Lecture Notes on the Theory of Plates and Shells

This book presents the theory of plates and shells on the basis of the three-dimensional parent theory. The authors explore the thinness of the structure to represent the mechanics of the actual thin three-dimensional body under consideration by a more tractable two-dimensional theory associated with an interior surface. In this way, the relatively complex three-dimensional continuum mechanics of the thin body is replaced by a far more tractable two-dimensional theory. To ensure that the resulting model is predictive, it is necessary to compensate for this 'dimension reduction' by assigning additional kinematical and dynamical descriptors to the surface whose deformations are modelled by the simpler two-dimensional theory. The authors avoid the various ad hoc assumptions made in the historical development of the subject, most notably the classical KirchhoffLove hypothesis requiring that material lines initially normal to the shell surface remain so after deformation. Instead, suchconditions, when appropriate, are here derived rather than postulated.

Auteur

David J. Steigmann is Professor in the Department of Mechanical Engineering, University of California, Berkeley. He is Fellow of the Society of Engineering Science (Elected 2010), Lecturer, Midwest Mechanics Tour (2009-10 academic year) and Visiting Research Professor, 2013 and 2015: Universita di Roma, la Sapienza. He is Recipient of Levi-Civita Prize, 2013. He is Recipient of Engineering Science Medal, conferred by the Society of Engineering Science, for 'Singular Contributions to Engineering Science' (2013). A special issue of the journal Continuum Mechanics and Thermodynamics is dedicated to D.J. Steigmann. Mircea Bîrsan is Professor, Faculty of Mathematics, University Duisburg-Essen, Germany (since 2014), and Associate Professor, Department of Mathematics, University "Alexandru Ioan Cuza" of Iasi, Romania (2007-2013). He is Recipient of the prizes "Gheorghe Lazar" of the Romanian Academy (2007) for the contributions on the deformation of elastic Cosserat shells and "Nicolae Teodorescu" of the Academy of Romanian Scientists (2012) for the articles published in 2010-2011. Milad Shirani earned his Ph.D. from the Department of Mechanical Engineering at the University of California, Berkeley. He was the recipient of the Robert F. Steidel Fellowship (UC Berkeley) in 2021 and the Paul Naghdi Fellowship (UC Berkeley) in 2020.

Contenu

Chapter 1. Tensor Analysis in Euclidean Space Using Curvilinear Coordinates.- Chapter 2. Local Geometry of Deformation.- Chapter 3. Hyperelastic Solids: Purely Mechanical Theory.- Chapter 4. Linearly elastic plates.- Chapter 5. Linear Shell Theory.- Chapter 6. Nonlinear equations for plates and shells.- Chapter 7. Buckling of elastic plates.- Chapter 8. Saint-Venant Problem for general cylindrical shells.