Local buckling of thin-walled structures by the boundary element method.

*(English)*Zbl 1244.74138Summary: In this work a multi-region boundary element formulation for linear local buckling analysis of assembled plate and shallow shell structures is presented. The assembly is divided into sub-regions. In each sub-region, the formulation is formed by coupling boundary element formulations of shear deformable plate bending and two-dimensional plane stress elasticity. Domain integrals appearing in the formulation (due to the curvature and due to the domain load) are transformed into equivalent boundary integrals. Membrane stresses at discrete domain points of each sub-region (plate or shallow shell) in the assembly are obtained from the prebuckling state, resulting in a set of linear buckling equations in terms of the buckling deflection and the buckling load factor. Buckling equation is presented as a standard eigenvalue problem. Results are compared with FEM solutions and it is shown that good accuracy can be achieved with the present multi-region BEM formulation.

##### MSC:

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

74G60 | Bifurcation and buckling |

##### Keywords:

assembled plates and shallow shells; buckling; shear deformation theory; boundary element method
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\textit{P. M. Baiz} and \textit{M. H. Aliabadi}, Eng. Anal. Bound. Elem. 33, No. 3, 302--313 (2009; Zbl 1244.74138)

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##### References:

[1] | Basu, P.K.; Akhtar, M.N., Interactive and local buckling of thin walled members, Thin-walled struct, 12, 335-352, (1991) |

[2] | Zienkiewicz OC, Taylor R. The finite element method. Solid mechanics, vol. 2. Oxford: B-H; 2000. |

[3] | Plank, R.J.; Wittrick, W.H., Buckling under combined loading of thin, flat-walled structures by a complex finite strip method, Int J numer methods eng, 8, 323-339, (1974) · Zbl 0276.73026 |

[4] | Ohga, M.; Kawaguchi, K.; Shigematsu, T., Buckling analysis of thin-walled members with closed cross sections, Thin-walled struct, 22, 51-70, (1995) |

[5] | Bedair, O.K., A contribution to the stability of stiffened plates under uniform compression, Comput struct, 66, 535-570, (1998) · Zbl 0973.74549 |

[6] | Aliabadi MH. The boundary element method. Application to solids and structures, vol. 2. Chichester: Wiley; 2001. |

[7] | Manolis, G.D.; Beskos, D.E.; Pineros, M.F., Beam and plate stability by boundary elements, Comput struct, 22, 917-923, (1986) · Zbl 0578.73070 |

[8] | Syngellakis, S.; Elzein, A., Plate buckling loads by the boundary element method, Int J numer method eng, 37, 1763-1778, (1994) · Zbl 0804.73073 |

[9] | Nerantzaki, M.S.; Katsikadelis, J.T., Buckling of plates with variable thickness—an analog equation solution, Eng anal boundary elem, 18, 149-154, (1996) |

[10] | Lin, J.; Duffield, R.C.; Shih, H.R., Buckling analysis of elastic plates by boundary element method, Eng anal boundary elem, 23, 131-137, (1999) · Zbl 0953.74072 |

[11] | Purbolaksono, J.; Aliabadi, M.H., Buckling analysis of shear deformable plates by the boundary element method, Int J numer methods eng, 62, 537-563, (2005) · Zbl 1077.74055 |

[12] | Baiz, P.M.; Aliabadi, M.H., Linear buckling analysis of shear deformable shallow shells by the boundary domain element method, Comput modelling eng sci, 13, 19-34, (2006) · Zbl 1357.74034 |

[13] | Baiz, P.M.; Aliabadi, M.H., Buckling analysis of shear deformable shallow shells by the boundary element method, Eng anal boundary elem, 31, 361-372, (2007) · Zbl 1195.74216 |

[14] | Chinnaboon, B.; Chucheepsakul, S.; Katsikadelis, J.T., A BEM-based meshless method for elastic buckling analysis of plates, Int J struct stability dyn, 7, 81-89, (2007) · Zbl 1205.74174 |

[15] | Katsikadelis JT, Yiotis A. Linear buckling analysis of cylindrical shell panels using BEM. In: Proceedings of the eighth HSTAM international congress on mechanics, Patras, Greece, 12-14 July; 2007. p. 889-96. |

[16] | Tanaka, M.; Miyazaki, K., A direct BEM for elastic plate-structures subjected to arbitrary loadings, (), 4-3/4-16 |

[17] | Dirgantara, T.; Aliabadi, M.H., Boundary element analysis of assembled plate structures, Commun numer methods eng, 17, 749-760, (2001) · Zbl 1017.74078 |

[18] | Wen, P.H.; Aliabadi, M.H.; Young, A., Crack growth analysis for multi-layered airframe structures by boundary element method, Eng fract mech, 71, 619-631, (2004) |

[19] | Di Pisa C. Boundary element analysis of multi-layered panels and structures. PhD thesis, Department of Engineering, Queen Mary University of London; 2005. |

[20] | Tanaka, M.; Miyazaki, K., Elastic buckling analysis of assembled plate structures by boundary element method, (), 537-546 · Zbl 0613.73077 |

[21] | Anderson E, Bai Z, Bischof C, Blackford S, Demmel J, Dongarra J, et al. LAPACK users’ guide, 3rd edition. Society for Industrial and Applied Mathematics; 1999. · Zbl 0934.65030 |

[22] | ABAQUS Inc. Documentation, version 6.7-1; 2007. |

[23] | Allen, H.G.; Bulson, P.S., Background to buckling, (1980), McGraw-Hill Book Company UK |

[24] | Dirgantara, T.; Aliabadi, M.H., A new boundary element formulation for shear deformable shells analysis, Int J numer methods eng, 45, 1257-1275, (1999) · Zbl 0930.74072 |

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