On Stability and the Worst Imperfection Shape in Solids with Nearly Simultaneous Eigenmodes

Of interest here is the influence of imperfections on the stability ofelastic systems. discrete or continuous. with nearly simultaneous modes. The majority of such structures show an extreme sensitivity of their first instability load to the shape of these small amplitude but unavoidable imperfections. The determination of the worst such possible shape is thus a very important issue from the design standpoint. Following a general analysis of the stability of arbitrary elastic systems with nearly simultaneous bifurcation eigenmodes in the presence of imperfections. conditions are given for the determination of the worst imperfection shape which minimizes Ihe first local load manimum. For the case of coincident eigenmodes Ihe answer 10 the worst shape problem is considerably simplified. for it is determined from the equilibrium branch of rhe perfect structure on which the load drops more rapidly.