Stability Constraints in Optimization of Cracked Columns Subjected to Compressive Follower Load
Sz. Imiełowski, Modal forms of columns subjected to generalized follower force, [in:] Theoretical Foundation of Civil Engineering, X Ukrainian-Polish Transaction, W. Szczesniak [Ed.], 10, 141–150, 2002. 2.
Sz. Imiełowski, R. Bogacz, W. Kurnik, Fixed point in frequency domain of structures subjected to generalized follower force, Machine Dynamic Problems, 25, 3/4, 169–182, 2001.
J.L. Claudon, Characteristic curves and optimum design of two structures subjected to circulatory loads, J. de Mecanique, 14, 3, 531–543, 1975.
M. Hanaoka, K. Washizu, Optimum design of Beck’s column, Computers and Structures, ll, 6, 473–480, 1980.
R. Bogacz, O. Mahrenholtz, On stability of column under circulatory load, Archives of Mechanics, 38, 3, 281–287, 1986.
R. Bogacz, H. Irretier, O. Mahrenholtz, Optimal design of structures under nonconservative forces with stability constraints, Bracketing of eigenfrequencies of continuous structures. Proc. Euromech 112, Budapest, Hungary, 43–65, 1979.
M. Zyczkowski, A. Gajewski, Optimal structural design, Proc. IUTAM Symp. Non- Conservative Problems of Elastic Stability, Herrenhalb/Karlsruhe 1969, Springer Verlag, 295–30l, 1971.
Y. Tada, Y. Seguchi, K. Kema, Shape determination of nonconservative structural systems by the inverse variational principle. Memoirs of the Faculty of Engineering, Kobe University, 32, 45–61, 1985.
M. Zyczkowski, Stability of bars and bar structures, in: Strength of structural elements, M. Zyczkowski [Ed.], 242–381, Elsevier, 1991.
W.M. Ostachowicz, M. Krawczuk, Analysis of the effect of cracks on the natural frequencies of a cantilever beam, Journal of Sound and Vibration (Academic Press), 150, 2, 191–201, 1991.
M. Krawczuk, W.M. Ostachowicz, Influence of cracks on dynamic stability of column, Journal of Sound and Vibration (Academic Press), 167, 3, 541–555, 1993.
Y. Tada, R. Matsurnoto, A. Oku, Shape determination of nonconservative structural systems, Proc. 1st Int. Conf. Computer Aided Optimum Design of Structures: Recent Advances, Southampton, 13–21, Springer, Berlin 1989.
R. Bogacz, Sz. Imiełowski, Remarks on stability of discrete-continuous structure under circulatory load, J. Theor. Appl. Mechanics, 4, 32, 903–919, 1994.
Q. Wang, A comprehensive stability analysis of a cracked beam subjected to follower compression, Int. Journal of Solids and Structures, 41, 4875–4888, 2004.