TY - JOUR
T1 - On the continuation for variational inequalities depending on an eigenvalue parameter
AU - Miersemann, Erich
AU - Mittelmann, Hans
AU - Törnig, W.
PY - 1989
Y1 - 1989
N2 - 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.
AB - 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.
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U2 - 10.1002/mma.1670110107
DO - 10.1002/mma.1670110107
M3 - Article
AN - SCOPUS:84988163665
SN - 0170-4214
VL - 11
SP - 95
EP - 104
JO - Mathematical Methods in the Applied Sciences
JF - Mathematical Methods in the Applied Sciences
IS - 1
ER -