Danijela Brzović

WYD method for an eigen solution of coupled problems

Designing efficient and stable algorithm for finding the eigenvalues andeigenvectors is very important from the static as well as the dynamic aspectin coupled problems. Modal analysis requires first few significant eigenvectorsand eigenvalues while direct integration requires the highest value toascertain the length of the time step that satisfies the stability condition.The paper first presents the modification of the well known WYDmethod for a solution of single field problems: an efficient and numericallystable algorithm for computing eigenvalues and the correspondingeigenvectors. The modification is based on the special choice of thestarting vector. The starting vector is the static solution of displacements forthe applied load, defined as the product of the mass matrix and the unitdisplacement vector. The starting vector is very close to the theoreticalsolution, which is important in cases of small subspaces.Additionally, the paper briefly presents the adopted formulation for solvingthe fluid-structure coupled systems problems which is based on a separatesolution for each field. Individual fields (fluid and structure) are solvedindependently, taking in consideration the interaction information transferbetween them at every stage of the iterative solution process. The assessmentof eigenvalues and eigenvectors for multiple fields is also presented. This eigenproblem is more complicated than the one for the ordinary structural analysis,as the formulation produces non-symmetrical matrices.Finally, a numerical example for the eigen solution coupled fluidstructureproblem is presented to show the efficiency and the accuracy ofthe developed algorithm.

Numerical Model for Fluid–Structure Coupled Problems Under Seismic Load

This chapter briefly describes the numerical models for the simulation of fluid–structure coupled problems. The applied models are primarily intended to simulate the fluid–structure dynamic interaction in seismic conditions. The partition scheme of coupled (multi-field) problems is briefly described as the most common approach for the fluid–structure dynamic analysis. Models can simulate the most important effects of plane and spatial structures that are in direct contact with the fluid. Some of models’ possibilities are illustrated in numerical analyses of the seismic behavior for four practical examples.