Eliminating shear-locking in meshless methods: A critical overview and a new framework for structural theories

Computational Methods in Applied Sciences

Volumn 5, Issue , 2007, Pages 123-145

  Tiago, Carlos ^a   Leitão, Vitor M A ^a  

^a INSTITUTO SUPERIOR TÉCNICO   (Portugal)

Author keywords

Meshless approximations; Shear locking; Structural models

Indexed keywords

EID: 84964049285     PISSN: 18713033     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-1-4020-6095-3_7     Document Type: Conference Paper

References (27)

1. S. N. Atluri, H.-G. Kim, and J. Y. Cho. A critical assessment of the truly Meshless Local Petrov-Galerkin (MLPG), and Local Boundary Integral Equation (LBIE) methods. Computational Mechanics, 24(5): 348-372, 1999.
2. S. Beissel and T. Belytschko. Nodal integration of the element-free Galerkin method. Computer Methods in Applied Mechanics and Engineering, 139(1-4): 49-74, 1996.
3. T. Belytschko, Y. Y. Lu, and L. Gu. Element-Free Galerkin Methods. International Journal for Numerical Methods in Engineering, 37(2): 229-256, 1994.
4. J. Y. Cho and S. N. Atluri. Analysis of shear flexible beams, using the meshless local Petrov-Galerking method, based on a locking-free formulation. Engineering Computations, 18(1-2): 215-240, 2001.
5. S. De and K.-J. Bathe. Displacement/pressure mixed interpolation in the method of finite spheres. International Journal for Numerical Methods in Engineering, 51(3): 275-292, 2001.
6. P. de T. R. Mendonca, C. S. de Barcellos, and A. Duarte. Investigations on the hp-cloud method by solving Timoshenko beam problems. Computational Mechanics, 25(2-3): 286-295, 2000.
7. J. Dolbow and T. Belytschko. Volumetric locking in the element free Galerkin method. International Journal for Numerical Methods in Engineering, 46(6): 925-942, 1999.
8. B. M. Donning and W. K. Liu. Meshless methods for shear-deformable beams and plates. Computer Methods in Applied Mechanics and Engineering, 152(1-2): 47-71, 1998.
9. C. A. Duarte and J. Tinsley Oden. H-p clouds - An h-p meshless method. Numerical Methods for Partial Differential Equations, 12(6): 673-705, 1996.
10. O. Garcia, E. A. Fancello, C. S. de Barcellos, and C. A. Duarte. hp-Clouds in Mindlin's thick plate model. International Journal for Numerical Methods in Engineering, 47(8): 1381-1400, 2000.
11. T. J. R. Hughes. The Finite Element Method: Linear Static and Dynamic Finite Element Analysis. Dover Publications, Mineola, NY, 2000.
12. T. J. R. Hughes and T. E. Tezduyar. Finite elements based upon mindlin plate theory with particular reference to the four-node isoparametric element. Journal of Applied Mechanics, Transactions of the ASME, 48(3): 587-596, 1981.
13. W. Kanok-Nukulchai, W. Barry, K. S.-Yasoontorn, and P. H. Bouillard. On elimination of shear locking in the element-free Galerkin method. International Journal for Numerical Methods in Engineering, 52(7): 705-725, 2001.
14. P. Lancaster and K. Šalkauskas. Surfaces genarated by moving least squares methods. Mathematics of Computation, 37(155): 141-158, 1981.
15. W. K. Liu, S. Jun, and Y. F. Zhang. Reproducing kernel particle methods. International Journal for Numerical Methods in Engineering, 20(8-9): 1081-1106, 1995.
16. W.-K. Liu, S. Li, and T. Belytschko. Moving least-square reproducing kernel methods (I): Methodology and convergence. Computer Methods in Applied Mechanics and Engineering, 143(1-2): 113-154, 1997.
17. Y. Y. Lu, T. Belytschko, and L. Gu. A new implementation of the element free Galerkin method. Computer Methods in Applied Mechanics and Engineering, 113(3-4): 397-414, 1994.
18. D. S. Malkus and T. J. R. Hughes. Mixed finite element methods-reduced and selective integration techniques: A unification of concepts. Computer Methods in Applied Mechanics and Engineering, 15(1): 63-81, 1978.
19. W. D. Pilkey and W. Wunderlich. Mechanics of Structures: Variational and Computational Methods, CRC Press, second edition, 2003.
20. G. Prathap. The Finite Element Method in Structural Mechanics: Principles and Practice of Design of Field-Consistent Elements for Structural and Solid Mechanics, Solid Mechanics and Its Applications, Vol. 24, Kluwer Academic Publishers, 1993.
21. J. C. Simo and M. S. Rifai. A class of mixed assumed strain methods and the method of incompatible modes. International Journal for Numerical Methods in Engineering, 29(8): 1595-1638, 1990.
22. N. Sukumar, B. Moran, and T. Belytschko. The natural element method in solid mechanics. International Journal for Numerical Methods in Engineering, 43(5): 839-887, 1998.
23. C. Tiago and V. Leitao. On the procedures to eliminate shear locking in meshless methods. In V. Leitao, C. Alves, and C. Duarte (Eds), ECCOMAS Thematic Conference on Meshless Methods, Lisbon, Portugal, 2005, pp. A14.1-A14.8.
24. C. Tiago and P. Pimenta. Geometrically exact analysis of space frames by a meshless method. In V. Leitao, C. Alves, and C. Duarte (Eds), ECCOMAS Thematic Conference on Meshless Methods, Lisbon, Portugal, 2005, pp. C44.1-C44.8
25. C. Tiago and P. M. Pimenta. Geometrically exact analysis of shells by a meshless approach. In C. A. Mota Soares (Ed.), Third European Conference on Computational Mechanics - Solids, Structures and Coupled Problems in Engineering, Lisbon, Portugal, June 2006.
26. D. Wang and J.-S. Chen. Locking-free stabilized conforming nodal integration for meshfree Mindlin-Reissner plate formulation. Computer Methods in Applied Mechanics and Engineering, 193(12-14): 1065-1083, 2004.
27. O. C. Zienkiewicz, R. L. Taylor, and J. M. Too. Reduced integration technique in general analysis of plates and shells. International Journal for Numerical Methods in Engineering, 3(2): 275-290, 1971.