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Schalentheorie: Statik Und Dynamik Imperfektionsempfindlicher Schalenbeulfälle
Paperback
Technology & EngineeringGeneral Construction & Renovation
ISBN13: 9783658529345
Publisher: Springer Vieweg
Published: Jan 16 2027
Pages: 417
Language: German
Das Lehrbuch behandelt klassische und neuere Schalentheorien und stellt numerische Ergebnisse für rotationssymmetrische Schalentragwerke zur Verfügung. Die Beschreibung der Schalengeometrie erfolgt mit der Differentialgeometrie gekrümmter Flächen in Tensorschreibweise. Im Rahmen der 1. Approximation der Schalenbiegetheorie werden die klassischen Schalentheorien nach Love, Reissner und Naghdi entwickelt, die die Deformation des Schalenraumes mit einer drei-Parameter-Theorie beschreiben. Die Grundgleichungen der linearen drei-Parameter-Theorien werden für Rotationsschalen in Matrizenschreibweise dargestellt und mit dem Übertragungsmatrizenverfahren für ausgewählte Schalentragwerke numerisch gelöst. Schalentheorien höherer Ordnung geben Hinweise auf das asymptotische Verhalten der klassischen Theorien.
Das nichtlineare Tragverhalten von Schalen wird im Rahmen der Theorie moderater Rotationen untersucht, die für bautechnische Anwendungen hinreichend genau ist und hier als Grundlage der nichtlinearen Stabilitätstheorie dient. Die für die Baupraxis wichtigen imperfektionsempfindlichen Schalenbeulfälle werden mit einer Störungstheorie numerisch analysiert und in einem einheitlichen Bemessungsansatz zusammengefasst. Eine tiefergreifende physikalische Interpretation der Beulprozesse erfolgt für Schalen unter zeitveränderlichen Lasten mit Berücksichtigung der Massenträgheit. Numerische Ergebnisse verdeutlichen die Phänomenologie und zeigen, dass die Grenzlasten imperfektionsempfindlicher Schalenbeulfälle unter statischer Last Sonderfälle des allgemeineren Tragverhaltens unter zeitveränderlichen Einwirkungen sind.
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