The least squares stochastic finite element method in structural stability analysis of steel skeletal structures

• Autorzy: Kamiński M. , Szafran J.

Identyfikatory

DOI

10.1515/ijame-2015-0020

• Języki publikacji: EN

Abstrakty

EN

The main purpose of this work is to verify the influence of the weighting procedure in the Least Squares Method on the probabilistic moments resulting from the stability analysis of steel skeletal structures. We discuss this issue also in the context of the geometrical nonlinearity appearing in the Stochastic Finite Element Metod equations for the stability analysis and preservation of the Gaussian probability density function employed to model the Young modulus of a structural steel in this problem. The weighting procedure itself (with both triangular and Dirac-type) shows rather marginal influence on all probabilistic coefficients under consideration. This hybrid stochastic computational technique consisting of the FEM and computer algebra systems (ROBOT and MAPLE packages) may be used for analogous nonlinear analyses in structural reliability assessment.

Słowa kluczowe

EN

weighted least squares method; stochastic finite element method; generalized stochastic perturbation technique; stability problems; steel skeletal structures

PL

technika zaburzeń; konstrukcja szkieletowa; analiza stabilności

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mechanics and Engineering
• Rocznik: 2015
• Tom: Vol. 20, no. 2
• Strony: 299--318
• Opis fizyczny: Bibliogr. 17 poz., rys., tab., wykr.

Twórcy

autor

Kamiński M.

• Department of Structural Mechanics Faculty of Civil Engineering Architecture and Environmental Engineering Al. Politechniki 6, 90-924 Łódź, POLAND

autor

Szafran J.

• Department of Structural Mechanics Faculty of Civil Engineering Architecture and Environmental Engineering Al. Politechniki 6, 90-924 Łódź, POLAND

Bibliografia

• [1] Elishakoff I. (1983): Probabilistic Methods in the Theory of Structures. – New York: Wiley-Interscience.
• [2] Elishakoff I. (2000): Uncertain buckling: its past, present and future. – International Journal of Solids and Structures, vol. 37, pp.6869-6889.
• [3] Elishakoff I., Li Y.W. and Starnes J.H. (2001): Nonclassical Problems in the Theory of Elastic Stability. – Cambridge: Cambridge University Press.
• [4] Hadianfard M.A. and Razani R. (2003): Effects of semi-rigid behavior of connections in the reliability of steel frames. – Journal of Structural Safety, vol.25, pp.123–138.
• [5] Kamiński M. (2013): The Stochastic Perturbation Method for Computational Mechanics. – Chichester: Wiley.
• [6] Kamiński M. and Solecka M. (2013). Optimization of the aluminium and steel telecommunication towers using the generalized perturbation-based Stochastic Finite Element Method. – Journal of Finite Elements Analysis and Design, vol.63, No.1, pp.69-79.
• [7] Kamiński M. and Strąkowski M. (2013): On the least squares stochastic finite element analysis of the steel skeletal towers exposed to the fire. – Archives of Civil and Mechanical Engineering, vol.13, pp.242-253.
• [8] Kleiber M. (1985): Finite Element Method in Nonlinear Continuum Mechanics (in Polish). – Warsaw-Poznań: Polish Scientific Publishers.
• [9] Kleiber M. and Hien T.D. (1992): The Stochastic Finite Element Method. – Chichester, Wiley.
• [10] Kleiber M. and Hien T.D. (1997): Parameter sensitivity of inelastic buckling and post-buckling response. – Computer Methods in Applied Mechanics and Engineering, vol.145, pp.239-262.
• [11] Melchers R.E. (1987): Structural Reliability. Analysis and Prediction. – Chichester: Ellis Horwood Limited.
• [12] Papadopoulos V., Stefanou G. and Papadrakakis M. (2009): Buckling analysis of imperfect shells with stochastic non-Gaussian material and thickness properties. – International Journal of Solids and Structures, vol.46, pp.2800-2808.
• [13] ROBOT Structural Analysis Professional 2011, User’s Manual (2010). Autodesk Inc.
• [14] Sadovský Z. and Drdácký M. (2001): Buckling of plate strip subjected to localised corrosion — a stochastic model. - J. Thin-Walled Struct. 39, pp.247-259.
• [15] Schafer B.W. and Graham-Brady L. (2006): Stochastic post-buckling of frames using Koiter's method. – International Journal of Structural Stability and Dynamics, vol.6, pp.333-358.
• [16] Steinböck, Jia X., Höfinger G., Rubin H. and Mang H.A. (2008): Remarkable postbuckling paths analyzed by means of the consistently linearized eigenproblem. – International Journal for Numerical Methods in Engineering, vol.76, pp.156-182.
• [17] Timoshenko S.P. and Gere J.M. (1961): Theory of Elastic Stability (second ed.). – New York: McGraw-Hill.