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Lecture Notes on the Theory of Plates and Shells: Classical and Modern Developments

By (author) David J. Steigmann, By (author) Mircea BÃ®rsan, By (author) Milad Shirani

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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 â€˜dimension reductionâ€™ 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 Kirchhoffâ€“Love 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.Â

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