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See detailComparative study of reduced-order methods for geometrically nonlinear structures
Khurshudyan, Amalya UL

Doctoral thesis (2017)

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 ... [more ▼]

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. [less ▲]

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