Computer Analysis of Dynamic Reliability of Some Concrete Beam Structure Exhibiting Random Damping
More details
Hide details
Department of Structural Mechanics, Łódź University of Technology, Al. Politechniki 6, 90-924, Łódź, Poland
Online publication date: 2021-01-29
Publication date: 2021-03-01
International Journal of Applied Mechanics and Engineering 2021;26(1):45-64
An efficiency of the generalized tenth order stochastic perturbation technique in determination of the basic probabilistic characteristics of up to the fourth order of dynamic response of Euler-Bernoulli beams with Gaussian uncertain damping is verified in this work. This is done on civil engineering application of a two-bay reinforced concrete beam using the Stochastic Finite Element Method implementation and its contrast with traditional Monte-Carlo simulation based Finite Element Method study and also with the semi-analytical probabilistic approach. The special purpose numerical implementation of the entire Stochastic perturbation-based Finite Element Method has been entirely programmed in computer algebra system MAPLE 2019 using Runge-Kutta-Fehlberg method. Further usage of the proposed technique to analyze stochastic reliability of the given structure subjected to dynamic oscillatory excitation is also included and discussed here because of a complete lack of the additional detailed demands in the current European designing codes.
Mayers A. (2009): Vibration acceptance criteria.– Australian Bulk Handling Review: issue March/April.
DIN 4150 1-3:2001: Vibrations in buildings.
AS 2670.1-201 Australian Standards: Evaluation of human exposure to whole-body vibration, Part 1: General requirements.
Cornell C.A. (1968): Engineering seismic risk analysis.– Bulletin of Seismological Society of America, vol.58, No.5, pp.1583-1606.
Madsen H.O., Krenk S. and Lind N.C. (1986): Methods of Structural Safety.– Prentice Hall, Englewood Cliffs.
Melchers R.E. and Beck A.T. (2018): Structural Reliability Analysis and Prediction.– John Wiley & Sons, Hoboken, NJ, p.497.
Valdebenito M.A., Jensen H.A., Schuëller G.I. and Caro F.E. (2012): Reliability sensitivity estimation of linear systems under stochastic excitation.– Computers and Structures, vol.92-93, pp.257-268.
Soize C. (2013): Stochastic modelling of uncertainties in computational structural dynamics – Recent theoretical advances.– J. of Sound and Vibration, vol.332, No.10, pp.2379-2395.
Roberts J.B. and Spanos P.D. (1990): Random vibration and statistical linearization.– Chichester, Wiley.
Muscolino G., Ricciardi G. and Vasta M. (1997): Stationary and non-stationary probability density function of non-linear oscillators.– Int. J. of Non-Linear Mechanics, vol.32, No.6, pp.1051-1064.
Roberts J.B. and Spanos P.D. (1986): Stochastic averaging: an approximation method of solving random vibration problems.– Int. J. Non-Linear Mechanics, vol.21, No.2, pp.111-134.
Sobczyk K, Wędrychowicz S. and Spencer B.F. (1996): Dynamics of structural systems with spatial randomness.– Int. J. of Solids and Structures, vol.33, No.11, pp.1651-1669.
Goller B., Pradlwarter H.J. and Schuëller G.I. (2013): Reliability assessment in structural dynamics.– Journal of Sound & Vibration, vol.332, pp.2488-2499.
Kamiński M. (2013): The Stochastic Perturbation Method for Computational Mechanics.– Chichester, Wiley.
Kamiński M. and Corigliano A. (2015): Numerical solution of the Duffing equation with random coefficients.– Meccanica, vol.50, pp.1841-1853.
Hughes T.J.R. (2000): The Finite Element Method – Linear Static and Dynamic Finite Element Analysis.– New York, Dover Publications, Inc.
Hutton D.V. (2004): Fundamentals of Finite Element Analysis.– McGraw-Hill.
Han S.H., Benaroya H. and Wei T. (1999): Dynamics of transversely vibrating beams using four engineering theories.– Journal of Sound and Vibration, vol.225, No.5, pp.935-988.
Liao S., Zhang Y. and Chen D. (2019) Runge-Kutta Finite Element Method based on the characteristic for the incompressible Navier-Stokes equations.– Advanced Applied Mathematics & Mechanics, vol.11, pp.1415-1435.
Botasso C.L. (1997): A new look at finite elements in time: a variational interpretation of Runge-Kutta methods.– Applied Numerical Mathematics vol.25, pp.355-368.
Eurocode 0 (2005): Basis of structural design. EN 1990:2002/A1.– European Committee for Standardization, Brussels.
Pradlwarter H.J. and Schuëller GI. (2010): Uncertain linear systems in dynamics: Efficient stochastic reliability assessment.– Computers and Structures, vol.88, pp.74-86.
Kamiński M. (2015): On the dual iterative stochastic perturbation-based finite element method in solid mechanics with Gaussian uncertainties.– International Journal for Numerical Methods in Engineering, vol.104, No.11, pp.1038-1060.
Journals System - logo
Scroll to top