鋼箱計算失效應變的沖擊試驗

王君杰+李軍+孟德巍

建筑科學與工程學報2014年文章編號：16732049(2014)01005006

收稿日期：20131107

基金項目：國家重點基礎研究發展計劃（“九七三”計劃）項目（2013CB036305）；國家自然科學基金項目（51278373）；

交通運輸部西部交通建設科技項目（2007 318 822 34）

作者簡介：王君杰（1962），男，遼寧本溪人，教授，博士研究生導師，工學博士，

摘要：為研究船橋碰撞有限元分析中鋼板的網格尺寸與鋼材計算失效應變之間的關系，進行了3個鋼箱模型的落錘沖擊試驗。采用LSDYNA軟件對試驗模型進行了有限元建模和碰撞計算，并與試驗結果進行了對比。定義了一個相關系數來反映試驗結果與計算結果之間的相關性，并據此定義了與網格尺寸相關的計算失效應變合理取值區間。研究結果表明：為得到合理精度的計算結果，鋼板的計算失效應變的取值應隨鋼板網格尺寸變化，使用大的網格尺寸時應采用小的失效應變，使用小的網格尺寸時應采用大的失效應變；將計算失效應變合理取值區間與自適應網格剖分技術結合，可以在保證計算精度的同時，提高計算效率。

關鍵詞：鋼箱；網格尺寸；失效應變；計算精度；自適應網格剖分；沖擊試驗

中圖分類號：U661.72文獻標志碼：A

Impact Test on Computational Failure Strain of Steel BoxesWANG Junjie, LI Jun, MENG Dewei

（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 shipbridge 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 LSDYNA 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

對于橋梁船撞設計，能夠把握船撞橋的碰撞力特征和破壞形態具有重要的實際意義。隨著計算機技術的快速發展，特別是有限元技術的日益進步和成熟，數值模擬分析在橋梁船撞設計和防撞設施設計上逐漸得到了廣泛的應用。與此同時，數值仿真計算結果的可靠性和如何使用有限元技術對此類碰撞問題進行有效的模擬日益成為關注的焦點。建立有限元模型是有限元分析過程的關鍵，而網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格形式體現出來。

對于固體碰撞問題，研究發現網格尺寸與材料失效應變的取值存在一定的相關性［15］。Lehmann等［1］、Kitamura等［2］、Paik等［3］分別基于一系列的碰撞試驗或鋼板拉伸試驗總結得出：必要的數值失效應變（在有限元模型中調整該值以匹配試驗數據）是網格尺寸的函數，總的趨勢是大尺寸的網格需要定義較小的數值失效應變。Pedersen［6］，Kitamura等［2］和高震等［7］將這種現象解釋為：較大的單元降低了高應力點的應力，以致撕裂不能及時發生，提高了結構抗力；大的網格尺寸使用較小的失效應變是考慮了裂縫、侵蝕和沖擊荷載等的影響。然而，由于碰撞的實際行為狀態非常重要，因而一個算例或一個試驗的結果很難直接應用于其他碰撞情況。船橋碰撞中的不確定因素很多，而這些因素又會對碰撞結果產生極大的影響。換言之，當分析的問題稍有不同時，就可能需要對網格尺寸與失效應變的關系進行調整。

本文中筆者基于3次碰撞試驗研究了網格尺寸和失效應變取值之間的關系，對碰撞破壞問題中的網格劃分方法進行了進一步的探討。

1模型設計與測試

本文中以船舶正向撞擊鋼結構防撞設施為背景進行了3次試驗，其初始能量(碰撞前系統的能量)比約為1∶2∶3。由于試驗中沖頭的初始動能基本全部由被撞鋼箱吸收，因此3次試驗中被撞鋼箱吸收的能量比例也約為1∶2∶3（表1），并由此來實現被撞鋼箱結構不同程度的破壞，試驗安裝見圖1。試驗中的主動撞擊結構由上導向板、落錘、下導向板及撞擊鐵塊組成。試驗時，由電動葫蘆通過掛彈鉤將主動撞擊結構提升至預定的跌落高度，然后掛彈鉤通電釋放主動撞擊結構，主動撞擊結構自由跌落并沖擊鋼結構防撞設施縮尺模型，從而使被撞鋼箱出現不同程度的破壞。3次試驗的結構布置見圖2。

試驗中的被撞鋼箱具體尺寸參見文獻［8］。由于被撞鋼箱鋼板較薄(4.62 mm)，焊接過程中產生的殘余應力將對結構的性能產生很大影響，故在焊接結束后對被撞鋼箱進行了鋼板回火處理、焊縫質

表1試驗工況

Tab.1Testing Cases試驗

編號撞擊質量/kg跌落高度/m沖擊速度/

endprint

(m·s-1)初始動能/

(kN·m)19 7681.85.94172 307.529 7684.18.97392 478.2314 0284.59.39618 634.8圖1試驗安裝

Fig.1Test Installation圖2試驗的結構布置

Fig.2Structural Arrangements of Tests量檢查和鋼板的靜態拉伸試驗等。

試驗中，對沖擊過程中主動撞擊錘的加速度和被撞鋼箱上選取點的應變響應進行測量，對沖擊結束后被撞鋼箱上一些選取的點進行人工位移測量，使用高速攝影設備對沖擊過程中被撞鋼箱的變形情況進行輔助性的記錄。測量系統見圖3。

圖3測量系統

Fig.3Measurement System2數值計算方法

在大量分析和比較的基礎上，本文中使用如下的計算參數：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屬性；采用CowperSymonds公式［9］［（σYd/σY=1+(ε/C)q，其中，σYd為材料動態失效應變，σY為材料靜態失效應變，ε為應變率，C，q均為材料常數］來考慮應變率的影響，并結合粘塑性公式來減少考慮應變率時的響應噪聲，本試驗中被撞鋼箱為Q235軟鋼，C=40.4，q=1/5；采用材料的實際應力應變關系；鋼材的失效模式采用最大有效塑性應變失效模式，失效模式表述為εpeff≥εfailure，即當有限元模型中單元的應變超過設定值時，單元失效，失效后的單元從模型中刪除。3數值計算結果符合度檢驗方法

由于沖頭相對于被撞鋼箱來說剛度極大，因此在試驗中，沖頭可以近似地視為剛體，故在得到沖頭的加速度時程后，可以根據牛頓第二定律得到碰撞過程中的碰撞力時程。

在進行船舶碰撞的有限元仿真分析時，主要關注以下2個方面的結果：①船舶與橋梁或防撞結構之間的撞擊力特征，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。

為了討論不同網格尺寸對應的最佳失效應變取值，本文中定義描述試驗加速度結果與數值仿真結果之間差別的2個指標或準則：①計算值與測量值之間的相關系數，采用Pearson相關系數r；②峰值加速度計算值與測量值之間的相對誤差e。r，e的計算方法分別為

r=XY-XYN/

(X2-(X)2N)(Y2-(Y)2N)(1)

e=amax-a′maxamax(2)

式中：X，Y為2個數值序列；amax為最大加速度測量值； a′max為最大加速度計算值。

3次試驗測量得到的加速度試驗結果見圖4，其中，g為重力加速度。試驗結果表明，開始段均具有明顯的周期約為0.003 8 s的波動段，且該波動段在第1次試驗中響應最大，在第3次試驗中響應最小，

圖4加速度試驗結果及其修正

Fig.4Acceleration Test Results and Amendment初步判定該響應與試驗場地地基有關［10］。本文中采用HilbertHuang［1112］原理修正了第1次和第2次試驗的波動段加速度試驗結果。4網格剖分與失效應變的關系

考慮被撞鋼箱上的殼單元邊長為2 cm的情形，將單元的失效應變μ分別取為0.12，0.15，0.20，0.25，0.30，研究單元失效應變對加速度數值模擬結果的影響，結果見圖5。

圖5失效應變對加速度計算結果的影響

Fig.5Effects of Failure Strain on Acceleration

Computational Results由圖5可以看出，失效應變取值不同，得到的計算結果差別很大，這說明失效應變的合理取值對船橋碰撞數值模擬計算結果的合理性和可靠性是十分重要的。

本文中對被撞鋼箱劃分了7種網格尺寸，網格單元邊長l分別為0.5，1，1.4，2，2.5，3，5 cm，并采用多種失效應變（最小失效應變0.05，最大失效應變0.6）來研究失效應變和網格尺寸的關系。相關系數與加速度峰值相對誤差的計算結果見圖6，7。

圖6相關系數計算結果

Fig.6Computational Results of Correlation Coefficient從圖6，7可以看出：

（1）失效應變取值為0.05時（很小時），不同網格尺寸下的計算結果均與試驗結果差別很大，總體上來說，加速度計算結果與試驗結果之間的相關系數較小，且可能出現非常大的峰值加速度，這說明失效應變取值過小不能合理預測鋼箱發生塑性損傷時的沖擊反應。

（2）隨著失效應變的增大，大尺寸網格可以率先計算得到較好的結果，隨著失效應變繼續增加，小尺寸的網格依次得到精度較好的計算結果。

（3）存在一個失效應變的取值區間［εLf，εUf］，εLf為區間的下界，εUf為區間的上界，當失效應變在此區間取值時可獲得較高精度的計算結果。這個取值區間的范圍隨網格尺寸變化：網格尺寸大，失效應變取值區間寬度??；反之，網格尺寸小，則失效應變區間寬度大。

（4）當網格尺寸足夠小時，對于本試驗，網格尺寸不宜大于1 cm，失效應變取0.35~0.50是合理的，但是同時也可以看出，合理的失效應變取值與鋼箱遭受的沖擊破壞程度可能有關。

圖8為最優失效應變范圍。從圖8可以看出，對于同一網格的不同失效應變情形，相關系數總是先增大再減小。據此定義［εLf，εUf］為合理取值區間。合理取值區間的下界εLf和上界εUf根據相關系數r＞0.9的條件確定。圖8中綜合了3次試驗的加速度結果，得到了適用于3次試驗的失效應變合理取值區間的下界和上界。圖8中顯示合理區間的下界和上界均隨著網格尺寸的增大而逐步變小，上界變化相對較快，區間范圍隨網格尺寸的增大而變小。

從圖8還可以看出，如果采用大網格模型進行分析，則必須謹慎地定義失效應變；如果采用小網格模型進行分析，則可以適當地將失效應變取得大一點，以計算結果逐步穩定時為宜。

有限元仿真模擬的另一項重要內容是對結構的變形模式或破壞形式進行捕捉。圖9中給出了第3次試驗中被撞鋼箱背面鋼板出現的褶皺和0.5 cm以及5 cm網格計算對該褶皺捕捉情況的對比。由此可見，0.5 cm網格對該褶皺的描述非常好，且結構變形光滑平順，而5 cm網格則完全沒有表現出該處出現的褶皺。這表明當需要研究結構的變形模式或破壞模式時，應該劃分尺寸較小的網格。5結語

(1)網格尺寸與失效應變是相關的，即單元的失效應變依賴于網格的尺寸，使用大尺寸網格時應采用較小的失效應變，且失效應變的定義較為敏感；使用小尺寸網格時應采用較大的失效應變，且失效應變的定義不敏感，因此，根據相關系數定義了合理失效應變區間。網格大則合理失效應變取值區間小，網格小則合理失效應變取值區間大。

(2)為保證計算結果的精度，建議計算時可逐步細化模型中網格的尺寸并對失效應變的取值進行較大幅度的變化，當失效應變的取值在較大范圍內變圖7加速度峰值相對誤差計算結果

Fig.7Computational Results of Relative Error of Peak Acceleration圖8最優失效應變范圍

Fig.8Optimum Failure Strain Interval化而對計算結果的影響較小時，可以認為已經獲得了較好的計算模型。

(3)采用自適應網格剖分并結合最優失效應變區間概念進行計算分析，可以在獲得同等計算精度的同時節省大量的建模時間和計算分析時間。

endprint

（4）需要注意的是，本文中的結論是在縮尺模型試驗中獲得的，其適用性還有待在足尺試驗或實際船橋碰撞事故中得到進一步驗證。圖9試驗與計算褶皺的對比

Fig.9Comparisons of Folds Between Test and Computational Results參考文獻：

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［6］ZHOU X H,WANG S J.Stability Theory and Its Applications of Thinwalled 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，本文中的結論是在縮尺模型試驗中獲得的，其適用性還有待在足尺試驗或實際船橋碰撞事故中得到進一步驗證。圖9試驗與計算褶皺的對比

Fig.9Comparisons of Folds Between Test and Computational Results參考文獻：

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):429441.

［2］KITAMURA O.FEM Approach to the Simulation of Collision and Grounding Damage［J］.Marine Structures,2002,15(4/5):403428.

［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,2003:71107.

［4］SERVIS D,SAMUELIDES M,LOUKA T,et al.The Implementation of Finite Element Codes for the Simulation of Shipship Collision［J］.Journal of Ship Research,2002,46(4):239247.

［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):443460.

［6］PEDERSEN P T.Ship Impacts:Bow Collisions［J］.International Journal of Impact Engineerin,1993,13(2):163187.

［7］高震，顧永寧，胡志強.結構沖擊試驗的校準計算［J］.船舶力學，2005,9(2):7782.

GAO Zhen,GU Yongning,HU Zhiqiang.Benchmark Study of Structural Impact Test［J］.Journal of Ship Mechanincs,2005,9(2):7782.

［8］李軍.沖擊數值模擬可靠性的試驗檢驗［D］.上海：同濟大學，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，東南大學，浙江大學，等.地基與基礎［M］.2版.北京：中國建筑工業出版社，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):23172345.

［12］HUANG N E,SHEN Z,LONG S R,et al.The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and Nonstationary Time Series Analysis［J］.Proceedings of the Royal Society A,1998,454(1971):903995.（上接第15頁）

associated with CSA S13607 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 widthtothickness ratio. For typical Csection wall studs investigated herein, the difference on the nominal axial strength is primarily influenced by the flange widthtothickness ratio wf/t. If the flange widthtothickness 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 S13607, 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 S13607, with the maximum difference being 8.9%.References:［1］CSA S13607,North American Specification for the Design of Coldformed Steel Structural Members［S］.

［2］GB 50018—2002,Technical Code of Coldformed Thinwall Steel Structures［S］.

［3］JGJ 227—2011,Technical Specification for Lowrise Coldformed Thinwall 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.Coldformed Steel Design［M］.New York:John Wiley & Sons,2010.

［6］ZHOU X H,WANG S J.Stability Theory and Its Applications of Thinwalled 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，本文中的結論是在縮尺模型試驗中獲得的，其適用性還有待在足尺試驗或實際船橋碰撞事故中得到進一步驗證。圖9試驗與計算褶皺的對比

Fig.9Comparisons of Folds Between Test and Computational Results參考文獻：

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):429441.

［2］KITAMURA O.FEM Approach to the Simulation of Collision and Grounding Damage［J］.Marine Structures,2002,15(4/5):403428.

［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,2003:71107.

［4］SERVIS D,SAMUELIDES M,LOUKA T,et al.The Implementation of Finite Element Codes for the Simulation of Shipship Collision［J］.Journal of Ship Research,2002,46(4):239247.

［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):443460.

［6］PEDERSEN P T.Ship Impacts:Bow Collisions［J］.International Journal of Impact Engineerin,1993,13(2):163187.

［7］高震，顧永寧，胡志強.結構沖擊試驗的校準計算［J］.船舶力學，2005,9(2):7782.

GAO Zhen,GU Yongning,HU Zhiqiang.Benchmark Study of Structural Impact Test［J］.Journal of Ship Mechanincs,2005,9(2):7782.

［8］李軍.沖擊數值模擬可靠性的試驗檢驗［D］.上海：同濟大學，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，東南大學，浙江大學，等.地基與基礎［M］.2版.北京：中國建筑工業出版社，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):23172345.

［12］HUANG N E,SHEN Z,LONG S R,et al.The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and Nonstationary Time Series Analysis［J］.Proceedings of the Royal Society A,1998,454(1971):903995.（上接第15頁）

associated with CSA S13607 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 widthtothickness ratio. For typical Csection wall studs investigated herein, the difference on the nominal axial strength is primarily influenced by the flange widthtothickness ratio wf/t. If the flange widthtothickness 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 S13607, 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 S13607, with the maximum difference being 8.9%.References:［1］CSA S13607,North American Specification for the Design of Coldformed Steel Structural Members［S］.

［2］GB 50018—2002,Technical Code of Coldformed Thinwall Steel Structures［S］.

［3］JGJ 227—2011,Technical Specification for Lowrise Coldformed Thinwall 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.Coldformed Steel Design［M］.New York:John Wiley & Sons,2010.

［6］ZHOU X H,WANG S J.Stability Theory and Its Applications of Thinwalled 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