Comparative study of reduced-order methods for geometrically nonlinear structures

The dissertation is devoted to the comparison and development of techniques for
model order reduction (MOR) of geometrically nonlinear elastic structures in the
static limit.
The MOR procedure works in the following way: the structure is first discretized
into finite elements and a discretized system of algebraic equations is obtained, in
which the stiffness matrix depends on the unknown vector. The system is then
projected to a lower order space. The choice of the basis of the projection space is
made according to the methods developed in the thesis. To this end, three techniques
are developed here based on different choices of the basis functions.
Comparative analysis of the suggested methods is carried out in the case of
two-dimensional structures (Euler-Bernoulli beam, multi-span beam and frame). In
order to be able to compare the results with those obtained by the MOR techniques
which are developed, the benchmark problems which are examined are first solved
analytically.
Results of computations carried out in Python and are then discussed.