A 2.5 Dimensional indirect trefftz method to model linear elastic soils

Hannes Englert, Fei Qu, Gerhard Muller

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

This contribution presents a 2.5-dimensional, frequency domain approach to model linear elastic soils, based on Indirect Trefftz Elements. 2.5-dimensional solution procedures allow a convenient way to model structures that are periodic in one direction. The solution of the problem is carried out in the frequency domain. One dimension is transformed to the wave number domain using a Fourier Transformation. The problem is solved for each wave number separately and the results are reproduced by superposing the different wave number solutions. For each wave number, Indirect Trefftz Elements are used to solve the differential equation governing the considered problem, allowing to model problems with boundaries of moderate complexity. With the help of a Helmholtz decomposition, the Lame differential equation is split up in its irrotational and solenoidal parts, with each of the fields approximated by a truncated set of wave functions. The used wave functions inherently satisfy the governing equation of the problem. Inter-element continuity is enforced using a Galerkin approach. Compared to conventional Finite Element Approaches the method incorporates the wave characteristics of the solution directly since the shape functions are chosen as a linear combination of propagating and evanescent waves. Inclusion of radiating boundary conditions is straightforward. The resulting systems of equations are smaller as compared to Finite Elements, which can reduce solving time for the soil model effectively. As a drawback, the method suffers from matrices that are fully populated and include complex entries.

Original languageEnglish
Title of host publicationEURODYN 2020 - 11th International Conference on Structural Dynamics, Proceedings
EditorsManolis Papadrakakis, Michalis Fragiadakis, Costas Papadimitriou
PublisherEuropean Association for Structural Dynamics
Pages2955-2965
Number of pages11
ISBN (Electronic)9786188507210
StatePublished - 2020
Event11th International Conference on Structural Dynamics, EURODYN 2020 - Virtual, Athens, Greece
Duration: 23 Nov 202026 Nov 2020

Publication series

NameProceedings of the International Conference on Structural Dynamic , EURODYN
Volume2
ISSN (Print)2311-9020

Conference

Conference11th International Conference on Structural Dynamics, EURODYN 2020
Country/TerritoryGreece
CityVirtual, Athens
Period23/11/2026/11/20

Keywords

  • 2.5 Dimensional Problems
  • Indirect Trefftz Method
  • Soil-structure Interaction
  • Wave Based Method

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