An Introduction to Differential Geometry with Applications to Elasticity

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The book presents a comprehensive exploration of curvilinear coordinates, emphasizing a direct proof of the three-dimensional Korn inequality. It delves into the nonlinear and linear equations by W.T. Koiter for modeling thin elastic shells, establishing the existence, uniqueness, and regularity of solutions through advanced mathematical concepts. Chapters 3 and 4 introduce differential geometry notions, enhancing the understanding of boundary value problems in elasticity and shell theory. The work is supported by research grants and references previous publications.