Abstract:
This thesis presents the linear and nonlinear analysis of thin shell structures.
The linear formulation is based on three finite elements namely the: four nodes
degenerated shell element (DE4), the four nodes flat shell element (FE4) and
the nine nodes degenerated shell element (DE9). Each one of these elements
has six degrees of freedom per node. Additional elements have been developed;
these are: the four nodes element, employing the Mixed Interpolation of
Tensorial Components approach (MITC) proposed by Bathe to avoid shear
locking applied on DE4 and FE4 , the NonConforming Element (NCE) to
improve the behavior in bending situations, and the nine nodes element with
Selective Reduced Integration (SRI) and Weighted Modified Integration
(WMI). These elements are used to overcome the shear and membrane lock in
lieu of using reduced integration.
The verification of linear formulation was based on using patch test. The DE4
element passes all patch tests except the pure bending test, while the other
elements pass the tests partially. Further verification was done by using
numerical examples; and the elements perform very well when the results are
compared with exact ones as they are in good agreement.
The problems of shear and membrane locks result in the divergence of the
solution for these shells with increase in the number of elements. A solution is
proposed to correct the convergence curve to be asymptotic to the exact
solution curve by using extrapolation. This was done by selecting a Weibull
model to correlate the displacement and mesh size through the number of
joints. The model depends on parameters; the values of which depend on the
values of displacements before the divergence occurs. Good results are
obtained when applying the method in different numerical examples for the
DE4 element.
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