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Stability of Slender Non-Conservative Columns Made of Thermo-Active Gradient Materials

Kurnik W.

Machine Dynamics Problems

2008

Vol. 32, No. 4

50-66

The paper is concerned with stability analysis of slender thin-walled cantilever beam subjected to axial distributed follower load, modelled as Leipholz columns and made of functionally gradient materials. Both transverse and longitudinal material gradients are studied as a result of different phase mixture with inclusion of thermo-active shape memory alloy (SMA). Attention is focused on the effect of phase transformation in SMA caused by increase of temperature and resulting in considerable changes of the local visco-elastic material properties which in turn affect system stability. Equivalent homogeneous beam stiffness and internal Kelvin-Voigt loss factor are determined using Kirchhoff's hypothesis and the visco-elastic principle. Partial equation of transverse column vibration is transformed to ordinary equations by means of two-mode Galerkin's discretisation based on the cantilever beam functions. Eigen-value behaviour and critical follower force are studied for various material gradient configurations. A concept of intelligent column is proposed utilizing longitudinal material functionality induced by non-uniform temperature distribution.

FE analysis of geometrically nonlinear static problems with follower loads

Kozák I., Nándori F., Szabó T.

Computer Assisted Mechanics and Engineering Sciences

1999

Vol. 6, No. 3-4

369-383

In the paper a general purpose finite element software for the simulation of piezoelectronic materials and structronic (structure and electronic) systems is presented. The equations of coupled electromechanical problems are given in a weak form, which are basis of the development of 1D, 2D, 3D as well as multilayered composite shell elements. The smart structures finite element code includes static and dynamic analysis, where also controlled problems can be simulated. Two test examples are presented to compare the numerical results with measurements.