Fundamental equations for dynamic elastic large deflection analysis are formulated to simulate the snap-through behaviour which takes place when a plate undergoes secondary buckling under inplane compressive load. The formulation is in an analytical manner. Then, a series of calculation was performed applying the proposed formulation to investigate into the fundamental characteristics of the snap-through phenomenon at the secondary buckling when a rectangular plate is subjected to uni-axial thrust in the direction of its longer side. Similar calculation is also performed applying elastic/elastopalstic large deflection analysis FEM code. It has been found that:
The actual loading path with minimum energy consumption is automatically simulated among multipaths by performing dynamic analysis.
Along the unloading path in the post-ultimate strength range, snap-through sometimes takes place.
Initial deflection of the primary buckling mode increases the snap-through load whereas that of the secondary buckling mode reduces the snap-through load.
The recent trend in ship structural design is to have reduced scantlings, owing to highly accurate mathematical formulations and capability of advanced computational systems as well as to the development of higher tensile strength steel with superior property for welding. Problem related to buckling strength assessment has again become important due to these developments and relevance of revising the standards for buckling strength assessment has been widely accepted. Such a design method needs an accurate estimation of the post-buckling behaviour of plates. On the other hand, it is well known that a thin plate beyond the primary buckling may snap to another equilibrium state of a different deflection mode. This is called secondary buckling (Nakamura et al. 1994). In this paper, first, fundamental equations for dynamic elastic large deflection analysis are formulated to simulate the snapthrough behaviour which takes place when a plate undergoes secondary buckling under in-plane compressive load.
