A combined approach of the MLPG method and nonlinear programming for lower-bound limit analysis

CMES - Computer Modeling in Engineering and Sciences

Volumn 28, Issue 1, 2008, Pages 39-55

  Chen, S S ^a   Liu, Y H ^a   Cen, Z Z ^a  

^a TSINGHUA UNIVERSITY   (China)

Author keywords

Limit analysis; MLPG method; Natural neighbour interpolation; Non linear programming; Self equilibrium stress

Indexed keywords

BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; CHLORINE COMPOUNDS; DYNAMIC PROGRAMMING; LINEAR PROGRAMMING; LINEARIZATION; MATHEMATICAL PROGRAMMING; NONLINEAR PROGRAMMING; PLASTICS; RELIABILITY ANALYSIS; SOLUTIONS; TECHNOLOGY;

BASIS VECTORS; COMPLEX METHODS; ELASTO-PLASTIC; ENGINEERING APPLICATIONS; ESSENTIAL BOUNDARY CONDITIONS; INCREMENTAL ANALYSIS; ITERATION PROCEDURE; LIMIT ANALYSES; LIMIT ANALYSIS; LIMIT LOADS; LINEAR COMBINATION; LOCAL WEAK FORMS; LOWER-BOUND THEOREM; MESHLESS; MESHLESS LOCAL PETROV-GALERKIN METHOD; MLPG METHOD; MLPG METHODS; MONOTONICALLY; NATURAL NEIGHBOUR INTERPOLATION; NUMERICAL EXAMPLES; PLASTIC COLLAPSE; PLASTIC LIMIT ANALYSIS; SELF-EQUILIBRIUM; SELF-EQUILIBRIUM STRESS; SOLUTION PROCEDURES; SUB-PROBLEMS; TRIAL FUNCTIONS;

RELIABILITY;

EID: 49149109642     PISSN: 15261492     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (38)

1. Andreaus, U.; Batra, R. C.; Porflri, M. (2005): Vibrations of cracked Euler-Bernoulli beams using meshless local Petrov-Galerkin (MLPG) method, CMES: Computer Modeling in Engineering & Sciences, vol. 9, no. 2, pp. 111-131.
2. Atluri, S. N.; Zhu, T. (1998): A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics, Computational Mechanics, vol. 22, pp. 117-127.
3. Atluri, S. N.; Zhu, T. (2000): The meshless local Petrov-Galerkin (MLPG) approach for solving problems in elasto-statics, Computational Mechanics, vol. 25, pp. 169-179.
4. Belytschko, T. (1972): Plane stress shakedown analysis by finite elements, International Journal for Numerical Methods in Engineering, vol. 14, pp. 619-675.
5. Belytschko, T.; Lu, Y. Y.; Gu, L. (1994): Element free Galerkin methods, International Journal for Numerical Methods in Engineering, vol. 37, pp. 229-256.
6. Cai, Y. C.; Zhu, H. H. (2004): A meshless local natural neighbour interpolation method for stress analysis of solids, Engineering Analysis with Boundary Elements, vol. 28, pp. 607-613.
7. Chen, H. F.; Liu, Y. H.; Cen, Z. Z.; Xu, B. Y. (1999): On the solution of limit load and reference stress of 3-D structures under multi-loading systems, Engineering Structures, vol. 21, pp. 530-537.
8. Ching, H. K.; Batra, R. C. (2001): Determination of crack tip fields in linear elastostatics by the meshless local Petrov-Galerkin (MLPG) method, CMES: Computer Modeling in Engineering & Sciences, vol. 2, no. 2, pp. 273-290.
9. Corradi, L.; Luzzi, L.; Vena, P. (2006): Finite element limit analysis of anisotropic structures, Computer Methods in Applied Mechanics and Engineering, vol. 195, pp. 5422-5436.
10. Corradi, L.; Zavelani, A. (1974): A linear programming approach to shakedown analysis of structures, Computer Methods in Applied Mechanics and Engineering, vol. 3, pp. 37-53.
11. Conn, M. Z.; Maier, G.; Grierson, D. (1979): Engineering Plasticity by Mathematical Programming, Pergamon Press, New York.
12. Genna, F. (1988): A nonlinear inequality, finite element approach to the direct computation of shakedown load safety factors, International Journal of Mechanical Sciences, vol. 30, no. 10, 769-789.
13. Gingold, R. A.; Moraghan, J. J. (1977): Smoothed particle hydrodynamics: theory and applications to non-spherical stars, Monthly Notices of the Royal Astronomical Society, vol. 181, pp. 375-389.
14. Green, P. J.; Sibson, R. R. (1978): Computing Dirichlet tessellations in the plane, Computer Journal, vol. 21, pp. 168-173.
15. Gross-Weege, J. (1997): On the numerical assessment of the safety factor of elasto-plastic structures under variable loading, International Journal of Mechanical Sciences, vol. 39, no. 4, pp. 417-433.
16. Gu, Y. T.; Liu, G. R. (2001): A meshless local Petrov-Galerkin (MLPG) method for free and forced vibration analyses for solids, Computational Mehanics, vol. 27, pp. 188-198.
17. Han, Z. D.; Atluri, S. N. (2004): Meshless local Petrov-Galerkin (MLPG) approaches for solving 3D problems in elasto-statics, CMES: Computer Modeling in Engineering & Sciences, vol. 6, no. 2, pp. 169-188.
18. Han, Z. D.; Liu, H. T.; Rajendran, A. M.; Atluri, S. N. (2006): The applications of meshless local Petrov-Galerkin (MLPG) approaches in high-speed impact, penetration and perforation problems, CMES: Computer Modeling in Engineering & Sciences, vol. 14, no. 2, pp. 119-128.
19. Han, Z. D.; Rajendran, A. M.; Atluri, S. N. (2005): Meshless local Petrov-Galerkin (MLPG) approaches for solving nonlinear problems with large deformation and rotation, CMES: Computer Modeling in Engineering & Sciences, vol. 10, no. 1, pp. 1-12.
20. Johnson, J. N.; Owen, J. M. (2007): A meshless local Petrov-Galerkin method for magnetic diffusion in non-magnetic conductors, CMES: Computer Modeling in Engineering & Sciences, vol. 22, no. 3, pp. 165-188.
21. Lin, H.; Atluri, S. N. (2001): The meshless local Petrov-Galerkin (MLPG) method for solving incompressible Navier-stokes equations, CMES: Computer Modeling in Engineering & Sciences, vol. 2, no. 2, pp. 117-142.
22. Liu, W. K.; Jun, S.; Zhang, Y. F. (1995): Reproducing kernel particle methods, International Journal for Numerical Methods in Fluids, vol. 20, pp. 1081-1106.
23. Liu, Y. H.; Zhang, X. F.; Cen, Z. Z. (2005): Lower bound shakedown analysis by the symmetric Galerkin boundary element method, Internationaljournal of Plasticity, vol. 21, pp. 21-42.
24. Ma, Q. W. (2005): MLPG method based on Rankine source solution for simulating nonlinear water waves, CMES: Computer Modeling in Engineering & Sciences, vol. 9, no. 2, pp. 193-209.
25. Maier, G.; Munro, J. (1982): Mathematical programming applications to engineering plastic analysis, Applied Mechanics Review, vol. 35, no. 12, pp.1631-1643.
26. Makrodimopoulos, A.; Martin, C. M. (2006): Lower bound limit analysis of cohesive-frictional materials using second-order cone programming, International Journal for Numerical Methods in Engineering, vol. 66, pp. 604-634.
27. Martin, J. B. (1975): Plasticity: Foundation and General results, MIT Press, Cambridge, MA.
28. Most, T. (2007): A natural neighbour-based moving least-squares approach for the element-free Galerkin method, International Journal for Numerical Methods in Engineering, vol. 71, pp. 224-252.
29. Nguyen, D. H.; Palgen, L. (1979): Shakedown analysis by displacement method and equilibrium finite elements, Proceedings of SMIRT-5, Berlin, Paper L3/3.
30. Pisano, A. A.; Fuschi, P. (2007): A numerical approach for limit analysis of orthotropic composite laminates, International Journal for Numerical Methods in Engineering, vol. 70, pp. 71-93.
31. Stein, E.; Zhang, G. (1992): Shakedown with nonlinear strain-hardening including structural computation using finite element method, International Journal of Plasticity, vol. 8, pp. 1-31.
32. Sukumar, N.; Moran, B.; Belytschko, T. (1998): The natural element method in solid mechanics, International Journal for Numerical Methods in Engineering, vol. 43, pp. 839-887.
33. Sukumar, N.; Moran, B.; Semenov, A. Yu.; Belikov, V. V. (2001): Natural neighbour Galerkin methods, International Journal for Numerical Methods in Engineering, vol. 50, pp. 1-27.
34. Wang, K.; Zhou, S. J.; Shan, G. J. (2005): The natural neighbour Petrov-Galerkin method for elasto-statics, International Journal for Numerical Methods in Engineering, vol. 63, pp.1126-1145.
35. Xiao, J. R. (2004): Local Heaviside weighted MLPG meshless method for two-dimensional solids using compactly supported radial basis functions, Computer Methods in Applied Mechanics and Engineering, vol. 193, pp. 117-138.
36. Xi, S. L.; Zhao, F. Z. (1983): Computational Methods of Optimization, Science and Technology Press of Shanghai, China (in Chinese).
37. Zhang, X. F.; Liu, Y. H.; Zhao, Y. N.; Cen, Z. Z. (2002): Lower bound limit analysis by the symmetric Galerkin boundary element method and the Complex method, Computer Methods in Applied Mechanics and Engineering, vol. 191, pp. 1967-1982.
38. Zhang, X. F.; Liu, Y. H.; Cen, Z. Z. (2004): Boundary element methods for lower bound limit and shakedown analysis, Engineering Analysis with Boundary Elements, vol. 28, pp. 905-917.