Abstract

The objective of this dissertation is the derivation of a

hierarchical formulation for the differential and integral

equations of a twelfth-order plate bending model for homogeneous

transversely isotropic materials, named after Poniatovskii and

Reissner. The hierachical characteristic means that the direct

reduction from the twelfth-order equation system automatically

leads to corresponding systems of lower-order. By the first

simplification we obtain the sixth-order equation system of

Reissner (and Mindlin) and, by taking the limit of the thickness

to zero or the shear stiffness to infinity, the fourth-order

Kirchhoff bending equation. The simplification from the

twelfth-order to the sixth-order system is performed by the

selection of particular values for the two coupling variables.

The differential equations of the twelfth-order model are

obtained by application of the Hellinger-Reissner mixed

variational principle. For the dimensional reduction we propose

as starting point an expansion of the displacements along the

plate thickness in the form of Legendre polynomials. In the

sequel we determine the corresponding stres ... mehr

Zugehörige Institution(en) am KIT |
Institut für Technische Mechanik (ITM) |

Publikationstyp |
Hochschulschrift |

Jahr |
2001 |

Sprache |
Deutsch |

Identifikator |
URN: urn:nbn:de:swb:90-AAA336720018 KITopen ID: 33672001 |

Erscheinungsvermerk |
Fak. f. Maschinenbau, Diss. v. 21.6.2001. |

Abschlussart |
Dissertation |

Fakultät |
Fakultät für Maschinenbau (MACH) |

Institut |
Institut für Technische Mechanik (ITM) |

Prüfungsdaten |
Diss. v. 21.6.2001 |

KIT – Die Forschungsuniversität in der Helmholtz-Gemeinschaft
KITopen Landing Page