Interaction and multiscale mechanics

  • 제1권3호
  • /
  • Pages.339-355
  • /
  • 2008
  • /
  • 1976-0426(pISSN)
  • /
  • 2092-6200(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

An efficient Galerkin meshfree analysis of shear deformable cylindrical panels

  • 투고 : 2008.01.30
  • 심사 : 2008.07.08
  • 발행 : 2008.09.25
⟨ 이전 논문 다음 논문 ⟩

초록

A Galerkin meshfree method is presented for analyzing shear deformable cylindrical panels. Based upon the analogy between the cylindrical panel and the curved beam a pure bending mode for cylindrical panel is rationally constructed. The meshfree approximation employed herein is characterized by an enhanced moving least square or reproducing kernel basis function that can exactly represent the pure bending mode and thus meets the requirement of Kirchhoff mode reproducing condition. The variational form is discretized using the efficient stabilized conforming nodal integration with a smoothed nodal gradient based curvature. The resulting meshfree formulation satisfies the integration constraint for bending exactness. Moreover, it is shown here that the smoothed gradient preserves several desired properties which are valid for the standard gradient obtained by direct differentiation, such as partition of nullity and reproduction of a constant strain field. The efficacy of the proposed approach is demonstrated by two benchmark cylindrical panel examples.

키워드

과제정보

연구 과제 주관 기관 : National Natural Science Foundation of China

참고문헌

  1. Lancaster, P. and Salkauskas, K. (1981), "Surfaces generated by moving least squares methods", Mathematics of Computation, 37, 141-158. https://doi.org/10.1090/S0025-5718-1981-0616367-1
  2. Belytschko, T., Lu, Y.Y. and Gu, L. (1994), "Element-free Galerkin methods", Int. J. Numer. Methods Eng., 37, 229-256. https://doi.org/10.1002/nme.1620370205
  3. Liu, W. K., Jun, S. and Zhang, Y.F. (1995), "Reproducing kernel particle methods", Int. J. Numer. Methods Fluids, 20, 1081-1106. https://doi.org/10.1002/fld.1650200824
  4. Chen, J.S., Pan, C., Wu, C.T. and Liu, W.K. (1996), "Reproducing kernel particle methods for large deformation analysis of nonlinear structures", Comput. Methods Appl. Mech. Eng., 139, 195-227. https://doi.org/10.1016/S0045-7825(96)01083-3
  5. Krysl, P. and Belytschko, T. (1996), "Analysis of thin shells by the element-free Galerkin method", Int. J. Solids Struct., 33, 3057-3080. https://doi.org/10.1016/0020-7683(95)00265-0
  6. Li, S., Hao W. and Liu, W.K. (2000), "Numerical simulations of large deformation of thin shell structures using meshfree method", Comput. Mech., 25, 102-116. https://doi.org/10.1007/s004660050463
  7. Li, S. and Liu, W.K. (2004), Meshfree Particle Methods, Springer, Germany.
  8. Hallquist, J.O. (2003), "Current and future developments of LS-DYNA II", Proceeding of 4th European LSDYNA Users Conference, ULM, Germany, May.
  9. Beissel, S. and Belytschko, T. (1996), "Nodal integration of the element-free Galerkin method", Comput. Methods Appl. Mech. Eng., 139, 49-74. https://doi.org/10.1016/S0045-7825(96)01079-1
  10. Dyka, C.T. and Ingel, R.P. (1995), "An approach for tensile instability in smoothed particle hydrodynamics", Comput. Struct., 57, 573-580. https://doi.org/10.1016/0045-7949(95)00059-P
  11. Randles, P.W. and Libersky, L.D. (2000), "Normalized SPH with stress points", Int. J. Numer. Methods Eng., 48, 1445-1462. https://doi.org/10.1002/1097-0207(20000810)48:10<1445::AID-NME831>3.0.CO;2-9
  12. Rabczuk, T., Belytschko, T. and Xiao, S.P. (2004), "Stable particle methods based on Lagrangian kernels", Comput. Methods Appl. Mech. Eng., 193, 1035-1063. https://doi.org/10.1016/j.cma.2003.12.005
  13. Chen, J.S., Wu, C.T., Yoon, S. and You, Y. (2001), "A stabilized conforming nodal integration for Galerkin meshfree methods", Int. J Numer. Methods Eng., 50, 435-466. https://doi.org/10.1002/1097-0207(20010120)50:2<435::AID-NME32>3.0.CO;2-A
  14. Chen, J.S., Yoon, S. and Wu, C.T. (2002), "Nonlinear version of stabilized conforming nodal integration for Galerkin meshfree methods", Int. J. Numer. Methods Eng., 53, 2587-2615. https://doi.org/10.1002/nme.338
  15. Chen, J.S., Wang, D. and Dong, S.B. (2004), "An extended meshfree method for boundary value problems", Comput. Methods Appl. Mech. Eng., 193, 1085-1103. https://doi.org/10.1016/j.cma.2003.12.007
  16. Wang, D. and Chen, J.S. (2004), "Locking-free stabilized conforming nodal integration for meshfree Mindlin- Reissner plate formulation", Comput. Methods Appl. Mech Eng., 193, 1065-1083. https://doi.org/10.1016/j.cma.2003.12.006
  17. Wang, D., Dong, S.B. and Chen, J.S. (2006), "Extended meshfree analysis of transverse and inplane loading of a laminated anisotropic plate of general planform geometry", Int. J. Solids Struct., 43, 144-171. https://doi.org/10.1016/j.ijsolstr.2005.03.068
  18. Wang, D. and Chen, J.S. (2004), "Constrained reproducing kernel formulation for shear deformable shells", Proceeding of the 6th World Congress on Computational Mechanics, Beijing, China, September.
  19. Wang, D. and Chen, J.S. (2006), "A locking-free meshfree curved beam formulation with the stabilized conforming nodal integration", Comput. Mech., 39, 83-90. https://doi.org/10.1007/s00466-005-0010-0
  20. Chen, J.S. and Wang, D. (2006), "A constrained reproducing kernel particle formulation for shear deformable shell in Cartesian coordinates", Int. J. Numer. Methods Eng., 68, 151-172. https://doi.org/10.1002/nme.1701
  21. Wang, D. (2006), "A stabilized conforming integration procedure for Galerkin meshfree analysis of thin beam and plate", Proceeding of the 10th Enhancement and Promotion of Computational Methods in Engineering and Science (EPMESC-X), Sanya, China, August.
  22. Wang, D. and Chen, J.S. (2008), "A Hermite reproducing kernel approximation for thin plate analysis with sub domain stabilized conforming integration", Int. J. Numer. Methods Eng., 74, 368-390. https://doi.org/10.1002/nme.2175
  23. Timoshenko, S.P. and Woinowsky-Krieger, S. (1959), Theory of Plates and Shells (2nd edn), McGraw-Hill, New York.
  24. Simo, J.C. and Hughes, T.J.R. (1985), "On the variational foundation of assumed strain method", J. Appl. Mech., 53, 51-54.
  25. MacNeal, R.H. and Harder, R.L. (1985), "A proposed standard set of problems to test finite element accuracy", Finite Elements in Analysis and Design, 1, 3-20. https://doi.org/10.1016/0168-874X(85)90003-4
  26. Liu, W.K., Law S.E., Lam, D. and Belytschko, T. (1986), "Resultant stress degenerated shell elements", Comput. Methods Appl. Mech. Eng., 55, 259-300. https://doi.org/10.1016/0045-7825(86)90056-3
  27. Koziey, B.L. and Mirza, F.A. (1997), "Consistent thick shell element", Comput. Struct., 65, 531-549. https://doi.org/10.1016/S0045-7949(96)00414-2
  28. Simo, J.C., Fox, D.D. and Rifai M.S. (1989), "On a stress resultant geometrical exact shell model. Part II: the linear theory; computational aspects", Comput. Methods Appl. Mech. Eng., 73, 53-92. https://doi.org/10.1016/0045-7825(89)90098-4
  29. Noguchi, H., Hawashima, T. and Miyamura, T. (2000), "Element free analysis of shell and spatial structures", Int. J. Numer. Methods Eng., 47, 1215-1240. https://doi.org/10.1002/(SICI)1097-0207(20000228)47:6<1215::AID-NME834>3.0.CO;2-M

피인용 문헌

  1. Three dimensional efficient meshfree simulation of large deformation failure evolution in soil medium vol.54, pp.3, 2011, https://doi.org/10.1007/s11431-010-4287-7
  2. A Circumferentially Enhanced Hermite Reproducing Kernel Meshfree Method for Buckling Analysis of Kirchhoff–Love Cylindrical Shells vol.15, pp.06, 2015, https://doi.org/10.1142/S0219455414500904
  3. Reproducing kernel based evaluation of incompatibility tensor in field theory of plasticity vol.1, pp.4, 2008, https://doi.org/10.12989/imm.2008.1.4.423
  4. Dispersion and transient analyses of Hermite reproducing kernel Galerkin meshfree method with sub-domain stabilized conforming integration for thin beam and plate structures vol.48, pp.1, 2011, https://doi.org/10.1007/s00466-011-0580-y
  5. A GALERKIN MESHFREE METHOD WITH STABILIZED CONFORMING NODAL INTEGRATION FOR GEOMETRICALLY NONLINEAR ANALYSIS OF SHEAR DEFORMABLE PLATES vol.08, pp.04, 2011, https://doi.org/10.1142/S0219876211002769
  6. A meshfree adaptive procedure for shells in the sheet metal forming applications vol.6, pp.2, 2013, https://doi.org/10.12989/imm.2013.6.2.137
  7. A Boundary Enhancement for the Stabilized Conforming Nodal Integration of Galerkin Meshfree Methods vol.12, pp.02, 2015, https://doi.org/10.1142/S0219876215500097
  8. Free vibration analysis of thin plates using Hermite reproducing kernel Galerkin meshfree method with sub-domain stabilized conforming integration vol.46, pp.5, 2010, https://doi.org/10.1007/s00466-010-0511-3
  9. Concrete fragmentation modeling using coupled finite element - meshfree formulations vol.6, pp.2, 2013, https://doi.org/10.12989/imm.2013.6.2.173
  10. An efficient nesting sub-domain gradient smoothing integration algorithm with quadratic exactness for Galerkin meshfree methods vol.298, 2016, https://doi.org/10.1016/j.cma.2015.10.008
  11. A Moving Kriging Interpolation Meshfree Method Based on Naturally Stabilized Nodal Integration Scheme for Plate Analysis pp.1793-6969, 2018, https://doi.org/10.1142/S0219876218501001
  12. Improved Element-Free Galerkin method (IEFG) for solving three-dimensional elasticity problems vol.3, pp.2, 2008, https://doi.org/10.12989/imm.2010.3.2.123
  13. Three-dimensional free vibration analysis of functionally graded fiber reinforced cylindrical panels using differential quadrature method vol.37, pp.5, 2008, https://doi.org/10.12989/sem.2011.37.5.529
  14. A novel meshfree model for buckling and vibration analysis of rectangular orthotropic plates vol.39, pp.4, 2008, https://doi.org/10.12989/sem.2011.39.4.579