Dynamic Buckling Of The Slab Structure Under Impact Loading

The dynamic buckling of elastic structures, such as beams and plates, when subjected to an axial impact at one end, is studied in the present paper based on the theory of stress wave propagation. Stress waves are bound to follow when structures are impacted along the axial direction. It is for the propagation of longitudinal waves that the buckling of the structures takes place and grows. In the course of the stress waves propagating, the buckling of structures appears locally. End conditions and consistency conditions at a stress wave front as well as the bifurcation conditions of the dynamic buckling are formulated according to the solution of disturbing equations obtained in this paper. Critical buckling loads and the associated buckling modes are presented. The time of buckling depends on the impact load. In general, when the load is large, the buckling occurs in short tune and the local position of the buckling may be near the impact end of the structures. Sometimes, the buckling appears close to the other end, which is because of the reflection of stress waves. The critical load is determined by the condition of bifurcation and is dependent on properties of the material, geometric parameters and supporting conditions of structures besides time. In the same instant the critical buckling loads vary under various support end conditions, i.e. the load is biggest for fixed support, smaller for simple and the lowest for free. It is showed that a non-symmetric buckling may occur in the symmetric structures when a symmetric impacted load is applied. With the wall thickness increasing, for plates, non-symmetric critical load is larger than symmetric one and with it decreasing, the non-symmetric critical load may be the lower than symmetric one. The buckling forms or corrugations are dependent on the load, wall thickness, and so on. For structures of variable-cross section, stress waves may transmit and reflect in the propagation. In this case, the critical load curves and modes are more complicated. The method, in this paper, provides a solving way for similar problems.