Shell Geometry and Classification

This course covers the fundamental concepts of shell geometry and classification. It starts with the derivation of first and second fundamental forms of surfaces, explaining the definition of curvature, normal curvature, and principal curvatures. The course introduces the theorem of Rodrigues and Weingarten formulas, essential in developing the fundamental equations for surfaces. It further discusses the concept of Gaussian curvature and its role in classifying shell surfaces. The course also delves into the classification of shell surfaces based on their shape, developability, and geometry. For instance, it explains how a conical shell can be formed by revolving a straight line around an axis. The course concludes with an overview of different shell theories, including Love’s and Kirchhoff Shell theory, and the Reissner and Naghdi shell theory.