Fast Simulation of Pyroshock Responses of a Conical Structure Using Rotation-Superposition Method

Transcription

1 Appled Mathematcs & Informaton Scences An Internatonal Journal 211 NSP 5 (2) (211), 187S-193S Fast Smulaton of Pyroshock Responses of a Concal Structure Usng Rotaton-Superposton Method Yongjan Mao 1, Yulong L 2, Hanjun Huang 1 and Junpng Wang 1 1 Insttute of Structural Mechancs, Chna Academy of Engneerng Physcs, Manyang 6219, Schuan, Chna 2 School of Aeronautcs, Northwestern Polytechncal Unversty, X an 7172, Shaanx, Chna Emal Address: lyulong@nwpu.edu.cn Receved Jun 8, 21; Revsed Jan 2, 211 Abstract: In space engneerng, the predcton of structural responses nduced by pyrotechnc devces s mportant for protectng the space hardware, especally the electronc components. Ths paper presents a fast smulaton of pyroshock responses of a concal space structure. Frstly, a fnte element analyss was performed and the responses to a load element were obtaned. Then, by ntroducng the quck method, Rotaton-Superposton Method, the structural responses nduced by varous numbers of explosve bolts were predcted and the effects of non-smultaneous ntatons were also analyzed. Ths study provdes a hgh-effcency approach for mult-case pyroshock responses predcton. Keywords: Pyroshock, structural response, numercal smulaton, Rotaton-Superposton Method 1 Introducton Presently, pyrotechnc devces are wdely used n space engneerng. The detonatons of those pyrotechnc devces wll nduce hgh-level structural responses wth the characterstcs of hgh frequency, short duraton and hgh peak acceleraton [1]. Ths knd of shock envronments wll nfluence, or even damage the space hardware. Accordng to Moenng s statstc [2], a sgnfcant number of falures of space hardware, especally of electronc components, resulted from pyroshock envronments. Thus, ths problem s pad much attenton by the engneers and scentsts. However, the predcton of pyroshock responses s dffcult because of the lack of effectve analytcal technques. Therefore, a number of researchers are attemptng n numercal technques development. Up to now, varous knds of numercal technques have been proposed [3], ncludng tme hstory analyss (THA) [4,5], response spectrum analyss (RSA) [6], statstcal energy analyss (SEA) [7] and a synthetc technque combnng THA and SEA [1]. Tradtonally, whchever method s used, each case needs a full analyss. Thus, for a mult-case problem, a correspondng number of smulatons have to be performed. But the trouble of ths way s that, a great number of hours are unavodable for modelng and

2 Fast Smulaton of Pyroshock Responses. 188 computng. As we know, varous schemes are usually consdered n desgn stage of a structure or system. Then a sgnfcant number of cases need to be analyzed n order to compare the dfferent schemes. So, ths practcal engneerng background requres a hgheffcency smulaton technque to be developed. Ths paper predcts the pyroshock responses of a cone-shaped structure n dfferent cases by employng the quck method, Rotaton-Superposton Method, whch was orgnally proposed by Mao et al [8,9] for lateral shock responses calculaton. Based on only one fnte element smulaton, the structural responses n varous cases were obtaned and compared. The example shows the method has very hgh effcency n analyzng mult-case pyroshock problems. 2 Rotaton-Superposton Method The detals of the Rotaton-Superposton Method can be found n [8,9]. Ths secton only gves a bref ntroducton. 2.1 Defnton Defnton 2.1. Assume an ax-symmetrcal structure V s loaded by F ( r, z) n the area Ω ( r, θ, z) V, and F ( r, z) can be decomposed as n 1 (,,, ) = F r θ z t F ( r, t), n 2, (2.1) = where, r, θ and z denote the cylndrcal coordnate system, t s tme, n s the number of load subsets and F ( =,1, L, n 1) s the th subset of F. If Ω ( r, θ, z) Ω s the loadng area of F and Ω ( r, θ θ, z) = Ω ( r, z), = 1, L, n 1, (2.2) F ( r, θ θ, t t ) = k F ( r, θ, t), = 1, L, n 1, (2.3) the load F on V s called a load of rotatonal smlarty. Where, angle and t denotes the potental tme delay. θ s the rotaton 2.2 Formulaton It s assumed that only a lnear elastc problem s consdered, and the ax-symmetrcal structure s loaded by F, a load of rotatonal smlarty. Now decompose F nto F ( =,1, L, n 1) accordng to Eq. (2.1), then the responses to F can be denoted as ( r, t), =,1, L, 1 R = R n, (2.4) where, R denotes the components of structural responses n the cylndrcal coordnate

3 Yongjan Mao et al 189 system, such as stress, stran and acceleraton. If R = R ( r, t) has been obtaned, then the responses to F s ( r, θ, t) = k R ( r, θ θ, t t ), = 1, L, n 1 R, (2.5) where, k = F F s determned by Eq. (2.3). Thus, the responses to F can be gven as 3 Problem and Modelng n 1 n 1 ( r, t) = R = kr( r, θ t t ) = = R. (2.6) 3.1 Problem Descrpton The sketch of the concal structure s gven n Fgure 3.1. The entre structure conssts of two concal shells and an electronc component smplfed as a thck-wall cylndrcal shell. Ths structure s connected wth a rocket vehcle by explosve bolts unformly located n the bgger-end plane. At a scheduled tme n flght, the explosve bolts are ntated, and the structure separates from the vehcle. Now the responses at locaton P,.e. the pyroshock envronments of the component need to be analyzed for desgn. º F -9º 9º Fgure 3.1: Sketch of the concal structure. The load of a sngle explosve bolt can be smplfed as a unform dynamc pressure wth the ampltude 25MPa, pulse duraton 5µs and loadng area Ф2mm. In fact, ths load corresponds an mpulse of 1.96N s. Because of the unformty of the explosve bolts, and ts locatons and load drectons, the loads have the characterstcs of rotatonal smlarty accordng to the above defnton 2.1. So the problem can be solved by the Rotaton- Superposton Method. 3.2 Fnte Element Modelng The fnte element software ANSYS/LS-DYNA s used for modelng and smulaton. The 1/2 model (º-18º) s bult as shown n Fgure 3.2.

4 Fast Smulaton of Pyroshock Responses. 19 Fgure 3.2: Fnte element model of the concal structure. The model s meshed nto SOLID 164 elements, wth nodes. All the materals are descrbed by the lnear elastc consttutve model wth the mass densty kg/m 3, elastc modulus 27GPa and Posson s rato.28. The º-18º secton s set as plane-symmetrcal boundary condton, and the others are kept free. Let F denote the load element located at º. The pressure ampltude s 1MPa, and the loadng area s the outer surface of the correspondng elements as shown n Fgure Results 4.1 Acceleraton Reponses to F Frstly, a part of axal (Z-drecton) acceleraton hstores (at the crcumference correspondng to pont P) are obtaned as shown n Fgure 4.1. These curves wll be used to calculate the acceleraton responses to varous numbers of explosve bolts. Fgure 4.1: Acceleraton responses to F. Fve acceleraton hstores, A, B, C, D and E were recorded, correspondng to the nodes 84, 673, 6721, 2752 and 27241, respectvely. The correspondng crcumferental angles are º, 45º, 9º, 135º and 18º, respectvely. 4.2 Acceleraton Responses to 4 and 8 Bolts For the condton of 4 explosve bolts, accordng to the ax-symmetry of the structure, rotatonal smlarty of the loads and the plane symmetry of the problem, the acceleraton response at the pont P can be derved as [ a( ) + a(9 ) + a( 9 ) + a(18 )] = 25( a + 2a ), A = + (4.1) ( 4) a27241

5 Yongjan Mao et al 191 The dervaton of the above equaton can be llustrated by Fgure 4.2, and the result s gven n Fgure 4.3(a). Smlarly, the acceleraton response to 8 bolts s as shown n Fgure 4.3(b). ( a + 2a + 2a + a ) A = 25 + a, (4.2) ( 8) Acceleraton Responses to 4 Bolts Non-smultaneously Intated Consder the ntaton delays of the 4 explosve bolts as: ms at º,.25ms at ±9º and.5ms at 18º, then the acceleraton response at the pont P can be expressed as [ a ( t) + 2a ( t +.25) + a (.5) ] A '( 4) = t +. (4.3) The correspondng result s plotted n Fgure 4.3(c). 4.4 Shock Response Spectrum (SRS) Analyss The maxmum SRS curves calculated from the acceleraton hstores shown n Fgures 4.3(a), (b) and (c) are gven n Fgure 4.3(d). From Fgure 4.3(d), we can fnd that the SRS to 8 explosve bolts s hgher than that to 4 bolts. Ths s manly because the total mpulse of 8 bolts s much hgher than 4 bolts. Meanwhle, the SRS to 4 bolts smultaneously ntated s a lttle hgher than nonsmultaneous ntatons. Ths s manly because the non-smultaneous ntatons affect the energy concentraton and output. F a(º) to F F Acceleraton Load element Explosve bolts (EB) rotate F 1 F F ncludng a(-9º) to F a(º) to F 1 superpos F 3 F 1 F a to F rotate F 2 a(º) to F=F +F 1 +F 2 +F 3 a(18º) to F F 2 a(º) to F 2 25 F rotate F 3 a(9º) to F a(º) to F 3 a(º) to EB +EB 1 +EB 2 +EB 3 Fgure 4.2: Illustraton of the Rotaton-Superposton Method for calculatng responses to 4 bolts by the responses to a sngle load element F.

6 Fast Smulaton of Pyroshock Responses explosve bolts: 2 8 explosve bolts: Acceleraton / g 1-1 Acceleraton / g (a) Tme / ms (b) Tme / ms Acceleraton / g (c) Fgure 4.3: Acceleraton responses and SRS analyss n varous load cases. (a) Acceleraton response to 4 explosve bolts. (b) Acceleraton response to 8 explosve bolts. (c) Responses to 4 bolts non-smultaneously ntated. (d) SRS analyss. 5. Summary Pyroshock responses predcton s of mportance for desgn of space structures. But presently t s dffcult because of the lack of effcent smulaton technques, especally for mult-case analyses. Ths paper presents an applcaton example of the Rotaton- Superposton Method n predctng pyroshock responses. The example shows that the quck method has very hgh effcency and convenence n mult-case structural responses predcton. Usng that, the responses n varous cases can be superposed only based on one fnte element smulaton. Ths study provdes a good approach for hgh-effcency predcton of pyroshock responses. References 4 bolts (non-smultaneously ntated) Tme / ms [1] NASA Techncal Standard: Pyroshock Test Crtera, NASA-STD-73, Natonal Aeronautcs and Space Admnstraton, USA, 1999 [2] C. J. Moenng, Shock & Vbraton Bull. 56(3) (1986), 3 7 [3] Y. J. Mao, H. J. Huang and Y. X. Yan, Adv. Mat. Res (21), [4] R. F. Wang, F. Y. Lu, Z. G. Yang and G. Lü, Mssles & Space Vehcles (4) (27), 17 2 [5] M. de Benedett, G. Garofalo, M. Zumpano and R. Barbon, Acta Astronautca 6(27), [6] E. L. Wlson, A. Der Kereghan and E. Bayo, Earthqu. & Struct. Dyn. 9 (1981), Maxmum shock response / g (d) bolts 8 bolts 4 bolts, non-smultaneous Frequency / Hz

7 Yongjan Mao et al 193 [7] R.J. Pnnngton and D. Lednk, J. Sound & Vbr. 189(2) (1996), [8] Y. J. Mao, Y. L. L, H. J. Deng and H. J. Huang, Chn. J. Comput. Mech. 27(3) (21), [9] Y. J. Mao, Y. L. L, H. J. Huang and H. J. Deng, Chn. J. Sold Mech. In press Yongjan Mao receved hs PhD degree n sold mechancs from Northwestern Polytechncal Unversty n 21. He s currently an assocated professor n Insttute of Structural Mechancs, Chna Academy of Engneerng Physcs. He has more than 2 papers publshed n journals. Hs research nterests are n the areas of structural shock dynamcs and dynamc behavors of materals. Yulong L receved hs PhD degree n sold mechancs from Northwestern Polytechncal Unversty (NPU) n He worked n Unversty of Calforna, San Dego n 1996, and worked n The Johns Hopkns Unversty n He s currently a professor n School of Aeronautcs, NPU. Up to now, he has 4 books and over 15 papers publshed. Hs research nterests are n the areas of dynamc behavors of materals and structural shock dynamcs. Hanjun Huang receved hs MS degree n engneerng mechancs from Chna Academy of Engneerng Physcs (CAEP) n 23. He s currently an assstant professor n Insttute of Structural Mechancs, CAEP. Hs research nterests are n the areas of experments and numercal smulatons of structural shock dynamcs. Junpn g Wang receved hs MS degree n engneerng mechancs from X an Jaotong Unversty n 21. He s currently an assstant professor n Insttute of Structural Mechancs, Chna Academy of Engneerng Physcs. Hs research nterests are n the areas of experments and numercal smulatons of structural shock dynamcs.

8 Appled Mathematcs & Informaton Scences An Internatonal 5 (2) (211), 33S-37S