Numerical aspects of coupling strongly frequency-dependent soil–foundation models with structural finite elements in the time-domain

Abstract In the literature relevant to soil–foundation–structure interaction problems a lot of results for the dynamic stiffness in the interface between the soil–foundation part and the structure have been published. However, in order to deal with transient excitations, a transformation into the time-domain is necessary. This contribution uses a well-described Pade-like rational representation, but adds some improvements concerning robustness, optimized treatment of spurious modes and numerical effectiveness. The benefits of the new findings are demonstrated by means of a typical application from foundation-engineering: very well prepared dynamic stiffness coefficients for groups of piles are used in order to treat transient excitations caused by an unbalanced rotor during running-up.

[1]  Gao Lin,et al.  High‐order doubly asymptotic open boundaries for scalar wave equation , 2009 .

[2]  Carolin Birk,et al.  An improved continued‐fraction‐based high‐order transmitting boundary for time‐domain analyses in unbounded domains , 2012 .

[3]  Mi Zhao,et al.  Stability and identification for rational approximation of frequency response function of unbounded soil , 2009 .

[4]  William H. Press,et al.  Book-Review - Numerical Recipes in Pascal - the Art of Scientific Computing , 1989 .

[5]  P. Ruge,et al.  Time‐domain analysis of unbounded media using mixed‐variable formulations , 2001 .

[6]  Isaac Harari,et al.  A survey of finite element methods for time-harmonic acoustics , 2006 .

[7]  D. Sorensen Numerical methods for large eigenvalue problems , 2002, Acta Numerica.

[8]  Julien Diaz,et al.  ROBUST HIGH ORDER NON-CONFORMING FINITE ELEMENT FORMULATION FOR TIME DOMAIN FLUID-STRUCTURE INTERACTION , 2005 .

[9]  C. Birk,et al.  Symmetric matrix-valued frequency to time transformation for unbounded domains applied to infinite beams , 2006 .

[10]  R. Clough,et al.  Dynamics Of Structures , 1975 .

[11]  Peter Ruge,et al.  A comparison of infinite Timoshenko and Euler–Bernoulli beam models on Winkler foundation in the frequency- and time-domain , 2007 .

[12]  Peter Nawrotzki,et al.  Statische und dynamische Berechnung von Turbinenfundamenten aus Stahlbeton , 2005 .

[13]  D. K. Baidya,et al.  Dynamic nonlinear response of pile foundations under vertical vibration—Theory versus experiment , 2010 .

[14]  T. Hagstrom Radiation boundary conditions for the numerical simulation of waves , 1999, Acta Numerica.

[15]  S. Tsynkov Numerical solution of problems on unbounded domains. a review , 1998 .

[16]  T. L. Geers IUTAM Symposium on Computational Methods for Unbounded Domains : proceedings of the IUTAM symposium held in Boulder, Colorado, USA, 27-31 July 1997 , 1998 .

[17]  William H. Press,et al.  Numerical recipes in C. The art of scientific computing , 1987 .

[18]  Eleanor Chu,et al.  Discrete and Continuous Fourier Transforms: Analysis, Applications and Fast Algorithms , 2008 .

[19]  Joseph E. Bowles,et al.  Foundation analysis and design , 1968 .

[20]  F. Hu Absorbing Boundary Conditions , 2004 .

[21]  Anil K. Chopra,et al.  Dynamics of Structures: Theory and Applications to Earthquake Engineering , 1995 .

[22]  Juan J. Aznárez,et al.  Dynamic stiffness of deep foundations with inclined piles , 2010 .

[23]  D. Givoli High-order local non-reflecting boundary conditions: a review☆ , 2004 .

[24]  J. H. Wilkinson,et al.  Handbook for Automatic Computation: Linear Algebra (Grundlehren Der Mathematischen Wissenschaften, Vol 186) , 1986 .

[25]  Thomas L. Geers IUTAM Symposium on Computational Methods for UnBound Domains , 1998 .

[26]  Ediansjah Zulkifli Consistent description of radiation damping in transient soil-structure interaction , 2008 .

[27]  Absorbing Boundary Conditions For Corner Regions , 2003 .

[28]  William H. Press,et al.  Numerical Recipes in Fortran 77 , 1992 .