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Bifurcation problems for discrete variational inequalities
Author(s) -
Mittelmann H. D.,
Törnig W.
Publication year - 1982
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670040116
Subject(s) - mathematics , discretization , eigenvalues and eigenvectors , variational inequality , bifurcation , buckling , convergence (economics) , mathematical analysis , bifurcation theory , beam (structure) , nonlinear system , physics , quantum mechanics , optics , economics , thermodynamics , economic growth
The buckling of a beam or a plate which is subject to obstacles is typical for the variational inequalities that are considered here. Birfurcation is known to occur from the first eigenvalue of the linearized problem. For a discretization the bifurcation point and the bifurcating branches may be obtained by solving a constrained optimization problem. An algorithm is proposed and its convergence is proved. The buckling of a clamped beam subject to point obstacles is considered in the continuous case and some numerical results for this problem are presented.