Decoupled scaled boundary finite element method for analysing dam–reservoir dynamic interaction

Abstract

In this study, an efficient method is developed for solving systems of partial differential equations governing seismic analysis of 2D dam reservoir interaction, in the frequency domain. Using Chebyshev higher-order polynomials as mapping function, special shape function, integration method of Clenshaw–Curtis and the integral form used to weighted residual method, coefficient matrices of the system of governing equations become diagonal. This means that the governing partial differential equation for each degree of freedom becomes independent from others. This feature and discretizing only boundaries of domain significantly reduce computational costs in comparison with other methods. In this regard, various problems such as dynamic analysis of empty gravity dam, calculating the hydrodynamic pressure on rigid dam, and dam–reservoir interaction analysis due to the horizontal motion of foundation are examined. Comparing the results of this method with other analytical/numerical methods shows high capability and accuracy of the proposed method.

KEYWORDS:

• Semi-analytical method
• decoupled differential equations
• dam–reservoir interaction
• reservoir boundary conditions
• frequency domain

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 74Sxx
• 65Dxx
• 35Lxx

Acknowledgements

The authors would like to acknowledge and express their special gratitude to anonymous reviewers, for their constructive comments that improved the quality of the manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.