An Introduction to Differential Geometry with Applications to Elasticity / by Philippe G. Ciarlet.

Springer eBooks

Three-Dimensional Differential Geometry -- Differential Geometry of Surfaces -- Applications to Three-Dimensional Elasticity in Curvilinear Coordinates -- Applications to Shell Theory.

This monograph presents the basic theorems of differential geometry in three-dimensional space, including a thorough coverage of surface theory. By means of a series of carefully selected and representative mathematical models this monograph also explains at length how these theorems are used in three-dimensional elasticity and in shell theory. The presentation is essentially selfcontained, with a great emphasis on pedagogy. In particular, no "a priori" knowledge of differential geometry or of elasticity theory is assumed, the only requirements are a reasonable knowledge of basic analysis, functional analysis, and some acquaintance with ordinary and partial differential equations.

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