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A new approximate model of nonlinearly elastic flexural shell and its numerical computation
Author(s) -
Shen Xiaoqin,
Li Kaitai,
Li Can
Publication year - 2014
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.21834
Subject(s) - mathematics , shell (structure) , cylinder , computation , invariant (physics) , mathematical analysis , metric (unit) , shell model , surface (topology) , geometry , physics , algorithm , operations management , materials science , atomic physics , economics , composite material , mathematical physics
In this article, we construct a two‐dimensional model for the nonlinearly elastic flexural shell using differential geometry and tensor analysis under the assumption that flexural energy is dominant, that is, the metric of middle surface remains invariant. We conduct a numerical experiment for special shell—a portion of cylinder shell, which is applied to the forces along the opposite direction of the normal vector. The displacements distribution of all points in the middle surface when the shell deforms is obtained. Numerical experiment results are consistent with the theory, which proves the validity of the proposed model. We then compare the proposed model and Ciarlet's model with 3D model, which proves that the proposed model is more approximate to 3D model than Ciarlet's. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1727–1739, 2014