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Complementarity eigenvalue problems for nonlinear matrix pencils
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DOI：10.1016/j.amc.2017.05.028.png)
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Abstract
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This work deals with a class of nonlinear complementarity eigenvalue problems that, from a mathematical point of view, can be written as an equilibrium model [A(lambda) B(lambda) [u [v C(lambda) D(lambda)] w] = 0]' u >= 0, v >= 0, u(T)v = 0, where the vectors u and v are subject to complementarity constraints. The block structured matrix appearing in this partially constrained equilibrium model depends continuously on a real scalar lambda is an element of Lambda. Such a scalar plays the role of a non-dimensional load parameter, but it may have also other physical meanings. The symbol A stands for a given bounded interval, possibly non-closed. The numerical problem at hand is to find all the values of lambda (and, in particular, the smallest one) for which the above equilibrium model admits a nontrivial solution. By using the so-called Facial Reduction Technique, we solve efficiently such a numerical problem in various randomly generated test examples and in two mechanical examples of unilateral buckling of columns. (C) 2017 Elsevier Inc. All rights reserved.
Keywords:
Unilateral buckling
Nonlinear complementarity eigenproblem
Nonpolynomial matrix pencil
Complementarity conditions
Zeros of a nonpolynomial function
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