王君杰+李軍+孟德巍
建筑科學(xué)與工程學(xué)報(bào)2014年文章編號(hào):16732049(2014)01005006
收稿日期:20131107
基金項(xiàng)目:國家重點(diǎn)基礎(chǔ)研究發(fā)展計(jì)劃(“九七三”計(jì)劃)項(xiàng)目(2013CB036305);國家自然科學(xué)基金項(xiàng)目(51278373);
交通運(yùn)輸部西部交通建設(shè)科技項(xiàng)目(2007 318 822 34)
作者簡介:王君杰(1962),男,遼寧本溪人,教授,博士研究生導(dǎo)師,工學(xué)博士,
摘要:為研究船橋碰撞有限元分析中鋼板的網(wǎng)格尺寸與鋼材計(jì)算失效應(yīng)變之間的關(guān)系,進(jìn)行了3個(gè)鋼箱模型的落錘沖擊試驗(yàn)。采用LSDYNA軟件對(duì)試驗(yàn)?zāi)P瓦M(jìn)行了有限元建模和碰撞計(jì)算,并與試驗(yàn)結(jié)果進(jìn)行了對(duì)比。定義了一個(gè)相關(guān)系數(shù)來反映試驗(yàn)結(jié)果與計(jì)算結(jié)果之間的相關(guān)性,并據(jù)此定義了與網(wǎng)格尺寸相關(guān)的計(jì)算失效應(yīng)變合理取值區(qū)間。研究結(jié)果表明:為得到合理精度的計(jì)算結(jié)果,鋼板的計(jì)算失效應(yīng)變的取值應(yīng)隨鋼板網(wǎng)格尺寸變化,使用大的網(wǎng)格尺寸時(shí)應(yīng)采用小的失效應(yīng)變,使用小的網(wǎng)格尺寸時(shí)應(yīng)采用大的失效應(yīng)變;將計(jì)算失效應(yīng)變合理取值區(qū)間與自適應(yīng)網(wǎng)格剖分技術(shù)結(jié)合,可以在保證計(jì)算精度的同時(shí),提高計(jì)算效率。
關(guān)鍵詞:鋼箱;網(wǎng)格尺寸;失效應(yīng)變;計(jì)算精度;自適應(yīng)網(wǎng)格剖分;沖擊試驗(yàn)
中圖分類號(hào):U661.72文獻(xiàn)標(biāo)志碼:A
Impact Test on Computational Failure Strain of Steel BoxesWANG Junjie, LI Jun, MENG Dewei
(State Key Laboratory for Disaster Reduction in Civil Engineering, Tongji University, Shanghai 200092, China)Abstract: In order to investigate the relations between the meshing size of steel plates and computational failure strain of steel in shipbridge collision finite element analysis, the drop hammer impact tests of three steel boxes were carried out. The finite element model was built and impact computation was conducted for test models using LSDYNA software, and the computational results were compared with the test results. A correlation coefficient was defined to obtain a reasonable failure strain interval related to the meshing size of the steel boxes. The research results show that in order to get reasonable computational accurcy, the values of computational failure strainshould vary with the meshing size of steel plates. The larger failure strain should be used for the smaller meshing size, and the smaller failure strain should be used for the larger meshing size. The computational accuracy and computational efficiency can be obtained at the same time through combining the reasonable computational failure strain interval and the adaptive meshing technology.
Key words: steel box; meshing size; failure strain; computational accuracy; adaptive meshing; impact test
0引言
對(duì)于橋梁船撞設(shè)計(jì),能夠把握船撞橋的碰撞力特征和破壞形態(tài)具有重要的實(shí)際意義。隨著計(jì)算機(jī)技術(shù)的快速發(fā)展,特別是有限元技術(shù)的日益進(jìn)步和成熟,數(shù)值模擬分析在橋梁船撞設(shè)計(jì)和防撞設(shè)施設(shè)計(jì)上逐漸得到了廣泛的應(yīng)用。與此同時(shí),數(shù)值仿真計(jì)算結(jié)果的可靠性和如何使用有限元技術(shù)對(duì)此類碰撞問題進(jìn)行有效的模擬日益成為關(guān)注的焦點(diǎn)。建立有限元模型是有限元分析過程的關(guān)鍵,而網(wǎng)格劃分是建立有限元模型的中心工作,模型的合理性很大程度上可以通過所劃分的網(wǎng)格形式體現(xiàn)出來。
對(duì)于固體碰撞問題,研究發(fā)現(xiàn)網(wǎng)格尺寸與材料失效應(yīng)變的取值存在一定的相關(guān)性[15]。Lehmann等[1]、Kitamura等[2]、Paik等[3]分別基于一系列的碰撞試驗(yàn)或鋼板拉伸試驗(yàn)總結(jié)得出:必要的數(shù)值失效應(yīng)變(在有限元模型中調(diào)整該值以匹配試驗(yàn)數(shù)據(jù))是網(wǎng)格尺寸的函數(shù),總的趨勢是大尺寸的網(wǎng)格需要定義較小的數(shù)值失效應(yīng)變。Pedersen[6],Kitamura等[2]和高震等[7]將這種現(xiàn)象解釋為:較大的單元降低了高應(yīng)力點(diǎn)的應(yīng)力,以致撕裂不能及時(shí)發(fā)生,提高了結(jié)構(gòu)抗力;大的網(wǎng)格尺寸使用較小的失效應(yīng)變是考慮了裂縫、侵蝕和沖擊荷載等的影響。然而,由于碰撞的實(shí)際行為狀態(tài)非常重要,因而一個(gè)算例或一個(gè)試驗(yàn)的結(jié)果很難直接應(yīng)用于其他碰撞情況。船橋碰撞中的不確定因素很多,而這些因素又會(huì)對(duì)碰撞結(jié)果產(chǎn)生極大的影響。換言之,當(dāng)分析的問題稍有不同時(shí),就可能需要對(duì)網(wǎng)格尺寸與失效應(yīng)變的關(guān)系進(jìn)行調(diào)整。
本文中筆者基于3次碰撞試驗(yàn)研究了網(wǎng)格尺寸和失效應(yīng)變?nèi)≈抵g的關(guān)系,對(duì)碰撞破壞問題中的網(wǎng)格劃分方法進(jìn)行了進(jìn)一步的探討。
1模型設(shè)計(jì)與測試
本文中以船舶正向撞擊鋼結(jié)構(gòu)防撞設(shè)施為背景進(jìn)行了3次試驗(yàn),其初始能量(碰撞前系統(tǒng)的能量)比約為1∶2∶3。由于試驗(yàn)中沖頭的初始動(dòng)能基本全部由被撞鋼箱吸收,因此3次試驗(yàn)中被撞鋼箱吸收的能量比例也約為1∶2∶3(表1),并由此來實(shí)現(xiàn)被撞鋼箱結(jié)構(gòu)不同程度的破壞,試驗(yàn)安裝見圖1。試驗(yàn)中的主動(dòng)撞擊結(jié)構(gòu)由上導(dǎo)向板、落錘、下導(dǎo)向板及撞擊鐵塊組成。試驗(yàn)時(shí),由電動(dòng)葫蘆通過掛彈鉤將主動(dòng)撞擊結(jié)構(gòu)提升至預(yù)定的跌落高度,然后掛彈鉤通電釋放主動(dòng)撞擊結(jié)構(gòu),主動(dòng)撞擊結(jié)構(gòu)自由跌落并沖擊鋼結(jié)構(gòu)防撞設(shè)施縮尺模型,從而使被撞鋼箱出現(xiàn)不同程度的破壞。3次試驗(yàn)的結(jié)構(gòu)布置見圖2。
試驗(yàn)中的被撞鋼箱具體尺寸參見文獻(xiàn)[8]。由于被撞鋼箱鋼板較薄(4.62 mm),焊接過程中產(chǎn)生的殘余應(yīng)力將對(duì)結(jié)構(gòu)的性能產(chǎn)生很大影響,故在焊接結(jié)束后對(duì)被撞鋼箱進(jìn)行了鋼板回火處理、焊縫質(zhì)
表1試驗(yàn)工況
Tab.1Testing Cases試驗(yàn)
編號(hào)撞擊質(zhì)量/kg跌落高度/m沖擊速度/
endprint
(m·s-1)初始動(dòng)能/
(kN·m)19 7681.85.94172 307.529 7684.18.97392 478.2314 0284.59.39618 634.8圖1試驗(yàn)安裝
Fig.1Test Installation圖2試驗(yàn)的結(jié)構(gòu)布置
Fig.2Structural Arrangements of Tests量檢查和鋼板的靜態(tài)拉伸試驗(yàn)等。
試驗(yàn)中,對(duì)沖擊過程中主動(dòng)撞擊錘的加速度和被撞鋼箱上選取點(diǎn)的應(yīng)變響應(yīng)進(jìn)行測量,對(duì)沖擊結(jié)束后被撞鋼箱上一些選取的點(diǎn)進(jìn)行人工位移測量,使用高速攝影設(shè)備對(duì)沖擊過程中被撞鋼箱的變形情況進(jìn)行輔助性的記錄。測量系統(tǒng)見圖3。
圖3測量系統(tǒng)
Fig.3Measurement System2數(shù)值計(jì)算方法
在大量分析和比較的基礎(chǔ)上,本文中使用如下的計(jì)算參數(shù):選擇在汽車碰撞分析中廣泛使用的多段線性塑性模型來代表鋼材在沖擊作用下的力學(xué)屬性;采用CowperSymonds公式[9][(σYd/σY=1+(ε/C)q,其中,σYd為材料動(dòng)態(tài)失效應(yīng)變,σY為材料靜態(tài)失效應(yīng)變,ε為應(yīng)變率,C,q均為材料常數(shù)]來考慮應(yīng)變率的影響,并結(jié)合粘塑性公式來減少考慮應(yīng)變率時(shí)的響應(yīng)噪聲,本試驗(yàn)中被撞鋼箱為Q235軟鋼,C=40.4,q=1/5;采用材料的實(shí)際應(yīng)力應(yīng)變關(guān)系;鋼材的失效模式采用最大有效塑性應(yīng)變失效模式,失效模式表述為εpeff≥εfailure,即當(dāng)有限元模型中單元的應(yīng)變超過設(shè)定值時(shí),單元失效,失效后的單元從模型中刪除。3數(shù)值計(jì)算結(jié)果符合度檢驗(yàn)方法
由于沖頭相對(duì)于被撞鋼箱來說剛度極大,因此在試驗(yàn)中,沖頭可以近似地視為剛體,故在得到?jīng)_頭的加速度時(shí)程后,可以根據(jù)牛頓第二定律得到碰撞過程中的碰撞力時(shí)程。
在進(jìn)行船舶碰撞的有限元仿真分析時(shí),主要關(guān)注以下2個(gè)方面的結(jié)果:①船舶與橋梁或防撞結(jié)構(gòu)之間的撞擊力特征,包括碰撞力輪廓和碰撞力峰值;②船舶或橋梁的破壞模式、破壞情形。
為了討論不同網(wǎng)格尺寸對(duì)應(yīng)的最佳失效應(yīng)變?nèi)≈?,本文中定義描述試驗(yàn)加速度結(jié)果與數(shù)值仿真結(jié)果之間差別的2個(gè)指標(biāo)或準(zhǔn)則:①計(jì)算值與測量值之間的相關(guān)系數(shù),采用Pearson相關(guān)系數(shù)r;②峰值加速度計(jì)算值與測量值之間的相對(duì)誤差e。r,e的計(jì)算方法分別為
r=XY-XYN/
(X2-(X)2N)(Y2-(Y)2N)(1)
e=amax-a′maxamax(2)
式中:X,Y為2個(gè)數(shù)值序列;amax為最大加速度測量值; a′max為最大加速度計(jì)算值。
3次試驗(yàn)測量得到的加速度試驗(yàn)結(jié)果見圖4,其中,g為重力加速度。試驗(yàn)結(jié)果表明,開始段均具有明顯的周期約為0.003 8 s的波動(dòng)段,且該波動(dòng)段在第1次試驗(yàn)中響應(yīng)最大,在第3次試驗(yàn)中響應(yīng)最小,
圖4加速度試驗(yàn)結(jié)果及其修正
Fig.4Acceleration Test Results and Amendment初步判定該響應(yīng)與試驗(yàn)場地地基有關(guān)[10]。本文中采用HilbertHuang[1112]原理修正了第1次和第2次試驗(yàn)的波動(dòng)段加速度試驗(yàn)結(jié)果。4網(wǎng)格剖分與失效應(yīng)變的關(guān)系
考慮被撞鋼箱上的殼單元邊長為2 cm的情形,將單元的失效應(yīng)變?chǔ)谭謩e取為0.12,0.15,0.20,0.25,0.30,研究單元失效應(yīng)變對(duì)加速度數(shù)值模擬結(jié)果的影響,結(jié)果見圖5。
圖5失效應(yīng)變對(duì)加速度計(jì)算結(jié)果的影響
Fig.5Effects of Failure Strain on Acceleration
Computational Results由圖5可以看出,失效應(yīng)變?nèi)≈挡煌?,得到的?jì)算結(jié)果差別很大,這說明失效應(yīng)變的合理取值對(duì)船橋碰撞數(shù)值模擬計(jì)算結(jié)果的合理性和可靠性是十分重要的。
本文中對(duì)被撞鋼箱劃分了7種網(wǎng)格尺寸,網(wǎng)格單元邊長l分別為0.5,1,1.4,2,2.5,3,5 cm,并采用多種失效應(yīng)變(最小失效應(yīng)變0.05,最大失效應(yīng)變0.6)來研究失效應(yīng)變和網(wǎng)格尺寸的關(guān)系。相關(guān)系數(shù)與加速度峰值相對(duì)誤差的計(jì)算結(jié)果見圖6,7。
圖6相關(guān)系數(shù)計(jì)算結(jié)果
Fig.6Computational Results of Correlation Coefficient從圖6,7可以看出:
(1)失效應(yīng)變?nèi)≈禐?.05時(shí)(很小時(shí)),不同網(wǎng)格尺寸下的計(jì)算結(jié)果均與試驗(yàn)結(jié)果差別很大,總體上來說,加速度計(jì)算結(jié)果與試驗(yàn)結(jié)果之間的相關(guān)系數(shù)較小,且可能出現(xiàn)非常大的峰值加速度,這說明失效應(yīng)變?nèi)≈颠^小不能合理預(yù)測鋼箱發(fā)生塑性損傷時(shí)的沖擊反應(yīng)。
(2)隨著失效應(yīng)變的增大,大尺寸網(wǎng)格可以率先計(jì)算得到較好的結(jié)果,隨著失效應(yīng)變繼續(xù)增加,小尺寸的網(wǎng)格依次得到精度較好的計(jì)算結(jié)果。
(3)存在一個(gè)失效應(yīng)變的取值區(qū)間[εLf,εUf],εLf為區(qū)間的下界,εUf為區(qū)間的上界,當(dāng)失效應(yīng)變?cè)诖藚^(qū)間取值時(shí)可獲得較高精度的計(jì)算結(jié)果。這個(gè)取值區(qū)間的范圍隨網(wǎng)格尺寸變化:網(wǎng)格尺寸大,失效應(yīng)變?nèi)≈祬^(qū)間寬度?。环粗?,網(wǎng)格尺寸小,則失效應(yīng)變區(qū)間寬度大。
(4)當(dāng)網(wǎng)格尺寸足夠小時(shí),對(duì)于本試驗(yàn),網(wǎng)格尺寸不宜大于1 cm,失效應(yīng)變?nèi)?.35~0.50是合理的,但是同時(shí)也可以看出,合理的失效應(yīng)變?nèi)≈蹬c鋼箱遭受的沖擊破壞程度可能有關(guān)。
圖8為最優(yōu)失效應(yīng)變范圍。從圖8可以看出,對(duì)于同一網(wǎng)格的不同失效應(yīng)變情形,相關(guān)系數(shù)總是先增大再減小。據(jù)此定義[εLf,εUf]為合理取值區(qū)間。合理取值區(qū)間的下界εLf和上界εUf根據(jù)相關(guān)系數(shù)r>0.9的條件確定。圖8中綜合了3次試驗(yàn)的加速度結(jié)果,得到了適用于3次試驗(yàn)的失效應(yīng)變合理取值區(qū)間的下界和上界。圖8中顯示合理區(qū)間的下界和上界均隨著網(wǎng)格尺寸的增大而逐步變小,上界變化相對(duì)較快,區(qū)間范圍隨網(wǎng)格尺寸的增大而變小。
從圖8還可以看出,如果采用大網(wǎng)格模型進(jìn)行分析,則必須謹(jǐn)慎地定義失效應(yīng)變;如果采用小網(wǎng)格模型進(jìn)行分析,則可以適當(dāng)?shù)貙⑹?yīng)變?nèi)〉么笠稽c(diǎn),以計(jì)算結(jié)果逐步穩(wěn)定時(shí)為宜。
有限元仿真模擬的另一項(xiàng)重要內(nèi)容是對(duì)結(jié)構(gòu)的變形模式或破壞形式進(jìn)行捕捉。圖9中給出了第3次試驗(yàn)中被撞鋼箱背面鋼板出現(xiàn)的褶皺和0.5 cm以及5 cm網(wǎng)格計(jì)算對(duì)該褶皺捕捉情況的對(duì)比。由此可見,0.5 cm網(wǎng)格對(duì)該褶皺的描述非常好,且結(jié)構(gòu)變形光滑平順,而5 cm網(wǎng)格則完全沒有表現(xiàn)出該處出現(xiàn)的褶皺。這表明當(dāng)需要研究結(jié)構(gòu)的變形模式或破壞模式時(shí),應(yīng)該劃分尺寸較小的網(wǎng)格。5結(jié)語
(1)網(wǎng)格尺寸與失效應(yīng)變是相關(guān)的,即單元的失效應(yīng)變依賴于網(wǎng)格的尺寸,使用大尺寸網(wǎng)格時(shí)應(yīng)采用較小的失效應(yīng)變,且失效應(yīng)變的定義較為敏感;使用小尺寸網(wǎng)格時(shí)應(yīng)采用較大的失效應(yīng)變,且失效應(yīng)變的定義不敏感,因此,根據(jù)相關(guān)系數(shù)定義了合理失效應(yīng)變區(qū)間。網(wǎng)格大則合理失效應(yīng)變?nèi)≈祬^(qū)間小,網(wǎng)格小則合理失效應(yīng)變?nèi)≈祬^(qū)間大。
(2)為保證計(jì)算結(jié)果的精度,建議計(jì)算時(shí)可逐步細(xì)化模型中網(wǎng)格的尺寸并對(duì)失效應(yīng)變的取值進(jìn)行較大幅度的變化,當(dāng)失效應(yīng)變的取值在較大范圍內(nèi)變圖7加速度峰值相對(duì)誤差計(jì)算結(jié)果
Fig.7Computational Results of Relative Error of Peak Acceleration圖8最優(yōu)失效應(yīng)變范圍
Fig.8Optimum Failure Strain Interval化而對(duì)計(jì)算結(jié)果的影響較小時(shí),可以認(rèn)為已經(jīng)獲得了較好的計(jì)算模型。
(3)采用自適應(yīng)網(wǎng)格剖分并結(jié)合最優(yōu)失效應(yīng)變區(qū)間概念進(jìn)行計(jì)算分析,可以在獲得同等計(jì)算精度的同時(shí)節(jié)省大量的建模時(shí)間和計(jì)算分析時(shí)間。
endprint
(4)需要注意的是,本文中的結(jié)論是在縮尺模型試驗(yàn)中獲得的,其適用性還有待在足尺試驗(yàn)或?qū)嶋H船橋碰撞事故中得到進(jìn)一步驗(yàn)證。圖9試驗(yàn)與計(jì)算褶皺的對(duì)比
Fig.9Comparisons of Folds Between Test and Computational Results參考文獻(xiàn):
References:[1]LEHMANN E,PESCHMANN J.Energy Absorption by the Steel Structure of Ships in the Event of Collisions[J].Marine Structures,2002,15(4/5):429441.
[2]KITAMURA O.FEM Approach to the Simulation of Collision and Grounding Damage[J].Marine Structures,2002,15(4/5):403428.
[3]PAIK J K,AMDAHL J,BARLTROP N.Collision and Grounding[C]//MANSOURE A E,ERTEKIN R C.Proceedings of the 15th International Ship and Offshore Structures Congress.San Diego:ISSC,2003:71107.
[4]SERVIS D,SAMUELIDES M,LOUKA T,et al.The Implementation of Finite Element Codes for the Simulation of Shipship Collision[J].Journal of Ship Research,2002,46(4):239247.
[5]NAAR H,KUJALA P,SIMONSEN B C,et al.Comparison of the Crashworthiness of Various Bottom and Side Structures[J].Marine Structures,2002,15(4/5):443460.
[6]PEDERSEN P T.Ship Impacts:Bow Collisions[J].International Journal of Impact Engineerin,1993,13(2):163187.
[7]高震,顧永寧,胡志強(qiáng).結(jié)構(gòu)沖擊試驗(yàn)的校準(zhǔn)計(jì)算[J].船舶力學(xué),2005,9(2):7782.
GAO Zhen,GU Yongning,HU Zhiqiang.Benchmark Study of Structural Impact Test[J].Journal of Ship Mechanincs,2005,9(2):7782.
[8]李軍.沖擊數(shù)值模擬可靠性的試驗(yàn)檢驗(yàn)[D].上海:同濟(jì)大學(xué),2009.
LI Jun.Experimental Examination of the Trustworthiness of Impact Numerical Simulation[D].Shanghai:Tongji University,2009.
[9]COWPER G R,Symonds P S.Strain Hardening and Strain Rate Effects in the Impact Loading of Cantilever Beams[R].Providence:Brown University,1958.
[10]華南理工大學(xué),東南大學(xué),浙江大學(xué),等.地基與基礎(chǔ)[M].2版.北京:中國建筑工業(yè)出版社,1991.
South China University of Technology, Southest University,Zhejiang University,et al.Soils and Foundations[M].2nd ed.Beijing:China Architecture & Building Press,1991.
[11]HUANG N E,WU M C,LONG S R,et al.A Confidence Limit for the Empirical Mode Decomposition and Hilbert Spectral Analysis[J].Proceedings of the Royal Society A,2003,459(2037):23172345.
[12]HUANG N E,SHEN Z,LONG S R,et al.The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and Nonstationary Time Series Analysis[J].Proceedings of the Royal Society A,1998,454(1971):903995.(上接第15頁)
associated with CSA S13607 will be greater than that of GB 50018—2002.
(4) The difference of the nominal axial strength between the two standards is primarily influenced by the flange widthtothickness ratio. For typical Csection wall studs investigated herein, the difference on the nominal axial strength is primarily influenced by the flange widthtothickness ratio wf/t. If the flange widthtothickness ratio wf/t is not less than 17.8, the difference on the nominal axial strength is dominated by the difference of flange effective width, and the nominal axial strength evaluated by GB 50018—2002 is less than that of CSA S13607, with the maximum difference being 31.9%. However, when wf/t is approximately less than 17.8, then the difference on the nominal axial strength is primarily governed by the difference of the web effective width and the nominal axial strength evaluated by GB 50018—2002 is slightly greater than that of CSA S13607, with the maximum difference being 8.9%.References:[1]CSA S13607,North American Specification for the Design of Coldformed Steel Structural Members[S].
[2]GB 50018—2002,Technical Code of Coldformed Thinwall Steel Structures[S].
[3]JGJ 227—2011,Technical Specification for Lowrise Coldformed Thinwall Steel Buildings[S].
[4]CHEN J.Stability of Steel Structures:Theory and Design[M].Beijing:Science Press,2008.
[5]YU W W,LABOUBE R A.Coldformed Steel Design[M].New York:John Wiley & Sons,2010.
[6]ZHOU X H,WANG S J.Stability Theory and Its Applications of Thinwalled Members[M].Beijing:Science Press,2009.
[7]XU L.Advanced Structural Steel Design[R].Waterloo:University of Waterloo,2012.
[8]Canadian Institute of Steel Construction.Handbook of Steel Construction[M].10th ed.Markham:Canadian Institute of Steel Construction,2010.
[9]Canadian Sheet Steel Building Institute (CSSBI).Lightweight Steel Frame Metric Section Properties[R].Cambridge:Canadian Sheet Steel Building Institute,2011.
endprint
(4)需要注意的是,本文中的結(jié)論是在縮尺模型試驗(yàn)中獲得的,其適用性還有待在足尺試驗(yàn)或?qū)嶋H船橋碰撞事故中得到進(jìn)一步驗(yàn)證。圖9試驗(yàn)與計(jì)算褶皺的對(duì)比
Fig.9Comparisons of Folds Between Test and Computational Results參考文獻(xiàn):
References:[1]LEHMANN E,PESCHMANN J.Energy Absorption by the Steel Structure of Ships in the Event of Collisions[J].Marine Structures,2002,15(4/5):429441.
[2]KITAMURA O.FEM Approach to the Simulation of Collision and Grounding Damage[J].Marine Structures,2002,15(4/5):403428.
[3]PAIK J K,AMDAHL J,BARLTROP N.Collision and Grounding[C]//MANSOURE A E,ERTEKIN R C.Proceedings of the 15th International Ship and Offshore Structures Congress.San Diego:ISSC,2003:71107.
[4]SERVIS D,SAMUELIDES M,LOUKA T,et al.The Implementation of Finite Element Codes for the Simulation of Shipship Collision[J].Journal of Ship Research,2002,46(4):239247.
[5]NAAR H,KUJALA P,SIMONSEN B C,et al.Comparison of the Crashworthiness of Various Bottom and Side Structures[J].Marine Structures,2002,15(4/5):443460.
[6]PEDERSEN P T.Ship Impacts:Bow Collisions[J].International Journal of Impact Engineerin,1993,13(2):163187.
[7]高震,顧永寧,胡志強(qiáng).結(jié)構(gòu)沖擊試驗(yàn)的校準(zhǔn)計(jì)算[J].船舶力學(xué),2005,9(2):7782.
GAO Zhen,GU Yongning,HU Zhiqiang.Benchmark Study of Structural Impact Test[J].Journal of Ship Mechanincs,2005,9(2):7782.
[8]李軍.沖擊數(shù)值模擬可靠性的試驗(yàn)檢驗(yàn)[D].上海:同濟(jì)大學(xué),2009.
LI Jun.Experimental Examination of the Trustworthiness of Impact Numerical Simulation[D].Shanghai:Tongji University,2009.
[9]COWPER G R,Symonds P S.Strain Hardening and Strain Rate Effects in the Impact Loading of Cantilever Beams[R].Providence:Brown University,1958.
[10]華南理工大學(xué),東南大學(xué),浙江大學(xué),等.地基與基礎(chǔ)[M].2版.北京:中國建筑工業(yè)出版社,1991.
South China University of Technology, Southest University,Zhejiang University,et al.Soils and Foundations[M].2nd ed.Beijing:China Architecture & Building Press,1991.
[11]HUANG N E,WU M C,LONG S R,et al.A Confidence Limit for the Empirical Mode Decomposition and Hilbert Spectral Analysis[J].Proceedings of the Royal Society A,2003,459(2037):23172345.
[12]HUANG N E,SHEN Z,LONG S R,et al.The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and Nonstationary Time Series Analysis[J].Proceedings of the Royal Society A,1998,454(1971):903995.(上接第15頁)
associated with CSA S13607 will be greater than that of GB 50018—2002.
(4) The difference of the nominal axial strength between the two standards is primarily influenced by the flange widthtothickness ratio. For typical Csection wall studs investigated herein, the difference on the nominal axial strength is primarily influenced by the flange widthtothickness ratio wf/t. If the flange widthtothickness ratio wf/t is not less than 17.8, the difference on the nominal axial strength is dominated by the difference of flange effective width, and the nominal axial strength evaluated by GB 50018—2002 is less than that of CSA S13607, with the maximum difference being 31.9%. However, when wf/t is approximately less than 17.8, then the difference on the nominal axial strength is primarily governed by the difference of the web effective width and the nominal axial strength evaluated by GB 50018—2002 is slightly greater than that of CSA S13607, with the maximum difference being 8.9%.References:[1]CSA S13607,North American Specification for the Design of Coldformed Steel Structural Members[S].
[2]GB 50018—2002,Technical Code of Coldformed Thinwall Steel Structures[S].
[3]JGJ 227—2011,Technical Specification for Lowrise Coldformed Thinwall Steel Buildings[S].
[4]CHEN J.Stability of Steel Structures:Theory and Design[M].Beijing:Science Press,2008.
[5]YU W W,LABOUBE R A.Coldformed Steel Design[M].New York:John Wiley & Sons,2010.
[6]ZHOU X H,WANG S J.Stability Theory and Its Applications of Thinwalled Members[M].Beijing:Science Press,2009.
[7]XU L.Advanced Structural Steel Design[R].Waterloo:University of Waterloo,2012.
[8]Canadian Institute of Steel Construction.Handbook of Steel Construction[M].10th ed.Markham:Canadian Institute of Steel Construction,2010.
[9]Canadian Sheet Steel Building Institute (CSSBI).Lightweight Steel Frame Metric Section Properties[R].Cambridge:Canadian Sheet Steel Building Institute,2011.
endprint
(4)需要注意的是,本文中的結(jié)論是在縮尺模型試驗(yàn)中獲得的,其適用性還有待在足尺試驗(yàn)或?qū)嶋H船橋碰撞事故中得到進(jìn)一步驗(yàn)證。圖9試驗(yàn)與計(jì)算褶皺的對(duì)比
Fig.9Comparisons of Folds Between Test and Computational Results參考文獻(xiàn):
References:[1]LEHMANN E,PESCHMANN J.Energy Absorption by the Steel Structure of Ships in the Event of Collisions[J].Marine Structures,2002,15(4/5):429441.
[2]KITAMURA O.FEM Approach to the Simulation of Collision and Grounding Damage[J].Marine Structures,2002,15(4/5):403428.
[3]PAIK J K,AMDAHL J,BARLTROP N.Collision and Grounding[C]//MANSOURE A E,ERTEKIN R C.Proceedings of the 15th International Ship and Offshore Structures Congress.San Diego:ISSC,2003:71107.
[4]SERVIS D,SAMUELIDES M,LOUKA T,et al.The Implementation of Finite Element Codes for the Simulation of Shipship Collision[J].Journal of Ship Research,2002,46(4):239247.
[5]NAAR H,KUJALA P,SIMONSEN B C,et al.Comparison of the Crashworthiness of Various Bottom and Side Structures[J].Marine Structures,2002,15(4/5):443460.
[6]PEDERSEN P T.Ship Impacts:Bow Collisions[J].International Journal of Impact Engineerin,1993,13(2):163187.
[7]高震,顧永寧,胡志強(qiáng).結(jié)構(gòu)沖擊試驗(yàn)的校準(zhǔn)計(jì)算[J].船舶力學(xué),2005,9(2):7782.
GAO Zhen,GU Yongning,HU Zhiqiang.Benchmark Study of Structural Impact Test[J].Journal of Ship Mechanincs,2005,9(2):7782.
[8]李軍.沖擊數(shù)值模擬可靠性的試驗(yàn)檢驗(yàn)[D].上海:同濟(jì)大學(xué),2009.
LI Jun.Experimental Examination of the Trustworthiness of Impact Numerical Simulation[D].Shanghai:Tongji University,2009.
[9]COWPER G R,Symonds P S.Strain Hardening and Strain Rate Effects in the Impact Loading of Cantilever Beams[R].Providence:Brown University,1958.
[10]華南理工大學(xué),東南大學(xué),浙江大學(xué),等.地基與基礎(chǔ)[M].2版.北京:中國建筑工業(yè)出版社,1991.
South China University of Technology, Southest University,Zhejiang University,et al.Soils and Foundations[M].2nd ed.Beijing:China Architecture & Building Press,1991.
[11]HUANG N E,WU M C,LONG S R,et al.A Confidence Limit for the Empirical Mode Decomposition and Hilbert Spectral Analysis[J].Proceedings of the Royal Society A,2003,459(2037):23172345.
[12]HUANG N E,SHEN Z,LONG S R,et al.The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and Nonstationary Time Series Analysis[J].Proceedings of the Royal Society A,1998,454(1971):903995.(上接第15頁)
associated with CSA S13607 will be greater than that of GB 50018—2002.
(4) The difference of the nominal axial strength between the two standards is primarily influenced by the flange widthtothickness ratio. For typical Csection wall studs investigated herein, the difference on the nominal axial strength is primarily influenced by the flange widthtothickness ratio wf/t. If the flange widthtothickness ratio wf/t is not less than 17.8, the difference on the nominal axial strength is dominated by the difference of flange effective width, and the nominal axial strength evaluated by GB 50018—2002 is less than that of CSA S13607, with the maximum difference being 31.9%. However, when wf/t is approximately less than 17.8, then the difference on the nominal axial strength is primarily governed by the difference of the web effective width and the nominal axial strength evaluated by GB 50018—2002 is slightly greater than that of CSA S13607, with the maximum difference being 8.9%.References:[1]CSA S13607,North American Specification for the Design of Coldformed Steel Structural Members[S].
[2]GB 50018—2002,Technical Code of Coldformed Thinwall Steel Structures[S].
[3]JGJ 227—2011,Technical Specification for Lowrise Coldformed Thinwall Steel Buildings[S].
[4]CHEN J.Stability of Steel Structures:Theory and Design[M].Beijing:Science Press,2008.
[5]YU W W,LABOUBE R A.Coldformed Steel Design[M].New York:John Wiley & Sons,2010.
[6]ZHOU X H,WANG S J.Stability Theory and Its Applications of Thinwalled Members[M].Beijing:Science Press,2009.
[7]XU L.Advanced Structural Steel Design[R].Waterloo:University of Waterloo,2012.
[8]Canadian Institute of Steel Construction.Handbook of Steel Construction[M].10th ed.Markham:Canadian Institute of Steel Construction,2010.
[9]Canadian Sheet Steel Building Institute (CSSBI).Lightweight Steel Frame Metric Section Properties[R].Cambridge:Canadian Sheet Steel Building Institute,2011.
endprint