FINITE ELEMENT DEVELOPMENT FOR GENERALLY SHAPED PIEZOELECTRIC ACTIVE LAMINATES PART I - LINEAR APPROACH UDC /046:515.3

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1 FACA UIVRSIAIS See: Mechc geeg Vo., o, 4, pp. - 4 FII LM DVLOPM FOR GRALLY SHAPD PIZOLCRIC ACIV LAMIAS PAR I - LIAR APPROACH UDC 64.4/46:55. Dg Moć,, He Köppe, Uch Gbbe Oo-o-Gece-Ueä Mgdebg, Fä fü Mcheb, I fü Mech, Ueäp, D-6 Mgdebg, Ge Fc of Mechc geeg, Ue of š Aed Medede 4, 8 š, Seb d Moeego Abc. he ceg eed fo ghegh ce eqe deeope of e d of e h hgh pecfc echc popee,.e. o beee echc popee d de. Fbe efoced e, hch cope od-beg phe poece beog o he gop of he o dced c e od. he e ed ed o ppco e pce ce, poo ppco, ec. Hoee, he beho of ce de of copoe e c be poed b ebeddg peoeecc pche beee e. he geec de he of ce ce h coobe dc epoe chcec. he ppe ge he goeg eqo fo ce eed e d decbe -ode degeeed he eee fo odeg of gee hped peoeecc ce e heeb d dpcee e ed Ke od: Fe ee Mehod, Degeeed She, Peoeecc ffec, Ace Sce. IRODUCIO he ceg eed fo ghegh ce eqe deeope of e d of e. A ge be of ppco, e pce ce, po ppco ec., eqe hgh pecfc echc popee,.e. o beee echc popee d de. Fbe efoced e, hch he e hgh egh d ffe deed deco d oe chcec ohe deco offe ch peo cobo of chcec. Ao, he e c ee he pecfc eqee of ce ce popee c be oed b djg he e of coe, he popoo, oeo of fbe, eqece of e ec., d h fc e h Receed oebe 7, 4

2 h D. MARIKOVIĆ, H. KÖPP, U. GABBR e oe of he o dced c e od []. Hoee, he beho of he ce de of copoe e c be fhe poed. Oe of he hee chcec of e h e poed o he obee h hoe e e cpbe of ecogg he chce d e of ee, d o ec ppope ode o ge he be pefoce o poec he eg. Fo fc e o ehb beho ece h poded h e ce obed h e. I he ece e he d of ce h ced eech pojec, de o he poe beef de ge of ppco, ch hpe coo, bo ppeo, oe eo, dge deeco, d he e [4, 7, ]. hee e ee d of coec be e, b he choce of peoeecc e he fo of h pch he ppope oe codeg eqed od d feqec e of cg d eg e ebeddg eqee he ce de of copoe e. he fe eee ehod he o poef ec echqe ee deeoped fo og od d c echc pobe geoec copced ego. he fde eqo goeg he beho of e e f ge, d, bed o, he e fe eee foo of he e pobe decbed.. COMPOSI LAMIAS COSIUIV QUAIOS he o coo c eee de of copoe e e pe d he. Hece, o-deo heoe e ppope fo ppoe of he c. A o-deo heo of he hd ode od o he fco of codo poed b he heo of ec. Hoee, o e od pobe, epec hoe og copoe ce, do o d ec oo, eqg oe o fd ppoe, b epeee oo. Ao, oe hod be e of he objece of odeg e he "ec effo cheed ccc" o. If he po objece o ge gee beho of he ce, ho g he d e fed oced e,.e. co-do, he o-deo heo of he f ode qe fco o ce. Le code gee hped ce de of copoe e, Fg.. Copoe e e oopc e d he coe eqo e o be deeoped he oc coode e (c.. codeg fe c-o, heeb he oc c.. dffe fo o dffee po of he d-fce he ce of gee hped dobe-ced d-fce. he ode hod coe h e odee hc ce d heefoe he f-ode he defoo heo (FSD ed. da h e Z Y X Refeece pe e - Fg.. Gee Shped Copoe Le d Ife C-o

3 Fe ee Deeope fo Gee Shped Peoeecc Ace Le P I - Le Appoch he heo bed o Md-Ree po [, 6]: gh e og pepedc o he d-fce e gh d eebe fe defoo, b doe o e ece pepedc o he d-fce. Hece, he dpcee fed decbed he oc c.. e of degee of feedo of d-fce po :, ( hee d e he -pe dpcee, he ee dpcee d d e he oo of he ee o od he - d -, epece, of he he d-fce po d he e fco of he d-fce po poo (o of he ppe e poe g fo he oo epeo h ge dpcee de o dffee defed oo. A e ce ed,.e. d dpcee, o he fed defed b ec eo, fo he dpcee fed he foog : f f ε ε κ ; ε ε κ ; ε ; ( f ε ( ( ε κ ; ε hee e c e dco beee he -pe {ε } {ε ε ε }, he fe {κ f } f f {κ κ κ f }, he ee he {ε } {ε ε } hee {κ f } e he ce of defoo. B pog he Hoo he ee ech e e obed e of edced e ffe co Q, hch e fo he po of eo o hce deco o h Q C - C C j / C, hee C e he co of he Hoo. Lee ego of ee oe he hce of he e ge he co-eco od, d he e coe eqo : {} [A] [B] [] { ε} {M} [B] [D] [] {κ f } ( {Q} [] [] [F] { ε} hee [][ ] e he -pe foce, [M][M M M ] e he bedg d oo oe, [Q][Q Q ] e he ee he e, [A] he eeo ffe, [D] he bedg ffe, [B] he bedg-eeo copg ffe d [F] he ee he ffe. he coeffce of he ffe ce e obed b ppope ego of e co hce deco []: ( ( A, B, D Q (,, d; F C d (4 d e he he coeco fco, hee 5/6. (

4 4 D. MARIKOVIĆ, H. KÖPP, U. GABBR. LIAR PIZOLCRIC COSIUIV QUAIOS AD PIZOLCRIC PACH POLARIZD I HICKSS DIRCIO Ahogh he hee pee he hoe ge of -eecc fed dg, he e peoeecc coe eqo c be ed ccepbe ppoo fo odeg ppoe he ce of ee e of eecc fed. he fo of he e peoeecc eqo d goeg heodc eqo deped o he choce of depede be [5]. Wh he dpcee bed fe eee ehod, echc dpcee d eecc poe e depede be. Hece, ppope o e echc {ε} d eecc fed {} depede be he he fo of he peoeecc coe eqo choe, ce he e obed dec hogh ec eo. he e peoeecc eqo e he [5, ]: { σ } [C ]{ ε} -[e] {} ε {D} [e]{ ε} [d ]{} hee {σ} he echc e eco, {D} he eecc dpcee eco, [C ] he peoeecc e Hoo co, [d ε ] he deecc pe ε co, d [e] he peoeecc copg. De o he bee of he peoeecc cec he e o feqe ed he fo of e h pche fo eg d cg ppoe o h ce ch hoe de of copoe e. he pche e dded beee e o e boded o he fce. he e o poed hce deco d hece, o he eecc fed hce deco,, codeed, o h he coe eqo he peo-e efeece e c be ee he foog fo: (5 σ σ σ D Q Q Q6 e Q Q Q e 6 Q Q Q e ε e ε ε d (6 hee {σ σ σ } e he -pe d fe ee, d he edced deecc pe hce deco d e j e he edced peoeecc copg co he efeece e of he ce. he ee he copoe e ecded fo eqo (6 bece he e decoped fo ohe copoe. he eecc fed hce deco defed b ϕ/, ϕ beg he eecc poe. Peoeecc e beog o he gop of deecc d he 4 h Me eqo ed h ce D /, ce hee o fee eecc chge he oe of deecc. Ug he 4 h Me eqo h D fo eo (6 hee he boe eo fo odced, e ob he foog dffee eqo fo ϕ: ϕ e ε ε e ( κ d d κ d h e co h epec o he hce coode,. (7

5 Fe ee Deeope fo Gee Shped Peoeecc Ace Le P I - Le Appoch 5 Iegg eqo (7 oe he hce coode,, d pog he bod codo, ϕ o he oe fce eecode d ϕ Φ o he ppe fce eecode, e ob he foog dbo of he eecc poe d eecc fed oe he hce of he h peoeecc e: ϕ e d h ( κ κ Φ ( (8 h Φ e ( κ κ ( ( h ε hee Φ he dffeece of eecc poe beee eecode of he h peo-e, he dce of he d-fce of he h peo-e o he d-fce of he e d h he hce of he h peo-e. he peoeecc e coe eqo e o: {} [A] {M} [B] {Q} [] [B] e [D] [D ] [] [] { ε} [] {κ f } [F] { } ε e [I] [I] [ε ]{e [] } Φ hee [D e ] he eecc-bedg copg ffe d h he ddo echc ffeg effec de o he eecc fed depedec o he ce of defoo (ee (, d [ ε ] oe he fed fo he ce efeece e o he efeece e of he h peo-e. Co of [D e ] e ge : (, f o j e e D e e j ( ( d, ohee d A e hod be dded codeg eo (. O he gh hd-de of eqo ( he [ ε ] pee. h c be epeed o. Oe of he ed eoed d eed o he fed oo. Aee, cod be deood h oe he peoeecc popee fo he peoe efeece e o he efeece e of he ce. Mo of he peocec beog o he gop of ee oopc e codeg echc e eecc popee, d h ce h o eeded. 4. DGRAD SHLL LM he degeeed he eee obed fo he D od eee hogh he degeeo poce, heeb he po f copbe h he Md-Ree ec po e de []. he f e of he degeeo poce h he dpcee of po he oe of he eee c be decbed e of gob degee of feedo of he ppope d-fce po, hee o d hee oo. Fheoe, he degee of feedo of d-fce po c be ob-

6 6 D. MARIKOVIĆ, H. KÖPP, U. GABBR ed hogh he epoo e of degee of feedo of d-fce ode. Hece, eogh o code he eee d-fce o, heeb he hce of he eee defed b e fo ech ode. hee dffee coode e (c.. e ed he foo of he eee: he gob c. (,,, c.. (,, d oc-g c.. (,,, Fg. b. he gob c.. he bc oe, e defed d d e of he e ge h coode e. he c.. fce he defo of he hpe fco d D ec ego. he oc-g c.. of cc poce ce ed fo he decpo of he eee geoe d bece of he oopc popee of copoe e. I be defed he eqe. g dge of he opec ppoch o deeop he -oded eee, he geoe of he d-fce he gob coode e ge b pec eo:,, ( hee (, e he f bqdc hpe fco defed he c.. d, d e he gob coode of he e ode. Hg decbed he d-fce geoe, e c defe he oc-g c.. o o he o e g he dfce ge pe d he hd oe, of coe, pepedc o : e,,, ( e. he oo ed he b (,, e. he o codo ed o f fo he pe e h he he o be he d-fce ge pe. o ddo codo poed. he o-obed e c be fhe ed he ce of oopc e []. Fo oopc e, ch copoe e, he oc-g c.. h be fed h epec o ce efeece e. he ce efeece e e defed e, h epec o hch he eqece of e of he e deeed. A fo,.e. fed ge f beee he ce efeece deco d oe of he -pe e eq ccepbe. Fo he e of pc e p oep oe of he -pe d he ce efeece deco,.e. f (Fg. c. Z Y X Md-fce he oc-g c.. po fo he decpo of he eee geoe. Fheoe, he e coe eqo d he oc-g c.. heefoe, he fed he o be deeoped he e c.. he hce of he he b c Peoeecc e c-o 4 pedefed ce efeece deco Fg.. Degeeed She ee, Co Seco C-o d Loc c..

7 Fe ee Deeope fo Gee Shped Peoeecc Ace Le P I - Le Appoch 7 ed o be deco o o he d-fce of he eee, h od e h. Le deoe he oc-g c.. b {,, } hee deee he eco of he b,.e.,,, d,, d e he deco coe of he eco h epec o he gob c.. b eco. Fo he decpo of he eee geoe he c.., e eed he geoe of he d-fce (, od hce of he eee, h, d he hce deco eco, hch he hd eco of he oc-g c.. b: h (4 Accodg o he po de he degeeo poce (d Md-Ree po e, ech ode h he oc-g c.. o oo degee of feedo, d, od he e g he d-fce ge pe. Upo foo of oo degee of feedo fo oc o gob c.. he dpcee fed obed e of gob od degee of feedo: h h (5 I ode o deeop he fed, he p dee of dpcee he oc-g c.,, d, h epec o he oc-g coode e eeded. A f, he p dee of dpcee he gob c.. (5 h epec o he coode e obed: ( ( ( ( ( ( ( ( ( h (6 he e fed pped fo he c.. o he gob c. b e of he cob ee:

8 D. MARIKOVIĆ, H. KÖPP, U. GABBR 8 (7 heeb he cob obed he foog e: [] h h h (8 F, he dee h he oc-g c.. e e obed b e of he foo h cope he copoe of he oc-g c.. b: ( he dee ( c be dded o he p eg o d p eg oo o. Fo he e of be, e h odce he foog oo:,,,,,, d e c e o: ( ( (, ( C, ( C, ( C, ( B h B" h, B(, B(, B( R δ δ δ ( hee,,,, δ he Koece de, d he foog oo ee odced: B" (, B ( ; (, C ; (, C ; (, C ( hee e he eee of he cob ee. I o gh-fod o deeop he e -dpcee eo b e of (. Ao, p depedg o hce coode c be dghed fo he p depede fo hce coode, o h e c e:

9 Fe ee Deeope fo Gee Shped Peoeecc Ace Le P I - Le Appoch { ε } f { } ε [B ] [B ] [BR] { } [B ]{ } R [BR ] [BR] { } ( hee {ε f } cope ebe d fe, d {ε } ee he, boh he oc-g c., { } e od o, { } { }, d { R } od oo, { R } { }, boh he gob c.. he bce o he gh hd de of eqo ( e fo eo ( d ccodg o he depedece o he hce coode. he e p of he e -dpcee, [B ]. h epeeo fce he c ee ego hce deco. A pec eo eeded he he dg degee of feedo codeed. he eee h fe degee of feedo he oc-g c.. (o o oo, b de o he foo hee e gee degee of feedo he gob c.. ( hee oo. Coeqe, fo pec poo of he eee, he he - of he ocg c.. cocde h oe of he gob coode e, he ffe co coepodg o he oo degee of feedo od h eq o eo. he eee o be co eogh, d gh dbce he od coepodg o h degee of feedo cod ce ec beho of he eee. he oo of he pobe c be cheed hogh he odco of ddo oo ffe b defg he goeg oo eeg h behe pe fco focg he oc oo be ppoe eq o.5 (/ - / ego po: Gh da (4 A (,, o hee Gh h o be ee ge h epec o he fco h ppeg he bedg eeg cco, G beg he he ode, he Yog ec ode d he o ced oo coeffce. I eogh o he. []. A oced befoe, he eecc fed deped o he echc fed, bede he dffeece of eecc poe beee eecode Φ. he dffeece of eecc poe ed o be co fo ech e d odced eecc degee of feedo, φ. Sce he dceed fed ed defed, he eecc fed c o be e : { } [Bφ ]{ } [Bφ]{ φ} (5 hee [B φ ] defe he p of he echc h cobe he defo of eecc fed (eqo (7 d ( d [B φ ] dgo h eee eq o /h o he dgo (eqo (. Pcc, [B φ ] p of he -dpcee gg he ebe d fe {ε f }, d he p deo h epec o hce coode ee o he [B R ] (ee ( cobg he defo of he dceed eecc fed. I ee he peo eco d o be ee he e eco h h depedec of he eecc fed o oo degee of feedo e ddo echc ffeg effec.

10 D. MARIKOVIĆ, H. KÖPP, U. GABBR he epeeed eee of Md pe d eqe o C -co fo he hpe fco, hch cco fo dge. Hoee, cepbe o ec pobe e-o ocg d h ce ddge. he eee hod poc ecoe he Kchhoff-Loe po of eo ee he he hce of he eee ed o eo. he bece of h codo ed o he ocg. S, he eee hod be cpbe of epeeg he ce of eeo bedg fo he e of he eee hce. If h codo o ffed, e pe bo ebe ocg. he f bqdc eee,.e. he - oded eee, doe o ffe eee ocg pobe, b ffe b-op coegece h he ceg edee of he eee. Oe of he pe d fco echqe o od h pobe eece d fo edced ego. he eece ego e op fo ecg pfo of he eee. O he ohe hd, ho h he fo edced ego echqe op he ce of doed ehe [8]. Hoee, h echqe ed o eo-eeg ("ho-g" ode d ddo echqe, e he o-ced b-ee, e o be ed fo he bo. 5. FII LM QUAIOS he goeg eqo of he ce dc beho ge b he Ho pcpe [7],.e. he e e he ph of he e co: ( L Wd (6 δ hee L epee he Lgg, d W he o of ee foce. he Lgg o be pope dped ode o cde he cobo fo eecc fed bede he cobo fo echc fed. Sce he echc d eecc fed e depede be, he goeg heodc eqo fo peoeecc e eecc ehp (eecc Gbb eeg, H []: H c ε ε e ε d ε [{ ε} { σ} {} {D}] d he Lgg defed e of echc ec eeg d eecc ehp L -H. Upo ego b p of ec eeg, he Ho pcpe fo he peoeecc co c be ee deeoped fo: V [ ρ{ δ} {} & { δε} [C ε ]{ ε} { δε} [e] {} { δ} [e]{ ε} { δ} [d ]{}]dv (7 { δ} { δfv }dv { δ} { δfs }ds { } { F } q ds Q δ δ P δφ δφ (8 V S hee F, F S d F P e he ee oe, fce (cg o fce S d po od, epece, q d Q e he fce (cg o fce S d po eecc chge, epece. De o he po of co Φ fo ech peoeecc e, S

11 Fe ee Deeope fo Gee Shped Peoeecc Ace Le P I - Le Appoch o he coepodg eecc od e codeed d hoe e he fo dbed fce eecc chge. Afe he dceo of he co he foog e of e-dcee eqo obed: M ]{ & } [K ]{ } [K ]{ φ } {f } ( [ φ e [ Kφ ]{ } [K φφ]{ φ} {q e } ( hee he foog ce d eco e defed o he eee ee: - : [M ] [ ] ρ[ ] dv ( - echc ffe : V ε [ ] [ B ] [ C ][ B ] [ B ] [ e] [ Bφ ] [ Bφ ] [][ e B ] [ Bφ ] [ d ] [ Bφ ] K dv ( V ( ε [ φ φ φ φ φ ] V - peoeecc copg : K ] [ B ] [ e][ B ] [ B ] [ d ][ B ] dv [K ε - deecc ffe : [Kφφ] [Bφ] [d ][Bφ] dv (4 V - echc od: { fe } [ ] {FV } dv [ ] {FS } ds [ ] {FP } (5 V - eecc chge: {q e } q ds (6 S hee [ ] e he od dpcee epoo ce. he eg e fe he f oe o he gh-hd de of ( epee he ed eoed ddo echc ffeg effec. I hod be poed o h h ffeg effec qe eggbe fo he pee c of peoeecc e. eehee, epecg hghe e of peoeecc copg co fo he fe c of peoeecc e, decded o eep he foo, bece h effec p oe po oe. S 6. XAMPL he foog epe offe pe deoo of he beho of he -ode degeeed he eee fo peoeecc ce e odced h ppe. he epe ge copo of he dpcee oo fo cped be ce h peoeecc co he ppe d oe de of he ce obed fo dffee F ode. Fge ho he geoe, poo of he co d echc d peoeecc popee (I dd [] ed fo oo of co. Fo he e of pc, choe c e. he peoeecc co he oppoe poo, hch e bedg oe he he e oge pped o boh of he.

12 D. MARIKOVIĆ, H. KÖPP, U. GABBR Me popee: be: Yog od 7. 4 / Poo o ν.45 Peoeecc e : c copce S / S. -6 / De ρ 7.8 g/c Peoeecc co d. -8 /V d /V d /V Deecc co ε /ε ε /ε 8 Fg.. Mode of Cped Be h Peoeecc Aco d Me Popee, Dpcee [],,65,7,5,,7,4, -,6 -,54 -,47 -,88 -,86 -,5 4 -,6 -, ,58 -,8777 -, -,8 -,68 -,67 -,66 -, -, -,4 -,5 -,88 -,876 -,5 -,466 -,75 -,4464 -,686 -,466 -, -,5 -,458 -,57 -,6 -,5648 -,5787 -,668 -,657 -,7 Legh [] She oe Seoof Heede Fg. 4. Dpcee of he Ceee fo Dffee Fe ee Mode

13 Fe ee Deeope fo Gee Shped Peoeecc Ace Le P I - Le Appoch Fo h epe coo oge of V ed. he peocec e of. hce e de of PZ e. he c defeco dced b ee pped oge e cced fo he D hehedo fe eee h ode pe eee d fo o ode h he eee. he D eee e fe eh d ge efee oo fo he copo. he Se-Loof eee d degeeed he eee boh e he e, ee ogh eh ( eee. he dg Fg. 4 cope he F oo of he dffee ode fo he c defeco og he be egh (ceee. he ce h ge bo epee he oo fo he ode h he 8-ode Se-Loof [] he eee. he e h qe bo ho he dpcee e fo he odced -ode degeeed he eee d he efeece oo ge b he bc ce. he D eee d Se-Loof he eee boh e dec oe. he degeeed he eee e ee oe fo dc, h fc d cc dpg o h he pefoed oo of he ce peodc oco coegg e o o he c oo. he e obed h he he eee ho good geee h he efeece oo. 7. COCLUSIOS he geec de epeeed he ppe he of ce ce h coobe dc epoe chcec. Copoe e oe of he o dced c e od choe od-beg e. Fheoe, h c e ge he cpb of eg d cg b odcg e de of peoeecc e beee og e, o bodg he o he fce of he copoe e. he heeb o pode ode fo h pe of ce. he fe eee ehod epee ce he o poef ehod fo c. heefoe, he objece of he ppe o decbe he deeope of fe eee deged fo odeg of gee hped copoe e h ebedded peoeecc ce copoe. he -ode degeeed he eee choe ce c ode b hped h e odee hc ce gee dobe ced d-fce d be hce of he ce. Ahogh deged fo odeg of -eed ce he eee e he dd e ppoch h c ee ego hce deco, hch pode hghe ec effecee. Fo he e e eo, he eee ed fo obg he gee oe beho of he ce d o fo codcg he he oced e of he ce. A fc h boh copoe e d peoeecc e beog o he gop of oopc e eqed ce pecfc ep deeope of he eee d he e decbed he ppe. he eee h echc degee of feedo ech ode d ddo e eecc degee of feedo, ech oe coepodg o peoeecc e. he dg degee of feedo eqe pec eo. Codeg eecc fed, oe cce qdc dbo of eecc poe oe he hce of he peoeecc pch e o cco. he fo edced ego offe pe d fco oo fo he ocg pobe pee h pe of eee. he eee eged he gee ppoe fe eee pcge COSAR (.feco.de, og deeoped he Ie of Mechc of he Oo-o-Gece Ue Mgdebg.

14 4 D. MARIKOVIĆ, H. KÖPP, U. GABBR RFRCS. Bhe K..: Fe ee Pocede geeg A, Pece-H, Ic., geood Cff, e ee, 8. Beheo. M.: CopoeMe: Mechc Beho d Sc A, Spge-Veg e Yo, Ic., 8. Chooh C S: Fe ee A: heo d Pogg, ecod edo, McG- H, Ic, e Deh, 5 4. Gdh M. V., hopo B. S.: SMe d Sce, Chp & H, 5. Ied.: Fde of Peoeecc, Ofod Ue Pe Ic., e Yo, 6 6. Ocho O. O., Redd..: Fe ee A of Copoe Le, Ke Acdec Pbhe, Dodech, Boo, Lodo, 7. Pefo V.: Fe ee Modeg of Peoeecc Ace Sce, PhD he, Ueé Lbe de Bee, 8. Php G.: he Fe ee Mehod Sc Mechc, Ke Acdec Pbhe, Dodech, Boo, Lodo. Peo A.: Vbo Coo of Ace Sce: A Iodco, Ke Acdec Pbhe, Dodech, Boo, Lodo, 7. Redd..: A Iodco ofe ee Mehod, McG-H, Ic,. Rohe K.: Lechb Veebde, ece Oo-o-Gece Ue,. Roe C. Z. e (ed.: Peoeecc, Aec Ie of phc, e Yo,. Io B. M.: "he eoof he eee" Ahe D. G. d Gghe R. H. (ed: Fe ee fo h She d Ced Mebe, Chpe, pge 7-., We, Mhe, F. L. e.: Fe ee Modeg of Copoe Me d Sce, Woodhed pbhg Ld. d CRC Pe LLC, Cbdge, RAZVO KOAČOG LMA ZA KOSRUKCI OPŠG OBLIKA OD KOMPOZIIH LAMIAA SA PIZOLKRIČIM KOMPOAMA DO I LIARI PRISUP Dg Moć, He Köppe, Uch Gbbe Se eć poeb oc he oj oh e o pecfč oj, j. o odoo ehčh e pecfče ge. L opo e, oj dže ojčj d ešeh šoj c, pdj gp jeeh ocoh e. O e e eć eo oe če he, p. oc e žj, pooj ehc d. Vš e pošj oc od oh e ože e poć egje peoečh počc eđ oje e. Oo dej je e h oc pj dč odgooo. U d de ooe jedče opoog opoe op je oč eee p "degeee je" čoo odeje oc opšeg ob od h, p če pedpojee e defoce poej. Kjče eč: eod očh eee, degee j, peoeeč efe, oc