ON A STABILITY OF THE BEAMS WITH AND WITHOUT ELASTIC FOUNDATION

AUTHOR(S) / AUTOR(I): Armin D. Berecki , Sanja J. Mihok , Lidija Z. Rehlicki Lukešević

Download Full Pdf   

DOI: 10.46793/ICSSM25.032B

ABSTRACT / SAŽETAK:

In this paper, we analyze the stability of the four beams with different types of boundary conditions on a Winkler-type elastic foundation. We examine both the nonlinear and linearized problems for all beams. We show influence of boundary conditions on the number of solutions for the unique values of the critical force and foundation stiffness. Finally, we compared results of this analysis with the results of classical Euler’s axially loaded rods for several types of boundary conditions without elastic foundation.

KEYWORDS / KLJUČNE REČI:

stability, beams, boundary conditions, elastic foundation

ACKNOWLEDGEMENT / PROJEKAT:

REFERENCES / LITERATURA:

• Atanacković, ,M., Stability Theory of Elastic Rods, World Scientific, 1997.
• Rehlicki, L.,Z., Janev, M.,B., Novakovic, B.,N., and Atanacković, T.,M., On post-critical behavior of a beam on an elastic foundation, International Journal of Structural Stability and Dynamics, 18(06):1850082, 2018.
• Glavardanov, N. Grahovac, A. Berecki, and M. Zigic. The inuence of foundation nonlinearity on the post-buckling behavior of a shearable rod near double eigenvalues, International Journal of Solids and Structures, 203:236-248, 2020.
• Golubitsky, M. and Schaeffer, D.,G., Singularities and groups in bifurcation theory: Volume I, Applied Mathematical Sciences, Springer, New York, 1985.
• Chow, S.,N., Hale, J.,K., Methods of Bifurcation Theory, Grundlehren der mathematischen Wissenschaften, Springer, New York, 2012.
• Atanacković, T.,M., Stability of rotating compressed rod with imperfections, Mathematical Proceedings of the Cambridge Philosophical Society, 101(3):593–607, 1987.