ON THE NONLINEAR DYNAMIC BUCKLING MECHANISM OF AUTONOMOUS DISSIPATIVENONDISSIPATIVE DISCRETE STRUCTURAL SYSTEMS

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.