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Herleitung verbesserter hierarchischer Plattenmodelle und deren Integralgleichungsformulierung [online]

Westphal, Tancredo jr.



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 stress field in order to
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Volltext §
DOI: 10.5445/IR/33672001
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Technische Mechanik (ITM)
Publikationstyp Hochschulschrift
Publikationsjahr 2001
Sprache Deutsch
Identifikator urn:nbn:de:swb:90-AAA336720018
KITopen-ID: 33672001
Verlag Universität Karlsruhe (TH)
Erscheinungsvermerk Fak. f. Maschinenbau, Diss. v. 21.6.2001.
Art der Arbeit Dissertation
Fakultät Fakultät für Maschinenbau (MACH)
Institut Institut für Technische Mechanik (ITM)
Prüfungsdaten Diss. v. 21.6.2001
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