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Duality Theory in Nonlinear Buckling Analysis for von Kármán Equations
Author(s) -
Yang Gao David
Publication year - 1995
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1995944423
Subject(s) - eigenvalues and eigenvectors , mathematics , buckling , nonlinear system , duality (order theory) , bifurcation theory , mathematical analysis , bifurcation , quadratic equation , pure mathematics , geometry , physics , quantum mechanics , thermodynamics
The nonlinear eigenvalue problem in buckling analysis is studied for von Kármán plates. By using the general duality theory developed by Gao‐Strang [1, 2] it is proved that the stability criterion for the bifurcated state depends on a reduced complementary gap function. The duality theory is established for nonlinear bifurcation problems. This theory shows that the nonlinear eigenvalue problem is eventually equivalent to a coupled quadratic dual optimization problem. A series of equivalent variational principles are constructed and a lower bound theorem for the first eigenvalue of the buckling factor is proved.