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.2177     Document Type: Article

References (37)

1. Zienkiewicz OC. The Finite Element Method. McGraw-Hill: London, 1977.
2. Wunderlich W, Stein E, Bathe KJ (eds). Nonlinear Finite Element Analysis in Structural Mechanics. Springer: New York, 1981.
3. Brebbia CA, Walker S. Boundary Element Techniques in Engineering. Newnes, Butterworths: London, 1980.
4. Banerjee PK, Butterfield R. Boundary Element Methods in Engineering Science. McGraw-Hill: London, 1981.
5. Cohn MZ, Maier G, Grierson D. Engineering Plasticity by Mathematical Programming. Pergamon Press: New York, 1979.
6. Maier G, Munro J. Mathematical programming applications to engineering plastic analysis. Applied Mechanics Review 1982; 35:1631-1643.
7. Sloan SW, Kleeman PW. Upper bound limit analysis using discontinuous velocity fields. Computer Methods in Applied Mechanics and Engineering 1995; 127:293-314.
8. Liu YH, Cen ZZ, Xu BY. A numerical method for plastic limit analysis of 3D structure. International Journal of Solids and Structures 1995; 32:1645-1658.
9. Zhang XF, Liu YH, Zhao YN, Cen ZZ. Lower bound limit analysis by the symmetric Galerkin boundary element method and the complex method. Computer Methods in Applied Mechanics and Engineering 2002; 191:1967-1982.
10. Zhang XF, Liu YH, Cen ZZ. Boundary element methods for lower bound limit and shakedown analysis. Engineering Analysis with Boundary Elements 2004; 28:905-917.
11. Ponter ARS, Carter KF. Limit state solutions based upon linear elastic solutions with a spatially varying elastic modulus. Computer Methods in Applied Mechanics and Engineering 1997; 140:237-258.
12. Capsoni A, Corradi L. A finite element formulation of the rigid-plastic limit analysis problem, International Journal for Numerical Methods in Engineering 1997; 40:2063-2086.
13. Christiansen E, Andersen KD. Computation of collapse states with von Mises type yield condition. International Journal for Numerical Methods in Engineering 1999; 46:1185-1202.
14. Capsoni A, Corradi L, Vena P. Limit analysis of orthotropic structures based on Hill's yield condition. International Journal of Solids and Structures 2001; 38:3945-3963.
15. Corradi L, Luzzi L, Vena P. Finite element limit analysis of anisotropic structures. Computer Methods in Applied Mechanics and Engineering 2006; 195:5422-5436.
16. Belytschko T, Lu YY, Gu L. Element-free Galerkin methods. International Journal for Numerical Methods in Engineering 1994; 37:229-256.
17. Lu YY, Belytschko T, Gu L. A new implementation of the element-free Galerkin method. Computer Methods in Applied Mechanics and Engineering 1994; 113:397-414.
18. Atluri SN, Zhu T. A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics. Computational Mechanics 1998; 22:117-127.
19. Gu YT, Liu GR. A meshless local Petrov-Galerkin (MLPG) method for free and forced vibration analyses for solids. Computational Mechanics 2001; 27:188-198.
20. Liu WK, Jun S, Zhang YF. Reproducing kernel particle methods. International Journal for Numerical Methods in Fluids 1995; 20:1081-1106.
21. Gingold RA, Moraghan JJ. Smoothed particle hydrodynamics: theory and applications to non-spherical stars. Monthly Notices of the Royal Astronomical Society 1977; 181:375-389.
22. Krysl P, Belytschko T. Analysis of thin plates by the element-free Galerkin method. Computational Mechanics 1995; 17:26-35.
23. Belytschko T, Tabbara M. Dynamic fracture using element-free Galerkin methods. International Journal for Numerical Methods in Engineering 1996; 39:923-938.
24. Martin JB. Plasticity: Foundation and General Results. MIT Press: Cambridge, MA, 1975.
25. Stein E, Zhang G. Shakedown with nonlinear strain-hardening including structural computation using finite element method. International Journal of Plasticity 1992; 8:1-31.
26. Stein E, Zhang G, Huang Y. Modeling and computation of shakedown problems for nonlinear hardening materials. Computer Methods in Applied Mechanics and Engineering 1993; 103:247-272.
27. Nayroles B, Touzot G, Villon P. Generalizing the finite element method: diffuse approximation and diffuse elements. Computational Mechanics 1992; 10:307-318.
28. Wang XC. Finite Element Method. Tsinghua University Press: China, 2003 (in Chinese).
29. Xi SL, Zhao FZ. Computational Methods of Optimization. Science and Technology Press of Shanghai: China, 1983 (in Chinese).
30. Belytschko T. Plane stress shakedown analysis by finite elements. International Journal of Mechanical Sciences 1972; 14:619-625.
31. Corradi L, Zavelani A. A linear programming approach to shakedown analysis of structures. Computer Methods in Applied Mechanics and Engineering 1974; 3:37-53.
32. Nguyen DH, Palgen L. Shakedown analysis by displacement method and equilibrium finite elements. Proceedings of SMIRT-5, Berlin, 1979; Paper L3/3.
33. Genna F. A nonlinear inequality, finite element approach to the direct computation of shakedown load safety factors. International Journal of Mechanical Sciences 1988; 30:769-789.
34. Gross-Weege J. On the numerical assessment of the safety factor of elasto-plastic structures under variable loading. International Journal of Mechanical Sciences 1997; 39:417-433.
35. Chen HF, Liu YH, Cen ZZ, Xu BY. On the solution of limit load and reference stress of 3-D structures under multi-loading systems. Engineering Structures 1999; 21:530-537.
36. Belytschko T, Hodge PG. Plane stress limit analysis by finite element. Journal of the Engineering Mechanics Division 1970; 96:931-944.
37. Zhang PX, Lu MW, Hwang KC. A mathematical programming algorithm for limit analysis. Acta Mechanica Sinica 1991; 7:267-274.