Document Zbl 0414.73036

Boundary conditions and mode jumping in the buckling of a rectangular plate. (English) Zbl 0414.73036

Commun. Math. Phys. 69, 209-236 (1979).

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MSC:

74G60	Bifurcation and buckling
74K20	Plates
47A70	(Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces

Keywords:

mode jumping; buckling of a rectangular plate; clamped boundary conditions; vertical displacement function; singularity theory of mappings; Lyapunov-Schmidt reduction; secondary bifurcation

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References:

[1]	Bauer, L., Keller, H.B., Reiss, E.L.: Multiple eigenvalues lead to secondary bifurcation. SIAM J. Appl. Math.17, 101-122 (1975) · Zbl 0276.73027
[2]	Chow, S.N., Hale, J.K., Mallet-Paret, J.: Application of generic bifurcations. I, II. Arch. Rat. Mech. Anal.59, 159-188 (1975);62, 209-235 (1976) · Zbl 0328.47036 · doi:10.1007/BF00249688
[3]	Golubitsky, M., Schaeffer, D.: A theory for imperfect bifurcation via singularity theory. Commun. Pure Appl. Math.32, 21-98 (1979) · Zbl 0409.58007 · doi:10.1002/cpa.3160320103
[4]	Golubitsky, M., Schaeffer, D.: Imperfect bifurcation in the presence of symmetry. Commun. Math. Phys.67, 205-232 (1979) · Zbl 0467.58019 · doi:10.1007/BF01238845
[5]	Magnus, R., Poston, T.: On the full unfolding of the von Kármán equations at a double eigenvalue. Battelle Math. Report No. 109. Geneva 1977
[6]	Matkowsky, B.J., Putnick, L.: Multiple buckled states of rectangular plates. International J. Nonlin. Mech.9, 89-103 (1973) · Zbl 0358.73056 · doi:10.1016/0020-7462(74)90001-8
[7]	Sattinger, D.H.: Group representation theory, bifurcation theory, and pattern formation. SIAM J. Math. Anal.8, 179-201 (1977) · Zbl 0396.47040 · doi:10.1137/0508013
[8]	Stein, M.: The phenomenon of change in buckle patterns in elastic structures. NASA technical report R-39 (1959)
[9]	Stein, M.: Loads and deformations of buckled rectangular plates. NASA technical report R-40 (1959)
[10]	Stoker, J.J.: Nonlinear elasticity. New York: Gordon and Breach 1968 · Zbl 0187.45801

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