### Abstract

The stability bound for the classical nonlinear Euler Beam is determined in the case that its deflection is limited by an obstacle parallel to the plane of the beam. Let a clamped or simply supported beam be axially compressed by a force P greater than P//0, where P//0 denotes the critical load. So far only a linear theory has been applied to analyze the stability of the solutions in contact with the obstacle and the jumping to a different state. Utilizing a free boundary problem formulation we analytically as well as numerically answer these questions for the nonlinear beam.

Original language | English (US) |
---|---|

Pages (from-to) | 516-532 |

Number of pages | 17 |

Journal | Mathematical Methods in the Applied Sciences |

Volume | 8 |

Issue number | 4 |

State | Published - 1986 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Mathematical Methods in the Applied Sciences*,

*8*(4), 516-532.

**FREE BOUNDARY PROBLEM AND STABILITY FOR THE NONLINEAR BEAM.** / Miersemann, E.; Mittelmann, Hans.

Research output: Contribution to journal › Article

*Mathematical Methods in the Applied Sciences*, vol. 8, no. 4, pp. 516-532.

}

TY - JOUR

T1 - FREE BOUNDARY PROBLEM AND STABILITY FOR THE NONLINEAR BEAM.

AU - Miersemann, E.

AU - Mittelmann, Hans

PY - 1986

Y1 - 1986

N2 - The stability bound for the classical nonlinear Euler Beam is determined in the case that its deflection is limited by an obstacle parallel to the plane of the beam. Let a clamped or simply supported beam be axially compressed by a force P greater than P//0, where P//0 denotes the critical load. So far only a linear theory has been applied to analyze the stability of the solutions in contact with the obstacle and the jumping to a different state. Utilizing a free boundary problem formulation we analytically as well as numerically answer these questions for the nonlinear beam.

AB - The stability bound for the classical nonlinear Euler Beam is determined in the case that its deflection is limited by an obstacle parallel to the plane of the beam. Let a clamped or simply supported beam be axially compressed by a force P greater than P//0, where P//0 denotes the critical load. So far only a linear theory has been applied to analyze the stability of the solutions in contact with the obstacle and the jumping to a different state. Utilizing a free boundary problem formulation we analytically as well as numerically answer these questions for the nonlinear beam.

UR - http://www.scopus.com/inward/record.url?scp=0022921122&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0022921122&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0022921122

VL - 8

SP - 516

EP - 532

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

SN - 0170-4214

IS - 4

ER -