3-D bending analysis of thick functionally graded plate in different boundary conditions using Element-Free Galerkin (EFG) method

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Sahand university of technology

Abstract

In this paper, the Element-Free Galerkin (EFG) method is employed to obtain three dimensional static behavior of thick functionally graded plates. The Poisson’s ratio is taken to be constant and the Young’s modulus is considered to be graded through the thickness of plate by an exponential function. The shape function is calculated using the 3D moving least squares (MLS) approximation. Because the MLS approximation lacks the Kronecker delta function property, therefore the constrained Galerkin weak-form is used. The Lagrange multiplier method is employed to enforce the essential boundary condition. Effects of weight functions, nodal density and the dimensionless size of the support domain are investigated and favorable value for the dimensionless size of the support domain is calculated. Also a new trigonometric weight function is introduced. Effects of functionally grading index, dimensionless thickness and boundary conditions on the stress and deformation of the plate are investigated. Several examples are presented for thick functionally graded plates under static load. Also in order to verify the obtained results, they are compared with the results of other data reported in the literature. Numerical results indicate that the rate of convergence of the proposed method is higher than that of finite element method especially for stress calculation.

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References

[1] Belytschko T, Lu YY, Gu L (1994) Element-free Galerkin methods. Int J Numer Meth Eng 37(2): 229-256.
[2] Liu GR, Gu YT (2005) An introduction to meshfree methods and their programming. Springer Science & Business Media 145, 196, 237, 254.
[3] Kieback B, Neubrand A, Riedel H (2003) Processing techniques for functionally graded materials. Mat Sci Eng A-Struct 362(1): 81-106.
[4] Vaghefi R, Baradaran GH, Koohkan H (2010) Three-dimensional static analysis of thick functionally graded plates by using meshless local Petrov–Galerkin (MLPG) method. Eng Anal Bound Elem 34(6): 564-573.
[5] Ching HK, Yen SC (2005) Meshless local Petrov-Galerkin analysis for 2D functionally graded elastic solids under mechanical and thermal loads. Compos Part B-Eng, Vol. 36, No. 3, pp. 223-240,.
[6] Qian LF, Batra RC, Chen LM (2004) Analysis of cylindrical bending thermoelastic deformations of functionally graded plates by a meshless local Petrov–Galerkin method. Comput Mech 33(4): 263-273.
[7] Qian LF, Batra RC, Chen LM (2004) Static and dynamic deformations of thick functionally graded elastic plates by using higher-order shear and normal deformable plate theory and meshless local Petrov–Galerkin method. Compos Part B-Eng 35(6–8): 685-697.
[8] Ferreira AJM, Batra RC, Roque CMC, Qian LF, Martins PALS (2005) Static analysis of functionally graded plates using third-order shear deformation theory and a meshless method. Compos Struct 69(4): 449-457.
[9] Sladek J, Sladek V, Zhang C (2005) Stress analysis in anisotropic functionally graded materials by the MLPG method. Eng Anal Bound Elem 29(6): 597-609.
[10] Sladek J, Sladek V, Hellmich C, Eberhardsteiner J (2007) Analysis of thick functionally graded plates by local integral equation method. Commun Numer Meth En 23(8): 733-754.
[11] Gilhooley DF, Batra RC, Xiao JR, McCarthy MA, Gillespie JW (2007) Analysis of thick functionally graded plates by using higher-order shear and normal deformable plate theory and MLPG method with radial basis functions. Compos Struct 80(4): 539-552.
[12] Vaghefi R, Baradaran G, Koohkan H (2009) Three-dimensional static analysis of rectangular thick plates by using the meshless local Petrov—Galerkin method. P I Mech Eng C-J Mec 223(9): 1983-1996.
[13] Zhao X, Liew KM (2009) Geometrically nonlinear analysis of functionally graded plates using the element-free kp-Ritz method. Comput Method Appl M 198(33-36): 2796-2811.
[17] Zhu P, Zhang LW, Liew KM (2014) Geometrically nonlinear thermomechanical analysis of moderately thick functionally graded plates using a local Petrov–Galerkin approach with moving Kriging interpolation. Compos Struct 107: 298-314.
[18] Memar Ardestani M, Soltani B, Shams S (2014) Analysis of functionally graded stiffened plates based on FSDT utilizing reproducing kernel particle method. Compos Struct 112: 231-240.
[19] مرادی دستجردی ر، فروتن م، عبداللهی بکتاش س (1390) تحلیل استاتیکی استوانه­هایی از جنس مواد هدفمند ارتوتروپیک با طول کوتاه به روش بدون المان. فصلنامه علمی پژوهشی مهندسی مکانیک جامدات، سال چهارم، شماره اول.
[20] نظری م‌م.، شریعتی م، اسلامی م‌.، حسنی ب (1392)تحلیل بدون المان مواد مرکب هدفمند حاوی ترک تحت بارگذاری حرارتی. فصلنامه مکانیک هوافضا 16-1 : (4)9.
 [21] Srinivas S, Rao AK (1973) Flexure of thick rectangular plates. J Appl Mech-T ASME 40(1): 298-299.
Journal of Solid and Fluid Mechanics
Volume 6, Issue 2
July and August 2016
Pages 109-120

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