Initial strain formulation without internal cells for elastoplastic analysis by triple-reciprocity BEM.

*(English)*Zbl 0977.74075Summary: In general, internal cells are required to solve elastoplasticity problems using a conventional boundary element method (BEM). However, in this case the merit of BEM, which is an easy method for the preparation of data, is lost. The conventional multiple-reciprocity boundary element method cannot be used to solve elastoplasticity problems because the distribution of initial strain or initial stress cannot be determined analytically. In this paper, we show that two-dimensional elastoplasticity problems can be solved without the use of internal cells, by using the triple-reciprocity boundary element method. An initial strain formulation is adopted, and the initial strain distribution is interpolated using boundary integral equations. A new computer programme is developed and applied to several problems.

##### MSC:

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

74C05 | Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials) |

##### Keywords:

strain hardening; thin-plate spline; interpolation; two-dimensional elastoplasticity problems; triple-reciprocity boundary element method; initial strain formulation
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\textit{Y. Ochiai} and \textit{T. Kobayashi}, Int. J. Numer. Methods Eng. 50, No. 8, 1877--1892 (2001; Zbl 0977.74075)

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##### References:

[1] | The Boundary Element Method Applied to Inelastic Problems. Springer: Berlin, 1983. |

[2] | Boundary Element Techniques?Theory and Applications in Engineering. Springer: Berlin, 1984; 252-266. |

[3] | (eds). The Multiple Reciprocity Boundary Element Method. Computational Mechanics Publications: Southampton, 1994; 25-43. |

[4] | Ochiai, Engineering Analysis with Boundary Elements 18 pp 111– (1996) |

[5] | Ochiai, Journal of Thermal Stresses 18 pp 603– (1995) |

[6] | Ochiai, Engineering Analysis with Boundary Elements 23 pp 167– (1999) · Zbl 0940.74076 |

[7] | Interpolation of scattered data by radial functions. In Topics in Multivariate Approximation, (eds). Academic Press: London, 1987; 47-61. |

[8] | Micchelli, Constructive Approximation 2 pp 12– (1986) · Zbl 0625.41005 |

[9] | Ochiai, Advances in Engineering Software 22 pp 113– (1995) · Zbl 05478751 |

[10] | Ochiai, Computer Aided Geometric Design 17 pp 233– (2000) · Zbl 0939.68151 |

[11] | Ochiai, Engineering Analysis with Boundary Elements 17 pp 295– (1996) |

[12] | Nayak, International Journal for Numerical Methods in Engineering 5 pp 113– (1972) · Zbl 0241.73034 |

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