Premium
On the continuation for variational inequalities depending on an eigenvalue parameter
Author(s) -
Miersemann Erich,
Mittelmann Hans D.,
Törnig W.
Publication year - 1989
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.1670110107
Subject(s) - continuation , mathematics , eigenvalues and eigenvectors , numerical continuation , variational inequality , beam (structure) , mathematical analysis , nonlinear system , bifurcation , computer science , physics , quantum mechanics , optics , programming language
Abstract In this paper we generalize recent theoretical results on the local continuation of parameter‐dependent non‐linear variational inequalities. The variational inequalities are rather general and describe, for example, the buckling of beams, plates or shells subject to obstacles. Under a technical hypothesis that is satisfied by the simply supported beam, we obtain the existence of a continuation of both the solution and the eigenvalue with respect to a local parameter. A numerical continuation method is presented that easily overcomes turning points. Numerical results are presented for the non‐linear beam.