An. Kounadis, ON THE NONLINEAR DYNAMIC BUCKLING MECHANISM OF AUTONOMOUS DISSIPATIVENONDISSIPATIVE DISCRETE STRUCTURAL SYSTEMS, Archive of applied mechanics, 66(6), 1996, pp. 395-408
Nonlinear dynamic buckling of nonlinearly elastic dissipative/nondissi
pative multi-mass systems, mainly under step load of infinite duration
, is studied in detail. These systems, under the same loading applied
statically, experience a limit point instability. The analysis can be
readily extended to the case of dynamic buckling under impact loading.
Energy, topological and geometrical aspects for the total potential e
nergy V, which is constrained to lie in a region of phase-space where
V less than or equal to 0, allow conclusions to be drawn directly rega
rding dynamic buckling. Criteria leading to very good, approximate and
lower/upper bound dynamic buckling estimates are readily established
without solving the highly nonlinear set of equations of motion. The t
heory is illustrated with several analyses of a two-degree-of-freedom
model.