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A Novel Reduced Spectral Function Approach for Finite Element Analysis of Stochastic Dynamical Systems

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Computational Methods in Stochastic Dynamics

Part of the book series: Computational Methods in Applied Sciences ((COMPUTMETHODS,volume 26))

Abstract

This work provides the theoretical development and simulation results of a novel Galerkin subspace projection scheme for damped dynamic systems with stochastic coefficients and homogeneous Dirichlet boundary conditions. The fundamental idea involved here is to solve the stochastic dynamic system in the frequency domain by projecting the solution into a reduced finite dimensional spatio-random vector basis spanning the stochastic Krylov subspace to approximate the response. Subsequently, Galerkin weighting coefficients have been employed to minimize the error induced due to the use of the reduced basis and a finite order of the spectral functions and hence to explicitly evaluate the stochastic system response. The statistical moments of the solution have been evaluated at all frequencies to illustrate and compare the stochastic system response with the deterministic case. The results have been validated with direct Monte-Carlo simulation for different correlation lengths and variability of randomness.

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Acknowledgements

AK acknowledges the financial support from the Swansea University through the award for Zienkiewicz scholarship. SA acknowledges the financial support from The Royal Society of London through the Wolfson Research Merit Award.

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Authors and Affiliations

  1. Swansea University, Singleton Park, Swansea, SA2 8PP, UK

    Abhishek Kundu & Sondipon Adhikari

Authors
  1. Abhishek Kundu
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  2. Sondipon Adhikari
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Correspondence to Abhishek Kundu .

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Editors and Affiliations

  1. Inst. Structural Analysis & Seismic Res., National Technical University of Athens, Iroon Polytechniou, Zografou Campus 9, Athens, 15780, Greece

    Manolis Papadrakakis

  2. Inst. Structural Analysis & Seismic Res., National Technical University of Athens, Iroon Polytechniou, Zografou Campus 9, Athens, 15780, Greece

    George Stefanou

  3. Inst. Structural Analysis & Seismic Res., National Technical University of Athens, Iroon Polytechniou, Zografou Campus 9, Athens, 15780, Greece

    Vissarion Papadopoulos

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Kundu, A., Adhikari, S. (2013). A Novel Reduced Spectral Function Approach for Finite Element Analysis of Stochastic Dynamical Systems. In: Papadrakakis, M., Stefanou, G., Papadopoulos, V. (eds) Computational Methods in Stochastic Dynamics. Computational Methods in Applied Sciences, vol 26. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5134-7_3

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  • DOI: https://doi.org/10.1007/978-94-007-5134-7_3

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-5133-0

  • Online ISBN: 978-94-007-5134-7

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