Engineering

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Linear elasticity

Power series

Applied mathematics

Shell theory

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Classical mechanics

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Finite element method

Calculus (dental)

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Shell (structure)

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Mechanics of Advanced Materials and Structures

Here, higher order models of elastic shells of revolution are developed using the variational principle of virtual power for 3-D equations of the linear theory of elasticity and generalized series in the coordinates of the shell thickness. Following the Carrera Unified Formulation (CUF), the stress and strain tensors, as well as the displacement vector, were expanded into series in terms of the coordinates of the shell thickness. As a result, all the equations of the theory of elasticity were transformed into the corresponding equations for the expansion coefficients in a series in terms of the coordinates of the shell thickness. All equations for shells of revolution of higher order are developed and presented here for cases whose middle surfaces can be represented analytically. The resulting equations can be used for theoretical analysis and calculation of the stress-strain state, as well as for modeling thin-walled structures used in science, engineering, and technology.

Carrera unified formulation (CUF) for the shells of revolution. Numerical evaluation