Stability Analysis of an Imperfect Slender Web Subjected to the Shear Load

Abstract:

The stability analysis of an imperfect slender web subjected to the shearing load is presented, a specialized code based on FEM has been created. The nonlinear finite element method equations are derived from the variational principle of minimum of total potential energy. To obtain the nonlinear equilibrium paths, the Newton-Raphson iteration algorithm is used. Corresponding levels of the total potential energy are defined. The peculiarities of the effects of the initial imperfections are investigated. Special attention is paid to the influence of imperfections on the post-critical buckling mode. Obtained results are compared with those gained using ANSYS system.

• Periodical: Applied Mechanics and Materials (Volume 837)
• Pages: 52-57
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.837.52
• Online since: June 2016
• Authors: Martin Psotný*
• Keywords: Buckling, Geometric Nonlinear Theory, Initial Imperfection, Postbuckling, Stability

References

[1] K. Washizu, Variational Methods in Elasticity and Plasticity, third ed., Pergamonn Press, New York, (1982).

[2] S. Saigal, I. Yang, Nonlinear Dynamic Analysis with 48 DOF Curved Thin Shell Element, International Journal for Numerical Methods in Engineering 22 (1985) 1115-1128.

DOI: 10.1002/nme.1620210611

[3] O. C. Zienkiewicz, R. L. Taylor, The Finite Element Method, Vol. 2, Solid and Fluid Mechanics, Dynamics and Non-Linearity, fourth ed., McGraw-Hill, London, (1991).

[4] M. A. Crisfield, Non-Linear Finite Element Analysis of Solids and Structures, Wiley&Sons, London, (1996).

[5] ANSYS User's Manual 13. 0, Swanson Analysis Systems, Inc., (2010).

[6] Z. Kala, J. Kala, M. Skaloud, B. Teply, Sensitivity Analysis of the Effect of Initial Imperfections on the Stress State in the Crack-Prone Areas of Breathing Webs, In: Proceedings of the Fourth Int. Conf. on Thin-walled Structures, 2004, Loughborough, England, UK, pp.499-506.

DOI: 10.1201/9781351077309-56

[7] M. Psotny, J. Ravinger, Post-Buckling Behaviour of Imperfect Slender Web, Engineering Mechanics Vol. 14, No. 6 (2007) 423-429.

[8] A. S. Volmir, Stability of deformable systems, Nauka, Moscow, 1967. (in Russian).

[9] P. S. Bulson, The Stability of Flat Plates, Chatto&Windus, London, (1970).

[10] F. Bloom, D. Coffin, Handbook of Thin Plate Buckling and Postbuckling, Chapman&Hall/CRC, Boca Raton, (2001).

[11] J. Rhodes, Some observations on the post-buckling behaviour of thin plates and thin-walled members, Thin-walled structures Vol. 41, No. 2-3 (2003) 207-226.

DOI: 10.1016/s0263-8231(02)00088-5

[12] J. Ravinger, Vibration of Imperfect Thin-Walled Panel. Part 1: Theory and Illustrative Examples. Part 2: Numerical Results and Experiment, Thin-Walled Structures Vol. 19, No 1 (1994) 1-36.

DOI: 10.1016/0263-8231(94)90002-7

[13] M. Psotny, Total Potential Energy Levels in the Post-Buckling, in: Proceedings of 13th International Scientific Conference VSU, 2013, Sofia, Bulgaria, Vol. I., pp. I- 296-299.

[14] J. Ravinger, M. Psotny, Stable and Unstable Paths in the Post-Buckling Behaviour of Slender Web, in: Proceedings of Coupled Instabilities in Metal Structures, Roma, 2004, p.67 – 75.

[15] Z. Bittnar, J. Sejnoha, Numerical Methods in Structural Mechanics 2, Publishing House CVUT, Praha, 1992. (in Czech).

[16] M. Psotny, Stable and unstable paths in geometrically nonlinear problems, Publishing House SvF STU, Bratislava, 2004. (in Slovak).