2023/05/14 by Giuseppe Tomassetti, Tomassetti, Giuseppe · 1 citation
Engineering · #35Q74 #74K25 #Classical Physics (physics.class-ph) #Composite Structure Analysis and Optimization #Elasticity and Material Modeling #FOS: Physical sciences #Structural Analysis and Optimization
paper · pdf · doi:10.48550/arxiv.2305.08884
openalex publication_date 2023/05/14 · openalex created_date 2023/05/18 · openalex updated_date 2026/07/28
In this tutorial, we provide a coordinate-free derivation of the system of equations that govern equilibrium of a thin shell that can undergo shear. This system involves tensorial fields representing the internal force and couple per unit length that adjacent parts of the shell exchange at their common boundary. By an appropriate decomposition of those quantities, we obtain a representation of the internal power in terms of time derivatives of suitable strain measures. Subsequently, we propose constitutive equations that employ these strain measures as independent variables. After specializing the theory to the case of unshearable shells, we linearize the resulting equations. As an application, we study the free vibrations of a pressurized spherical shell, showcasing the advantages of a coordinate-free perspective, which simplifies both the deduction and the solution of the final governing equations.