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Stability of two-DOF systems with clearances using FET

Kranjčević N., Stegic M., Vranković N.

Computer Assisted Mechanics and Engineering Sciences

2007

Vol. 14, No. 1

1-11

The finite element in time method (FET) is a fast and reliable implicit numerical method for obtaining steady state solutions of the periodically forced dynamical systems with clearances. Delineation of the stable and unstable solutions could help in predicting regular and chaotic motions of such dynamical systems and transitions to either type of response. Stability of the FET solutions can be investigated via the Floquet theory, without any special effort for calculating the monodromy matrix. The applicability of the stability analysis is demonstrated through the study of two-degree-of-freedom systems with clearances. Close agreement is found between obtained results and published findings of the harmonic balance method and the piecewise full decoupling method.

Shakedown of elastic-thermo-plastic structures

Vranković N., Stegic M., Kranjčević N.

Computer Assisted Mechanics and Engineering Sciences

2000

Vol. 7, No. 2

239-245

Recently formulated shakedown theorems for materials with temperature-dependent yield stress [1] are applied to evaluation of the elastic shakedown boundary. In order to simulate actual shakedown behavior of elastic-thermo-plastic structures resulting from experimental investigations, the material model of the German mild steel St 37 is considered. It is found that the obtained elastic shakedown boundaries are within the corresponding boundaries based on the classical shakedown theory. Two examples are compared with the well-known solutions obtained for the neglected yield stress dependence on temperature.