Interface Conditions and Loss of Stability for Stepped Columns


Article Preview

We discuss the dynamic behavior of stepped columns subjected to follower forces. In particular, limit cases which correspond to columns with hinges or cracks and concentrated lateral supports are studied for the stability limit. Typically, solutions suffer jumps in certain derivatives, which have to satisfy compatibility conditions. The influence of these interface conditions on the critical force is investigated. The aim is to optimize the location of such singularities and thus to obtain maximum critical loads, respectively worst case estimates for the loss of stability.



Edited by:

Tadeusz Uhl and Andrzej Chudzikiewicz




R. Bogacz et al., "Interface Conditions and Loss of Stability for Stepped Columns", Applied Mechanics and Materials, Vol. 9, pp. 41-50, 2008

Online since:

October 2007




[1] Bogacz R., Irretier H., Mahrenholtz O., 1979, Optimal design of structures under nonconservative forces with stability constrains, Bracketing of eigenfrequencies of continuous structures. Proc. Euromech 112, Budapest, Hungary, 43-65.

[2] Bogacz R., Niespodziana A., 1987, On stability of continuous Beck column with localized loss of rigidity, Inst. of Fundamental Techn. Research Reports, Vol. 27, 1-23.

[3] Mahrenholtz O., Bogacz R., 1981, On the shape of characteristic curves for optimal structures under non-conservative loads, Ingenieur-Archiv, Vol. 50, 141-148.

DOI: 10.1007/bf00539698

[4] Tada Y., Matsurnoto R., Oku A., 1989, Shape determination of nonconservative structural systems, Proc. 1st Int. Conf. Computer Aided Optimum Design of Structures: Recent Advances, Southampton, 13-21, Berlin: Springer.

[5] Przybyłowicz, P., 2004, Application of functionally graded material to non-conservative Beck column, In: Proceedings of the 11th PTKS Conference, August´ow, September 1-4, pp.52-57.

[6] Imiełowski Sz., 2002, Modal forms of columns subject to generalized follower force, Theoretical Foundation of Civil Engineering, X Ukrainian-Polish Translation, W. Szczesniak Ed., Warsaw, June 2002, V. 10, 141-150.

[7] Imiełowski Sz, Bogacz, R., 2001, Fixed point in frequency domain of structures subject to generalized follower force, Machine Dynamic Problems, Vol. 25, no. 3/4, 169-182.

[8] Bogacz, R., Frischmuth K., 2005, Transient Behavior of Columns under Follower Forces, Machine Dynamics Problems, Vol. 29 No. 4, pp.7-20.

[9] Blachut J., Gajewski A., 1980, A unified approach to optimal design of columns, Solid Mechanics Archives, Vol. 5, No. 4, 363-413.

[10] Gutkowski W., Mahrenholtz O., Pyrz M., 1993, Minimum weight design of structures under nonconservative forces, In: Optimization or Large Structural Systems (G.T.N. Rozvany, Ed. ), Series E: Applied Sciences, Vo1. 231 or NATO ASI Series), Vol. 2, 1087-1100, Kluwer Acad. Publ.

DOI: 10.1007/978-94-010-9577-8_56

[11] Hanaoka M., Washizu K., 1980, Optimum design of Beck's column, Computers and Structures, Vol. ll, No. 6, 473-480.

DOI: 10.1016/0045-7949(80)90054-1

[12] Imiełowski Sz., Mahrenholtz O., 1997, Optimization and sensitivity of stepped columns under circulatory load, Applied Mathematics and Computer Sciences, V. 7, 1, 155-170.

[13] Frischmuth K., Kosi´nski W., Lekszycki T., 1993, Free vibrations of finite memory material beams, Int. J. Engng Sci., 31, 3, 385-395.

DOI: 10.1016/0020-7225(93)90013-k

[14] Bogacz, R., Imiełowski Sz., 1990, On the discontinuous changes of critical force for columns with transverse-slidable joint under follower load, In: Stability or steel structures (Ivanyi M., Ed. ). Budapest: Akademiai Kiado, pp.355-363.

Fetching data from Crossref.
This may take some time to load.