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A Method for Determining the Lower Bound Dynamic Buckling Loads of Imperfection‐Sensitive Structures
Author(s) -
Wu B.
Publication year - 1997
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19970770611
Subject(s) - buckling , upper and lower bounds , perturbation (astronomy) , mathematics , differential equation , structural engineering , mathematical analysis , physics , engineering , quantum mechanics
A perturbation method based on the static stability criterion associated with the vanishing of the total potential energy on a certain equilibrium point on the unstable postbuckling path is presented for the determination of lower bound dynamic buckling loads of imperfection‐sensitive structures under step load of infinite duration. Attention is focused on the effect of various possible sources of structural imperfections on the dynamic buckling strength of perfect structures. Under the assumption that the effect of structural imperfections is of the first order, the method can give any desired higher‐order approximation to the lower bound dynamic buckling loads and the corresponding displacements without solving the system of differential equations of motion numerically. Especially, the method applies to finite‐degree‐of‐freedom systems as well as continuous ones. The application of the method is illustrated on two examples. The results demonstrate the significant effect of other imperfection sources, besides the shape imperfections having the shape of the classical buckling mode.