Nichtlineare Finite-Element-Methoden
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Nichtlineare Finite-Element-Methoden

Nichtlineare Finite-Element-Methoden


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About the Book

Die Anwendung der Finite-Element-Methode auf nichtlineare technische Probleme hat in den letzten Jahren - auch wegen der stark angestiegenen Rechnerleistung - erheblich zugenommen. Bei nichtlinearen numerischen Simulationen sind verschiedene Aspekte zu berücksichtigen, die das Wissen und Verstehen der theoretischen Grundlagen, der zugehörigen Elementformulierungen sowie der Algorithmen zur Lösung der nichtlinearen Gleichungen voraussetzen. Hierzu soll dieses Buch beitragen, wobei die Bandbreite nichtlinearer Finite-Element-Analysen im Bereich der Festkörpermechanik abgedeckt wird. Das Buch wendet sich an Studierende des Ingenieurwesens im Hauptstudium, an Doktoranden aber auch an praktisch tätige Ingenieure, die Hintergrundwissen im Bereich der Finite-Element-Methode erlangen möchten.

Table of Contents:
1. Einleitung.- 2. Nichtlineare Phänomene.- 2.1 Geomet rische Nichtlinearität.- 2.2 Physikalische Nichtlinearität.- 2.3 Nichtlinearität infolge von Randbedingungen.- 3. Kontinuumsmechanische Grundgleichungen.- 3.1. Kinematik.- 3.2 Bilanzgleichungen.- 3.3 Materialgleichungen.- 3.4 Schwache Form des Gleichgewichts, Variationsprinzipien.- 3.5 Linearisierungen.- 4. Räumliche Diskretisierung der Grundgleichungen.- 4.1 Generelles isoparametrisches Konzept.- 4.2 Diskretisierung der Grundgleichungen.- 5. Lösungsverfahren für zeitunabhängige Probleme.- 5.1 Lösung nichtlinarer Gleichungssysteme.- 5.2 Löser für lineare Gleichungssy steme.- 5.3 Beispielezu den Algorithmen und Cleichungslosem.- 6. Lösungsverfahren für zeitabhängige Probleme.- 6.1 Integration der Bewegungsgleichungen.- 6.2 Integration inelastischer Materialgleichungen beikleinen Deformationen.- 6.3 Integration der Materialgleichungen bei großen Deformationen.- 7. Stabilitätsproblerne.- 7.1 Vorbemerkungen.- 7.2 Direkte Berechnung von Stabilitätspunkten.- 7.3 Algorithmus für nichtlineare Stabilitätsprobleme.- 8. Adaptive Verfahren.- 8.1 Randwertproblem und Diskretisierung.- 8.2 Fehlerschätzer und -indikatoren.- 8.3 Fehlerschätzung für Plastizität.- 8.4 Netzverfeinerung.- 8.5 Adaptive Netzgenerierung.- 8.6 Beispiele.- 9. Spezielle Strukturelemente.- 9.1 Nichtlineares Fachwerkelement.- 9.2 Zweidimensionales geometrisch exaktes Balkenelement.- 9.3 Rotationssymmetrisches Schalenelement.- 9.4 Allgemeine Schalenelemente.- 9.5 Beispiele.- 10. Spezielle Kontinuumselemente.- 10.1 Anforderungen an Kontinuumselemente.- 10.2 Gemischte Elemente für Inkompressibilität.- 10.3 Stabilisierte finite Elemente.- 10.4 Enhanced Strain Element.- 11. Kontaktprobleme.- 1l.1 Kontaktkinernatik.- 11.2 KonstitutiveGleichungen in der Kontaktzone.- 11.3 Schwache Formulierung.- 11.4 Diskretisierung.- A. Tensorrechnung.- A.l Tensoralgebra.- A.1.l Definition eines Tensors.- A.1.2 Basisdarstellung von Vektoren und Tensoren.- A.1.3 Produkte von Vektoren und Tensoren.- A.1.4 Spezielle Formen von Tensoren.- A.1.5 Eigenwerte und Invarianten von Tensoren.- A.1.6 Tensoren höherer Stufe.- A.2 Tensoranalysis.- A.2.1 Differentiation nach einer reellen Variablen.- A.2.2 Gradientenbildung eines Feldes.- A.2.3 Divergenzbildung eines Feldes.- A.2.4 Rotation eines Vektorfeldes.- A.2.5 Ableitung der Invarianten nach einem Tensor.- A.2.6 Pull back und push forward Operationen.- A.2.7 Lie-Ableitung von Spannungstensoren.- A.2.8 Integralsätze.- Literatur.

Review :
From the reviews: "This book describes, besides the physical and mathematical background of finite element method (FEM), special discretization techniques and algorithms which have to be applied to nonlinear problems of solid mechanics. ... The book is intended for graduate students of mechanical and civil engineering who want to familiarize themselves with numerical methods applied to problems in solid mechanics. This book applies also to PhD students and engineers working in industry who need further background information on the application of finite elements to nonlinear problems." (Razvan Raducanu, Zentrablatt MATH, Vol. 1153, 2009)


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Product Details
  • ISBN-13: 9783540677475
  • Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
  • Publisher Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Height: 235 mm
  • No of Pages: 496
  • Returnable: N
  • ISBN-10: 354067747X
  • Publisher Date: 26 Jan 2001
  • Binding: Paperback
  • Language: German
  • Returnable: Y
  • Width: 155 mm


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