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Accuracy of finite difference representations for the transient response analysis of shells
Author(s) -
Underwood Philip
Publication year - 1973
Publication title -
earthquake engineering and structural dynamics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.218
H-Index - 127
eISSN - 1096-9845
pISSN - 0098-8847
DOI - 10.1002/eqe.4290020303
Subject(s) - instability , rotational symmetry , transient (computer programming) , finite difference , mathematics , stress resultants , finite difference method , mathematical analysis , finite element method , mechanics , physics , geometry , structural engineering , engineering , computer science , operating system
The frequency versus wave number characteristics of four O(Δ S 2 ) finite difference formulations for one‐dimensional linear shell (ring and axisymmetric) equations are investigated and compared with the exact continuum characteristics. It is found that three of the formulations give virtually identical results. These are half‐spacing techniques with equilibrium in terms of displacements or resultants and whole‐spacing with equilibrium in terms of displacements. The formulation based on whole‐spacing with equilibrium in terms of resultants produces some dramatically different results. These discrepancies partially explain some late time instability problems and critical time step behaviour that have been reported by other investigators.