CHINESE JOURNAL OF APPL IED MECHANICS Mar. 2009

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1 26 1 Vol. 26 No CHINESE JOURNAL OF APPL IED MECHANICS Mar : (2009) ( ) :,,,,,,,,,, : ; ; ; ; ; ; : TU31112 : A 1,,, [1 ],,, [ 15 ],, [2 ] ;, [ 324 ],,,,,, [527 ], [8 ],,,,,, [ 9 ], [10214 ],,,, [16219 ],, [20 ],,,, 3 : ( ) ; (J A07014) : : :,,1971,, ; E2mail : edu. cn

2 1, : 195,, 2 211, L, f,,, D, t q f / L, L/ rx ( rx, rx = Is/ A s Is ; A s ) Es, f s [15 ], : :L/ rx ; : f / L , Es/ 100, 1 NL_Beam3D [20 ], [21 ] [22 ] [9 ],, 1 2,,, (1) y0 y0, L/ 4 = sin 2 x L (1) : y0 ; x y0, L/ 4 1/ 4L,, e = L/ 1000 e = L/ 2000,, [23 ] L/ 6000, L/ 3000, L/ 3000 L/ ( P2 ), q/ ( Es I s/ L 3 ), Austin [24 ], e/ L, e/ L = 0 [25 ], ( S ) (M ),, L/ 2 L/ 4 3L/ 4,,, 2 ( b) L/ 4 3L/ 4, L/ 4 3L/ 4, ; L/ 4 3L/ 4,, e/ L, L/ 4 3L/ 4, 2 2 ( f / L = 012) 213,, 012, 340 Q235, 2 3 2

3 L/ 4 3L/ 4 2,,, [25 ],,,,, 0125, ; 0125, 3 2 ( f / L = 01 2) ,,, ; ( ),,,,, 5,,, qcr, ela = qcr / ( Es I s/ L 3 ) Timoshenko ela [26 ] Austin ela [27 ] 4, 01 3,, Austin, ; Timoshenko, 5 4,,

4 1, : 197,,, ( ), N 1/ 4, (2) qcr qcr = N 1/ 4 L 8 f / L f / L 2 (2) 6 Euler, K1 = 1 ss r x f S E S (3) : s ; S, K1 qcr, K1 = N 1/ 4 A s f s = qcrl A s f s ( f / L) 2 8 f / L 6, ( p p ) Euler (4), ;, Euler, 6,,,,, K1 = f (, f / L), K1 ( p ),, < p, K1 = C1 ( p - ) + C3 ( p ) p p 2 (5a) p p, K1 = 1/ 2 (5b) C1 = f L ( f L ) 2, C2 = f L ( f L ) 2, p = f L ( f L ) 2 6 K1 6 (5), (5) K qcr / ( Es I s/ L 3 ), 7 ( f / L = 01 2), ( e/ L = 0),,,,, 8 P2,,

198 26, 30 %,, P2,,,,, e/ L 1/ 3000, 200 3 %,,, 6 8,, 1 K2, K2 K1, K2 = f (, f / L) K1,, L/ 3000 K2,, (6) 01215 < p, K2 = 1 +

= - 01694 + 201457 f L - 221730 ( f L ) 2 (6a) (6b) 9 (6) K2, (6), K2, K2 K1,, 10 K2 = 110, 10 10 7 L/ 3000 9 K2 K2 K1, ( ) [28

5 198 26, 30 %,, P2,,,,, e/ L 1/ 3000, %,,, 6 8,, 1 K2, K2 K1, K2 = f (, f / L) K1,, L/ 3000 K2,, (6) < p, K2 = 1 + P1 ( ) P 2 p p, K2 = 1 + P1 ( ) P 3 p P1 = f L ( f L ) 2, P2 = f L ( f L ) 2, P3 = f L ( f L ) 2 (6a) (6b) 9 (6) K2, (6), K2, K2 K1,, 10 K2 = 110, L/ K2 K2 K1, ( ) [28 ], f / L = 012, L = 715m, D = 01121m, t = m, Es = 213 GPa, f s = 322MPa, L/ 3000 ss = 01687S, (3) = 0185, (2) 1 K1 = 01842

6 1, : 199 K1 A s f s qcr K2, N 1/ 4 = = 446 kn, (5) = 88kN/ m, (6) 2 = 01904,, N 1/ 4 = K2 K1 A s f s = 403kN, (2) qcr 10 % = 80kN/ m, 89kN/ m, 8215 kn/ m,,, [15 ] 8,, %, ), 2),, 3),, K1 4),,, K2 5) K1 K2,, [ 1 ] Langhaar H L, Boresi A P, Carver D R. Energy t heory of buckling of circular elastic rings and arches[ C]/ / Proceedings of Second U S National Congress of Applied Mechanics, ASME, 1954 : [ 2 ] Pi Y L, Bradford M A, Uy B. In2plane stability of arches [J ]. International Journal of Solids and Structures, 2002, 39 : [ 3 ] Komat su S, Shinke T. Practical Formulas for In2plane Load Carrying Capacity of Arches [ J ]. Journal of Structural Me2 chanics and Eart hquake Engineering J SCE, 1977, 254 : [ 4 ]. [ M ]. 2. :,2004. [ 5 ] Japan Road Association. Specification for Highway Bridge [ S]. Japan : Maruzen, [ 6 ] Galambos TV. Guide to Stability Design Criteria for Metal Structures ( Fifth Edition ) [ M ]. John Wiley &Sons Inc, [ 7 ] Verstappen I, Snijder H H, Bijlaard F S K, et al. Design rules for steel arches2in2plane stability [ J ]. Journal of Construct Steel Res, 1998, 46 : [ 8 ], [ M ]. 2. :, [ 9 ],. [ M ]. :,1999. [ 10 ] Hsu C S, Kuo C T, Plaut R H. Dynamic stability for clamped shallow arches under timewise step loads [J ]. AIAA Journal, 1969, 7 : [ 11 ] Cheung M S, Babcock C D. An energy approach to t he dynam2 ic stability of arches [ J ]. Journal of Applied Mechanics, ASME, 1970, 37 : [ 12 ] Schreyer H L. The effect of initial imperfections on the buck2 ling load of shallow circular arches [J ]. J Appl Mech, 1972 :

7 [13 ] Mak C K, Kao D W. Finite element analysis of buckling and post2buckling behaviors of arches with geometric imperfections [J ]. Computer & Structures, 1973, 3 : [ 14 ] Tadjbakhsh Iradj. Imperfection sensitivity of circular arches [J ]. J Appl Mech ASCE, 1983, 2 : [ 15 ],. [J ]., 2006, (2) :124. [ 16 ],,. [J ].,2002,19 (3) : [ 17 ],,. [J ].,2004,29 (4) : [ 18 ],,. [J ].,2005,15 (4) : [ 19 ],. [J ].,1999, (11) : [ 20 ],,. [J ].,2007, 24 (12) : [ 21 ],,,. [J ].,2004, (11) : [ 22 ]. [J ].,2002, 2 : [ 23 ] [ S], :,2000. [ 24 ] Austin WJ, Ross TJ. Elastic Bucking of Arches under sym2 metrical Loading [ J ]. Journal of the Structural Division ASCE, 1976, 102 (ST5) : [ 25 ]. [ D ]. :, [ 26 ] Timoshenko S P, Gere J M. Theory of Elastic Stability (2nd ed. ) [ M]. New York : Mc Graw2Hill, [ 27 ] Austin W J. In2Plane Bending and Buckling of Arches [J ]. Journal of Structural Division ASCE, 1971, 97 ( ST5) : [ 28 ],. [J ].,2007, 24 (6) :73278.

8 No. 1 CHIN ESE J OU RNAL OF A PPL IED M ECHAN ICS g Stress Fatigue Life Reliability Curve Analysis with Moment Method X u N an 1 W an g W eiqi ang 2 L i N ai gen 1 (Shandong Jianzhu University, , Ji nan, China) 1 (Shandong University, , Ji nan, China) 2 Abstract : The general model of stress fatigue life reliability was proposed by analyzing correlations between t he median and high reliability fatigue life about several kinds of probability distribution f unctions, such as Weibull Dist ributio n ( WD), Normal Dist ributio n ( ND), Expo nential Dist ributio n ( ED), etc. U nder t he condition t hat fatigue life obeys a probability distribution, this reliability formula is a speciality of t he gen2 eral formulas. Based on moment method of probability distribution f unctions, stress fatigue life reliability curve analysis suitable for five kinds of probability distributions were proposed. The median and high relia2 bilit y fatigue life curve equatio ns for 42CrMo hardened gear2toot h bending fatigue life data were estimated by means of st ress fatigue life reliabilit y curve analysis. Keywords : reli abilit y, st ress f ati g ue, p robabilit y dist ribution, f ati g ue li f e, moment met hod. Truncated Importance Sampling Method based on Optimization of Mixed Genetic Algorithm Zhang f eng L u z henz hou (School of Aeronautics, Nort hwestern Polytechnical University, , Xi an, China) Abstract : A truncated importance sampling met hod is employed for t he failure probability of parallel sys2 tem wit h multiple failure modes. The mixed genetic optimization algorit hm is chosen to search for t he t he mo st probable failure point in t he failure domain, and solve t he approximate reliability index of t he paral2 lel system. A 2sp here truncated importance sampling met hod for t he failure probability of parallel system is consisted of 2sp here truncation and importance sampling probability f unction. Comparing with the suc2 cessive sequential app ro ximatio n app roach and FORM, t he p resented met hod performs much more effi2 ciently t han Monte2Carlo met hod wit h higher accuracy, especially for the small failure probability. Keywords : mi xed genetic al gorit hms, 2s p here sam pli ng, im port ance sam pli ng, f ail ure p robabilit y. Equivalent Column Method f or Calculating Critical Load f or Steel Tubular Arch under Pure Compression W ei J i an gan g Chen B aochun W u Qi ng x ion g (College of Civil Engineering, Fuzhou University, , Fuzhou, China) Abstract : Focusing on parabolic steel t ubular arch wit h and wit hout initial crookedness subjected to distrib2 uted load, t he characteristics of elastic and elastic2plastic buckling are discussed based o n t he finite element analysis co nsidering dual2no nlinearit y. Analysis result s show t hat, rise2to2span ratio is an important factor

9 CH IN ESE J OU RNAL OF A PPL IED M ECHAN ICS Vol. 26 in critical loading of an arch, but which does not appear in t he present equivalent column met hod, t hus a met hod co nsidering influence of rise2to2span factor is p resented. An arch wit h initial defect buckles under critical load smaller t han t he buckling load for a perfect arch, so a coefficient considering t he lower critical loading due to initial defect is introduced into t he equivalent column met hod. A comparison wit h t he result s f rom dual nonlinearity finite element method indicates t he accuracy of met hod for estimating nonlinear crit2 ical loading of steel t ubular arch. Keywords : steel t ubul ar arch, st abilit y, equi v alent col um n met hod, rise2to2s p an ratio, i niti al crookedness, d ual2nonli nearit y. Notch f ilter feedback control f or chaotic motion of fluid conveying pipe B ao Ri don g 1 Gon g B i n 1 W en B an gchun 2 (Shenyang Institute of Chemical Technology,110142, Shenyang, China) 1 (Nort heastern University, , Shenyang, China ) 2 Abstract :The chaotic motion of a pipe single mode system of t he fixed supported at two ends under base excitation is actively controlled by introducing t he feedback of notch filter. The equations of bot h homo2 clinic and periodic orbit s of the unperturbed system are derived firstly, and t hen t he corresponding Melnik2 ov f unctions were deduced. Under t he conditions that t he Melnikov f unctions corresponding to t he homo2 clinic and periodic orbit s respectively have simple zeros, t he parameters satisfying to introduce the chaotic motion of the system into periodic orbit s, are obtained. The numerical simulation is carried out for t he re2 sponse of perturbed system, and t he simulation result s shows that t he system chaotic motion can be suc2 cessf ully induced to periodic motion. For different feedback gains of t he notch filter, t he responses of t he system converge on t he different stable periodic solutions. Keywords : f l ui d convey i ng pi pe, base excit ation, chaotic motion, notch f ilter, f eedback cont rol.

A *69>H>N6 #DJGC6A DG C<>C::G>C<,8>:C8:H /DA 'D 2:6G - ( - ) +"' ( + -"( (' (& -+" % '('%"' +"-2 ( -!"',- % )% -.C>K:GH>IN D; AF69>HH>6,-+

A *69>H>N6 #DJGC6A DG C<>C::G>C<,8>:C8:H /DA 'D 2:6G - ( - ) +' ( + -( (' (& -+ % '('%' +-2 ( -!',- % )% -.C>K:GH>IN D; AF69>HH>6,-+ The primary objective is to determine whether the structural efficiency of plates can be improved with variable thickness The large displacement analysis of steel plate with variable thickness at direction