Shell Mathematical Models

  • Dominique Chapelle
  • Klaus-Jürgen Bathe
Part of the Computational Fluid and Solid Mechanics book series (COMPFLUID)


In this chapter we describe and analyse the linear shell models that we consider in this book. We first describe the fundamental shell kinematics used. Then we discuss the “basic shell model” which is implicitly employed in general finite element solutions and from which other classical shell and plate models can be derived. We summarize the shell models that we call the “shear-membrane-bending model” and the “membrane-bending model”, and introduce the proper mathematical framework in which they define well-posed problems. As special cases of these shell models we obtain well-known plate models.


Shell Model Rigid Body Motion Plate Model Essential Boundary Condition Kinematical Assumption 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Dominique Chapelle
    • 1
  • Klaus-Jürgen Bathe
    • 2
  1. 1.INRIA Paris-RocquencourtLe ChesnayFrance
  2. 2.Massachusetts Institute of TechnologyCambridgeUSA

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