TY - GEN
T1 - A 2.5 Dimensional indirect trefftz method to model linear elastic soils
AU - Englert, Hannes
AU - Qu, Fei
AU - Muller, Gerhard
N1 - Publisher Copyright:
© 2020 European Association for Structural Dynamics. All rights reserved.
PY - 2020
Y1 - 2020
N2 - 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.
AB - 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.
KW - 2.5 Dimensional Problems
KW - Indirect Trefftz Method
KW - Soil-structure Interaction
KW - Wave Based Method
UR - http://www.scopus.com/inward/record.url?scp=85098721810&partnerID=8YFLogxK
M3 - Conference contribution
AN - SCOPUS:85098721810
T3 - Proceedings of the International Conference on Structural Dynamic , EURODYN
SP - 2955
EP - 2965
BT - EURODYN 2020 - 11th International Conference on Structural Dynamics, Proceedings
A2 - Papadrakakis, Manolis
A2 - Fragiadakis, Michalis
A2 - Papadimitriou, Costas
PB - European Association for Structural Dynamics
T2 - 11th International Conference on Structural Dynamics, EURODYN 2020
Y2 - 23 November 2020 through 26 November 2020
ER -