Hybrid method for the computation of dynamic soil-structure ...

FE-BE couplingThe dynamic soil-structure interaction forcesIntroductionHybrid methodTime Domain BEMFE-BE• FE model• Substructuring• FE equation• Implementation• Response• VerificationConclusions■ Soil-structure interaction force:f N s = ( F 0 −1s)α N s − ( N−1F 0 ) −1∑s Fs N−i f i s (33)i=1■ The structural response is written in terms of the degrees of freedom u b2 :N−1Q N ( )b 2= T q F0 −1s T u u N ( )b 2− T q F0 −1∑si=1F N−is f i s (34)Q N b 2= T q(F0s) −1T u u N b 2− Q N b 2 hist (35)■ This is introduced into the finite element equation:[ ] } { }M b1 b 1M b1 b 2{üN b1f intNb+ 1+M b2 b 1M b2 b 2ü N b 2f intNb 2[] { }0 0 u N b 10 T q (F 0 s) −1 =T u u N b 2{ } {f extNb 1+f extNb 20Q N b 2 hist}LMSSMat Hybrid method for the computation of dynamic soil-structure interaction in the time domain - p. 37/44