A three-dimensional boundary element stress and bending analysis of transversely/longitudinally graded plates with circular cutouts under biaxial loading.

*(English)*Zbl 1406.74075Summary: In the present paper, a full three-dimensional graded boundary element model adequate for elastostatic response investigation of heterogeneous plates fabricated from functionally graded materials (FGMs) with circular cutouts is presented. The local volume fractions of the constituent materials vary continuously in the transverse or longitudinal direction according to an exponential law. In contrast to all of the available works, influence of the bending-extension coupling due to asymmetric transverse distribution of the material properties is considered under a biaxial loading. The available works have used the plane stress assumption. A numerical implementation of Somigliana identity for three-dimensional elasticity of the isotropic heterogeneous plates is represented implicitly. On the basis of the constitutive and governing equations of the FGM plate and the weighted residual technique, an effective computational formulation is developed for the heterogeneous isotropic solid models. Verification is accomplished through comparisons made with results of ANSYS software for homogeneous models. Influence of the location of the cutout, effects of the distance from the boundary, and effects of the load ratio have also been studied and discussed in detail.

##### MSC:

74B05 | Classical linear elasticity |

74K20 | Plates |

74S15 | Boundary element methods applied to problems in solid mechanics |

##### Keywords:

functionally graded boundary element; three-dimensional elasticity; plate with circular cutout
PDF
BibTeX
XML
Cite

\textit{H. Ashrafi} et al., Eur. J. Mech., A, Solids 42, 344--357 (2013; Zbl 1406.74075)

Full Text:
DOI

**OpenURL**

##### References:

[1] | Aliabadi, M. H.; Wen, P. H., Boundary element methods in engineering and sciences, (2011), Imperial College Press London · Zbl 1283.65001 |

[2] | Asemi, K.; Akhlaghi, M.; Salehi, M., Dynamic analysis of thick short length FGM cylinders, Meccanica, 47, 1441-1453, (2012) · Zbl 1293.74158 |

[3] | Asgari, M.; Akhlaghi, M., Natural frequency analysis of 2D-FGM thick hollow cylinder based on three-dimensional elasticity equations, European Journal of Mechanics - A/Solids, 30, 72-81, (2011) · Zbl 1261.74016 |

[4] | Ashrafi, H.; Asemi, K.; Shariyat, M.; Salehi, M., Two-dimensional modeling of heterogeneous structures using graded finite element and boundary element methods, Meccanica, 48, 663-680, (2013) |

[5] | Chan, Y. S.; Gray, L. J.; Kaplan, T.; Paulino, G. H., Green’s function for a two-dimensional exponentially graded elastic medium, Proceedings of the Royal Society A, 460, 1689-1706, (2004) · Zbl 1095.74500 |

[6] | Chaves, E. W.V.; Fernandes, G. R.; Venturini, W. S., Plate bending boundary element formulation considering variable thickness, Engineering Analysis with Boundary Elements, 23, 405-418, (1999) · Zbl 0956.74068 |

[7] | Criado, R.; Gray, L. J.; Mantic, V.; Paris, F., Green’s function evaluation for three-dimensional exponentially graded elasticity, International Journal for Numerical Methods in Engineering, 74, 1560-1591, (2008) · Zbl 1159.74444 |

[8] | Criado, R.; Ortiz, J. E.; Mantic, V., Boundary element analysis of three-dimensional exponentially graded isotropic elastic solids, CMES - Computer Modeling in Engineering and Sciences, 22, 151-164, (2007) · Zbl 1184.74072 |

[9] | Croce, L. D.; Venini, P., Finite elements for functionally graded Reissner-Mindlin plates, Computer Methods in Applied Mechanics and Engineering, 193, 705-725, (2004) · Zbl 1106.74408 |

[10] | De Paiva, J. B.; Aliabadi, M. H., Bending moments at interfaces of thin zoned plates with discrete thickness by the boundary element method, Engineering Analysis with Boundary Elements, 28, 747-751, (2004) · Zbl 1130.74484 |

[11] | Deb Nath, S. K.; Wong, C. H.; Kim, S.-G., A finite-difference solution of boron/epoxy composite plate with an internal hole subjected to uniform tension/displacements using displacement potential approach, International Journal of Mechanical Sciences, 58, 1-12, (2012) |

[12] | Kashtalyan, M., Three-dimensional elasticity solution for bending of functionally graded plates, European Journal of Mechanics - A/Solids, 23, 853-864, (2004) · Zbl 1058.74569 |

[13] | Kubair, D. V.; Bhanu-Chandar, B., Stress concentration factor due to a circular hole in functionally graded panels under uniaxial tension, International Journal of Mechanical Sciences, 50, 732-742, (2008) · Zbl 1264.74075 |

[14] | Leme, S. P.L.; Aliabadi, M. H., Dual boundary element method for dynamic analysis of stiffened plate, Theoretical and Applied Fracture Mechanics, 57, 55-58, (2012) |

[15] | Leonetti, L.; Mazza, M.; Aristodemo, M., A symmetric boundary element model for the analysis of Kirchhoff plates, Engineering Analysis with Boundary Elements, 33, 1-11, (2009) · Zbl 1181.74146 |

[16] | Miyamoto, Y.; Kaysser, W. A.; Rabin, B. H., Functionally graded materials: design, processing and applications, (1999), Kluwer Academic Press Dordrecht, Netherlands |

[17] | Mohammadi, M.; Dryden, J. R.; Jiang, L., Stress concentration around a hole in a radially inhomogeneous plate, International Journal of Solids and Structures, 48, 483-491, (2011) · Zbl 1236.74092 |

[18] | Paris, F.; Canas, J., Boundary element method, (1997), Oxford University Press New York |

[19] | Singha, M. K.; Prakash, T.; Ganapathi, M., Finite element analysis of functionally graded plates under transverse load, Finite Elements in Analysis and Design, 47, 453-460, (2011) |

[20] | Suresh, S.; Mortensen, A., Functionally graded materials, (1998), Institute of Materials, IOM Communications London |

[21] | Sutradhar, A.; Paulino, G. H.; Gray, L. J., Symmetric Galerkin boundary element method, (2008), Springer New York · Zbl 1156.65101 |

[22] | Tanaka, M.; Bercin, A. N., Static bending analysis of stiffened plates using the boundary element method, Engineering Analysis with Boundary Elements, 21, 147-154, (1998) · Zbl 0939.74606 |

[23] | Timoshenko, S.; Goodier, J. N., Theory of elasticity, (1970), McGraw-Hill New York · Zbl 0266.73008 |

[24] | Van Der Ween, F., Application of the boundary integral equation method to Reissner’s plate model, International Journal for Numerical Methods in Engineering, 18, 1-10, (1982) |

[25] | Vel, S. S.; Batra, R. C., Exact solution for thermoelastic deformations of functionally graded thick rectangular plates, AIAA Journal, 40, 1421-1433, (2002) |

[26] | Wang, Hui.; Qin, Qing-Hua, Boundary integral based graded element for elastic analysis of 2D functionally graded plates, European Journal of Mechanics - A/Solids, 33, 12-23, (2012) · Zbl 1348.74336 |

[27] | Wen, P. H.; Aliabadi, M. H., Boundary element frequency domain formulation for dynamic analysis of Mindlin plates, International Journal for Numerical Methods in Engineering, 67, 1617-1640, (2006) · Zbl 1113.74087 |

[28] | Wen, P. H.; Aliabadi, M. H.; Young, A., Boundary element analysis of shear deformable stiffened plates, Engineering Analysis with Boundary Elements, 26, 511-520, (2002) · Zbl 1006.74545 |

[29] | Wen, P. H.; Sladek, J.; Sladek, V., Three-dimensional analysis of functionally graded plates, International Journal for Numerical Methods in Engineering, 87, 923-942, (2011) · Zbl 1242.74057 |

[30] | Yang, Q.; Gao, C.-F.; Chen, W., Stress analysis of a functional graded material plate with a circular hole, Archive of Applied Mechanics, 80, 895-907, (2010) · Zbl 1271.74293 |

[31] | Yun, W.; Rongqiao, X.; Haojiang, D., Three-dimensional solution of axisymmetric bending of functionally graded circular plates, Composite Structures, 92, 1683-1693, (2010) |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.