<DOC>
<DOCNO>
1294
</DOCNO>
<TITLE>
non-linear shallow shell analysis by the matrix force
method .
</TITLE>
<AUTHOR>
lansing,w., jones,i.w. and ratner,p.
</AUTHOR>
<BIBLIO>
nasa tn.d1510, 1962, 753.
</BIBLIO>
<TEXT>
  the matrix force method of redundant
structure analysis is currently
being extended by various users to cover
a number of non-linear problems .
one of these is the non-linear analysis
of heated cambered wings, such as
might be used in advanced flight vehicles .
in this case the approach used
by the present authors is equally applicable
to shallow shells, the formulation
of the strain-displacement and
equilibrium relations being a
finite element equivalent to that used
by marguerre .  the solution is
obtained by a combined iteration and step
by step procedure utilizing a
tangent flexibility matrix .  divergence
in the calculations indicates
that the range of stable configurations
has been exceeded .  cambered
plates subjected to several loadings are
given as examples,. for one, an
exact solution is available for comparison .
  it is believed that the basic concepts
involved in this shallow
shell analysis can be extended to apply
to other, more general shell
instability problems, and that useful
solutions to the latter are probably
within the capability of present day digital computers .
</TEXT>
</DOC>
