On the Non-Existence of Adjacent Equilibrium States at Bifurcation Points.
PRINCETON UNIV N J DEPT OF CIVIL AND GEOLOGICAL ENGINEERING
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In the adjacent equilibrium method of stability theory, it is assumed that, at a critical point on an equilibrium branch, there always exists for the same load, in addition to the fundamental equilibrium configuration, also adjacent equilibrium states. In the present paper, it is shown that for a number of structures adjacent equilibrium states indeed do not exist at bifurcation points thus proving that adjacent equilibrium states do not exist in general and hence that the physical argument of the adjacent equilibrium method is not generally valid. The proofs are based on the regular perturbation method.