Hybrid method for the computation of dynamic soil-structure ...
Hybrid method for the computation of dynamic soil-structure ...
Hybrid method for the computation of dynamic soil-structure ...
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FE-BE couplingThe <strong>dynamic</strong> <strong>soil</strong>-<strong>structure</strong> interaction <strong>for</strong>cesIntroduction<strong>Hybrid</strong> <strong>method</strong>Time Domain BEMFE-BE• FE model• Substructuring• FE equation• Implementation• Response• VerificationConclusionsFlexibility [1/NmHz]0.80.60.40.200 100 200 300 4001 x 10−5 Frequency [Hz]■ Flexibility relationship in <strong>the</strong> frequency domainˆα s (ω) = ˆF s (ω)ˆf s (ω)■ Flexibility relationship in time domainα s (t) =∫ t0F s (t − τ) f s (τ)dτ■ Asymptotic behaviour is accounted <strong>for</strong>[ˆF s (ω)] mm ∽ C mm1iω<strong>for</strong>ω → ∞Flexibility [1/Nm]86420−20 0.05 0.1 0.1510 x Time [s]cfr. waves in 1D bar: ˆF s (ω) = (iωρC p ) −1 .■ Time domain flexibility F s (t)C r = 186.40m/s →6 m186.40m/s = 0.032sLMSSMat <strong>Hybrid</strong> <strong>method</strong> <strong>for</strong> <strong>the</strong> <strong>computation</strong> <strong>of</strong> <strong>dynamic</strong> <strong>soil</strong>-<strong>structure</strong> interaction in <strong>the</strong> time domain - p. 35/44
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