Handbook of Thin Plate Buckling and Postbuckling


1.1 Buckling Phenomena

Problems of initial and postbuckling represent a particular class of bifurcation

phenomena; the long history of buckling theory for structures

begins with the studies by Euler [1] in 1744 of the stability of flexible

compressed beams, an example which we present in some detail below,

to illustrate the main ideas underlying the study of initial and postbuckling

behavior.





Although von Karman formulated the equations for

buckling of thin, linearly elastic plates which bear his name in 1910 [2],

a general theory for the postbuckling of elastic structures was not put

forth until Koiter wrote his thesis [3] in 1945 (see, also, Koiter [4], [5]);

it is in Koiter’s thesis that the fact that the presence of imperfections

could give rise to significant reductions in the critical load required to

buckle a particular structure first appears. General theories of bifurcation

and stability originated in the mathematical studies of Poincar´e

[6], Lyapunov [7], and Schmidt [8] and employed, as basic mathematical

tools, the inverse and implicit function theorems, which can be used

to provide a rigorous justification of the asymptotic and perturbation

type expansions which dominate studies of buckling and postbuckling

of structures. Accounts of the modern mathematical approach to bifurcation

theory, including buckling and postbuckling theory, may be

found in many recent texts, most notably those of Keller and Antman,

[9], Sattinger [10], Iooss and Joseph [11], Chow and Hale [12], and Golubitsky

and Schaeffer [13], [14]. Among the noteworthy survey articles

which deal specifically with buckling and postbuckling theory are those

of Potier-Ferry [15], Budiansky [16], and (in the domain of elastic-plastic

response) Hutchinson [17]. Some of the more recent work in the general

area of bifurcation theory is quite sophisticated and deep from a

mathematical standpoint, e.g., the work of Golubitsky and Schaeffer,


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