17 1 V o l. 17 N o CH IN ESE JOU RNAL O F COM PU TA T IONAL M ECHAN ICS February 2000 : A

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1 7 V o l. 7 N o. 000 CH IN ESE JOU RNAL O F COM PU TA T IONAL M ECHAN ICS February 000 : (000) Ξ, (, 0098) :,,,,,,, N ew tonr aph son,, : ; ; ; : TU 3933; O 48 : A 80, [, Geiger Fu ller ], [ 3, 4 ], 40 [ 4 ],,,, ( ),,,, [ 6 ] [ 7 ], Ξ : : : (964 ),,, Tsinghua Tongfang Optical Disc Co., Ltd. All rights reserved.

2 8 7,, L agrange N ew tonr aph son,, ( ), L agrange :, { e} = [u i v i w i u j v j w j ] T [k g L ] = E ga g ( [k g L ] + [k g G ]) { e} = {R e} - f g R - f g 0 () l lm m n l nm n - l - lm - n l l - lm - m - m n lm m - n l - nm - n n l nm n [k g G ] = P f g R = A ge g [ (B g N L ) T B g L + (B g N L ) T B g N L + (B g L ) T B g N L ]{ e} f g 0 = P 0 [- l - m - n l m n ] T B g N L = u i - u j v i - v j w i - B = [- l - m - n l m n ] w j u j - u i v j - v i w j - P 0 8 n, {R e}, l, m, n x, y, z,,a g 8 n, E g, f R g, f g 0 8 n L agrangian, 3 8 n w i Tsinghua Tongfang Optical Disc Co., Ltd. All rights reserved.

3 : 83 3 x = L ( + Ν) y = 0 (- Ν ) z = f = ( - Ν ) f m ax f m ax 8 n () f = ( - Ν ) f m ax (3) s = L - () 8f m ax 3L L + 6 3L f m ax f m ax (4) s F ds (5) 0 EA F, F 0, s = F 0L (6) (5), s = EA F F 0 ds dx (6) 6f m ax ( + ) (7) 3L, F 0 = F 0 L L - F 0 f m ax f m ax (8) (4) (7) (8), : f m ax = k L (9) k = - ( - F 0Α 8f m ax - ) g( F 0Α 6f m ax L 3L + f m ax 3L ) ; Α= L 6f m ax ( + ) EA 3L (9) (3), f = ( - Ν ) k L (0) 8 n 8 n+ { u}e = {u v w u v w } T () L = u - u (), { u} = [N ]{ u}e (3) { u} = [u v w ] T (4) [N ] = ( - Ν) 0 0 ( + Ν) ( - Ν) 0 0 ( + Ν) 0 - k ( - Ν ) 0 ( - Ν) k ( - Ν ) Tsinghua Tongfang Optical Disc Co., Ltd. All rights reserved. ( + Ν) (5)

4 84 7 L agrange 8 n 8 n+ L agrange Ε Ε= [ (dsγ ds ) - ] (6) ds ds λ 8 n 8 n+ ds γ = (dx + du) + (dy + dv) + (dz + dw ) (7) ds = (7) (8) (6) (dx ) + (dy ) + (dz ) (8) Ε= a + b (9) a = d [x ds y z ] d ds [u v w ]T = [A 0 ]{ u}e (0) [A 0 ] = G L b = d ds [u v w ] d ds [u v w ]T = { u} T e [A ]{ u}e () 0 - f m axν [N ]; [A ] = G [N ] T [N ]; G = [N ] = d [N ] dν =, (9) kν kν 0 0 L 4 + 4Ν f m ax () Ε= B { u}e (3) B = B L + B N L (4) B L ; B N L a = (- G B L = [a a a 3 - a - a - a 3 ] (5) B N L = b b b3 - b - b - b3 (6) L 4-4Ν kf m ax), a = 0, a3 = G f m axν b = [ ( 4 + 4k Ν ) (u - u ) - kν(w - w ) ]gg, b = (v - v ) g4g b3 = [- kν(u - u ) + 4 (w - w ) ]gg 3 d Ε= B d{ u}e (7) (3) (4) (5) (6) B = B L + B N L (8), {Ω}e = A B s T Ρds - {R }e = 0 (9) s Tsinghua Tongfang Optical Disc Co., Ltd. All rights reserved.

5 : 85 {Ω}e, {R }e ; A s 8 n, K ichhoff L agrange Ρ = E Ε+ Ρ0 (30) E, Ρ0 8 n K irchhoff (8) (7), (30) (9) [kl ] = EA s {Ω}e = ( [kl ] + [kg ]) { u}e + f R + f 0 - {R }e = 0 (3) GB LB T L dν ( ) - [kg ] = A s - = EA s G (B T N LB L + B T N LB N L + B LB T N L ) { u}edν; f 0 = A - s G [A ]Ρ0dΝ ( ) f R GB T L Ρ0dΝ - 4, [T ], [T ] = [ t ] = [ t ] [0 ] [0 ] [ t ] lx ly lz m x m y m z (3) (33) n x ny nz li, m i, n i (i = x y z ) i x, y, z, {U }e = [T ]{u}e; {R } = [T ]{R }e; {F R } = [T ]{f R } [K ] = [T ][k ][T ] T ; {F 0} = [T ]{f 0} {U }e, {R }, {F R }, {F 0} [K ],,,, ( [K L ] + [K G ]) { U }e = {R } - {F R } - {F 0} (34). 3 () (34) K T U = R - F (35) K T = K L + K G, F = F R + F 0, K G, K L, ; R ; F R, F 0, 3 N ew tonr aph son, ( m ) () i =, 0 K T ; Tsinghua Tongfang Optical Disc Co., Ltd. All rights reserved.

6 86 7 () i R = i i Κg R ( Κ= ) ; m i= (3) i F 0 = 0, i K 0 T g u 0 = i R i ( u) 0 = i u 0 ; (4) i u 0 i F ; (5) k = ; (6) i X k = i X k- + i ( u) k-, i f m k ax = i f m k- ax + i f m k- ax, i K k T; (7) i K k T g i u k = - i F k-, i ( u) k, i ( u) k i F k ; (8) i i u k+ = i u k + i ( u) k ; (9), i F k g R Ε i ( u) k, (0),, k = k +, (6) ; i+ (0) X 0 = i X 0 + i u k+, i+ f 0 m ax = i f 0 m ax + i f k+ m ax ; () i = i +, () m 4 4 Geiger : A = A 3 = 77cm, A 35 = A 57 = A 79 =. 77cm, A 34 = A 56 = A 78 = cm ; : A r = 36cm, A r4 =. 77cm, A r6 = cm ; : E = N g cm - : H 0 = 34kN, H 0 3 = 66kN, H 0 34 = kn, H 0 35 = 44kN, H 0 56 = 4. 7kN, H 0 57 = 9. 4kN, H 0 78 = 6. 8kN, H 0 79 =. 6kN ; : H 0 r = 87. 4kN, H 0 r4 = kN, H 0 r6 = kN,, : P 3 = 3 P, P 5 = 7 3 P, P 7 = 4 3 P, P 9 = 3 P 4 ;,, [ 7 ], 5 6 [ 7 ], 5 6 : Geiger,,,, ; Tsinghua Tongfang Optical Disc Co., Ltd. All rights reserved.

7 : 87 (a) 3 (b) (c) 5 (a) 3 (b) (c) 4 6 Geiger,,, 5,, [ ] Fuller R B. Inventions, the p atented w orks of R. B. F u ller[m ], Sṫ M artinπs P ress, N ew Yo rk, 983. [ ] Geiger D H. Geig er R oof S tructu re[p ], U nited States Patent, Patent N o , A p ril., 988. [ 3 ] Gerger D, Stefaniuk A and Chen D. T he design and construction of tw o cable dom es fo r the ko rean o lymp ics[r ]. P roceed ing s IA S S International S ym p osium, O saka, 986: [ 4 ] T erryw R. Geo rgia Dom e Cable Roof Construction T echniques[r ]. P roceed ing s of the IA S S Interna tional S ym p osium, A tlanta, U SA, 994: [5 ] Gasparini D A, Perdikaris P C and Kanj N. D ynam ic and Static Behavio r of Cable Dom e M odel[j ]. J ou rnal of S tructu ral E ng ineering, 989, 5 (): [6 ],, [J ], 996, (): 7. [7 ],, [J ] ( ), 997, 33 ( ): Tsinghua Tongfang Optical Disc Co., Ltd. All rights reserved.

8 88 7 [8 ] K rishna P. Cable S usp end ed R oof s[m ]. M cgraw H ill Inc. N ew Yo rk, 978. A m ixed f in ite elem en t increm en ta l m ethod for spa tia l non linear ana lysis of cable dom e structures TAN G J ianm in, ZHUO J iashou (Co llege of C ivil Engineering, Hohai U niversity, N anjing, 0098, China) Abstract Cab le dom e is longspan spatial com b ined structu re con sisting of com p ression po sts and ten sion cab les, its analysis is of geom etrical large defo rm ation, and is u sually very difficu lṫ In th is paper, app lied the fin ite elem en t m ethod and con sidered the characters of cab le dom e, tw onode cab le elem en t con sidering the effect of cab leπs sag w as estab lished based on the cab leπs equ ilib rium and geom etrical com patib ility. Com b ined th is cab le elem en t w ith the straigh tline m em ber elem en t, and in term s of the updated lagrangian descrip tion and virtual disp lacem en t p rincip le, the increm en tal equ ilib rium equation of cab le dom e w as ob tained. M ixed the increm en tal loading m ethod w ith the N ew tonr aph son iterative one, the com puter p rogram w as w ritten ou t and one exam p le w as com puted. T he resu lts show s that the m odel p resen ted in th is paper lead to good p recision and can be adop ted in the spatial non linear analysis of cab le dom e. Key words: cab le dom e; non linear analysis; increm en tal fin ite elem en t; m ixed m ethod Tsinghua Tongfang Optical Disc Co., Ltd. All rights reserved.