Finite-Element Analysis of Thin Elastic Shells With Residual Energy Balancing and the Role of the Rigid Body Modes

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Abstract
The thin cylindrical and spherical shells are computationwise distinct owing to the presence in the first and the absence in the latter of extensional modes. Introduction by numerical integration or allied means of discrete extensional modes in the cylindrical shell element considerably improves the discretization accuracy. Balancing the (residual) extensional energy with the discretization errors removes the radius-to-thickness ratio from the condition number of the stiffness matrix. No such computational contrivances are needed for the spherical shell whose global stiffness matrix is as well conditioned as that of a flat membrane, regardless of large radius-to-thickness ratios.

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