APPLICATION OF THE DISTRIBUTED TRANSFER FUNCTION METHOD AND THE RIGID FINITE ELEMENT METHOD FOR MODELLING OF 2-D AND 3-D SYSTEMS

Transcription

1 ODELOWIE IŻYIERSKIE ISS X Gc PPLICIO O HE DISRIBUED RSER UCIO EHOD D HE RIGID IIE ELEE EHOD OR ODELLIG O -D D -D SYSES RŁ HEI CEZRY ORLIKOWSKI chaca Egrg Dpartt Gdak Uvrt o choog -a: rah@pg.gda.p corko@pg.gda.p Suar. I th papr appcato o th Dtrbutd rar ucto thod ad th Rgd t Et thod or odg o -D ad -D t prtd. I th thod a atc bod dvdd to -D dtrbutd paratr t trp or pr. h ho bod dvdd to trp or pr dcrbd b a t o coupd parta drta uato. Sovg th uato th tat pac or t pob to obta th rpo o th t udr a tra ctato a a to prdct th t pctru.. IRODUCIO I th aa o th atc to or thr doa -D or -D t th t Et thod E d ud. h dcrtato thod d to a t o ordar drta uato. Hovr to obta accurat rut t car to app a grat ubr o t t ad to ov hgh ordr od a bg ubr o th cod ordr uato. h Dtrbutd rar ucto thod D a atratv approach or th aa o a ca o uch t ar o-doa. St dtrbutd paratr t ar gv tr o ar parta drta uato ar to upd paratr t th ca ao b dcrbd b th trar ucto thod. I th ca th dtrbutd trar ucto th corrpodg athatca od. It cota a orato about a t ad ab to obta th rpo udr a ctato ad to prdct th t pctru. Dtrbutd rar ucto thod do ot au a approato b upg tchu. h rpo o th t ca b prtd a act ad cod or. I th papr appcato o th Dtrbutd rar ucto thod ad th Rgd t Et thod or odg o -D ad -D t propod. h a atratv approach to th ko Strp Dtrbutd rar ucto thod SD. I th thod a atc bod dvdd to trp or pr -D dtrbutd paratr t. Each trp/pr rprt o-doa dtrbutd t ad t dcrbd b approprat cod ordr parta drta uato. B appcato o th Dtrbutd rar ucto thod th rpo o ach trp/pr ca b obtad a act ad cod or. h ho bod th dcrbd b a t o coupd parta drta uato. a th rpo ratd to th ho bod prtd a - act cod or. h thod a to o th D thod or o-doa dtrbutd paratr t.

2 98 R. HEI C. ORLIKOWSKI. RSER UCIO EHOD OR -D DISRIBUED PREER SYSE t t g.. O-doa dtrbutd paratr t Lt u codr th dtrbutd paratr t dcrbd b th o-doa -th ordr ar parta drta uato atr Lapac traorato th rpct to t th boudar codto K ad th ro ta codto or pcato hr: t ctato t rpo boudar codto oprator t - ko ucto cop paratr. Euato ca b traord to th tat pac or [] u hr: co L atrc copod o co L u } {. h outo o th uato ad ca b d th oog or [] d H G 5 hr: > < G 6 H 7 k G } { G 8 k H } { H. 9

3 PPLICIO O HE DISRIBUED RSER UCIO EHOD D HE RIGID 99 Hc th t rpo ca b prd a tgra or 5 th th tgra kr bg th Gr ucto o th t. h trar ucto o th dtrbutd t G k obtad b th Lapac traorato th rpct to t o th Gr ucto. h trar ucto cota a orato about th t ad ab to obta th rpo o th t udr a ta or tra ctato a a to prdct th t pctru ad tabt. h thod ca b ao appd or odg o cop dtrbutd-upd paratr t [ ].. RSER UCIO EHOD OR -D D -D DISRIBUED PREER SYSES h D ca b tdd to -D ad -D cotua [ 5]. I [ 5] to obta th approprat athatca od D ad E thod ar appd. I th papr a atratv approach propod. Itad o E th Rgd t Et thod RE [6] ud. I th RE th da o hap ucto ot appd. Coparg to covtoa approach prtd [ 5] th propod thod o odg uch or p ad ar or ptato. I th thod o odg th bod dvdd to trp or -D t - g. b ad pr or -D t - g. c. Each trp or pr rprt o-doa dtrbutd t ad t dcrbd b approprat cod ordr parta drta uato. Hovr th uato hav ao tr ratd to tracto bt trp/pr. Hc th gv t ca b dcrbd b a t o coupt tracto bt t cod ordr parta drta uato. a t t b trp c d t t pr g.. Spata dcrtato o D ad D bod: a c E b d D thod h drta uato ca b prtd th oog or: [ ] th boudar codto hr atrc cota drta uato coct atrc ar copod o boudar codto oprator. h uato a b rtt th tat pac rprtato: u

4 R. HEI C. ORLIKOWSKI hr: co I u atrc ca b obta ro I dtt atr. h rpo o th t dcrbd b ca b prtd th tgra or 5. It ab to obta th t gvau gucto ruc rpo ad th rpo to gv haroc ctato.. ILLUSRIVE EXPLE a p utratv ap t u codr th bra g. th th oog paratr: kg/ a pr ut ara / orc pr ut gth ab /5. g.. bra a -D atc bod h RE uato th ca th drc uato or bra t ca b rtt a. Dvdg b o obta ] [. 5 ug th uato 5 d ] [. 6 or ap th ca o trp or th uato 6 hav th or: ] [ ] [ b a b a

5 PPLICIO O HE DISRIBUED RSER UCIO EHOD D HE RIGID ] [ ] [ ad boudar codto:. bov uato ca b rtt th or o uato hr: dag dag I ad t th or hr. Sovg th tat pac uato ratd to th gv bra o rut hav b obtad. g. prt ruc charactrtc o th bra ro g. put orc at..5 ad output dpact..5. I th ab. atura ruc o th vtgatd bra or drt athatca od ar prtd. g.. ruc rpo o bra th bra ro g ruc [rad/] agtud [db] ruc rpo or 5 trp ruc rpo or trp

6 R. HEI C. ORLIKOWSKI ab.. atura ruc ω [rad/] o codrd bra RE Propod thod Eact 6 t ruc trp 6 trp t COCLUSIO I th papr appcato o th Dtrbutd rar ucto thod ad th Rgd t Et thod or odg o -D ad -D t propod. I th thod a atc bod dvdd to trp or pr. Each trp or pr rprt o-doa dtrbutd t ad t dcrbd b approprat cod ordr parta drta uato. B appcato o th Dtrbutd rar ucto thod th rpo o ach t ca b obtad a act ad cod or. h ho bod dvdd to trp or pr th dcrbd b a t o coupd parta drta uato. Sp utratv ap proov that propod approach ratv a ad covt or coputr codg. ckodgt h rarch upportd ro th cc budgt rourc 8- a th rarch proct 59 LIERURE. Yag B. a C..: rar ucto o o-dtoa dtrbutd paratr t. SE Joura o ppd chac 99 Vo. 59 p Yag B.: Dtrbutd trar ucto aa o cop dtrbutd paratr t. SE Joura o ppd chac 99 Vo. 6 p Orkok C.: odg aa ad th o dac t th bod graph appcato. Gdańk: WPG 5 [ Poh].. Yag B. Zhou J.: S - aatca outo o -d atct prob b th trp dtrbutd trar ucto thod. It. J. Sod Structur 996 Vo. o 7 p Park D.-H Yag B.: Dtrbutd trar ucto aa o ut-bod pratc atc od. It. J. o Structura Stabt ad Dac Vo. o.. 6. Wttbrodt E. dac-wóck I. Wocch S.: Dac o b utbod t. Rgd t Et thod Sprgr Br 6.