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We investigate bifurcation scenario of the von K'arm'an
equations defined inrectangular domains. Both simply supported
and partially clamped boundary conditionsare considered. First,
we study how various conjugate gradient (CG) type methodscan be
incorporated in the context of continuation methods to trace
solution curves of the discrete von K'arm'an equaitons. Next, we
discuss linear stabilitiesof the von K'arm'an equations with
partially clammped boundary conditions. Inparticular, the first
five eigenvalues and associated eigenfunctions of the linearized
von K'arm'an equations are obtained via computer algebra. These
CGtype methods are exploited to slove linear systems as well as
to detectsingularity along solution paths of the discrete
problem. Sample numericalresults are reported. Our results show
that for different boundary conditionsthe bifurcation scenario
of the von K'arm'an equations depends on the lengthof the
domain.
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