Abaqus梁的開裂模擬計算報告問題描述利用ABAQUS有限元軟件分析如圖1.1所示的鋼筋混凝土梁的裂縫開展。參考文獻Brenaetal.（2003）得到梁的基本數據：圖1.1Brenaetal.（2003）中梁C尺寸幾何尺寸：跨度3000mm，截面寬203mm，高406mm的鋼筋混凝土梁由文獻Chenetal.2011得材料特性：混凝土：抗壓強度fc’=35.1MPa，抗拉強度ft=2.721MPa，泊松比ν=0.2，彈性模量Ec=28020MPa；鋼筋：彈性模量為Ec=200GPa，屈服強度fys=fyc=440MPa，fyv=596MPa混凝土墊塊：彈性模量為Ec=28020MPa，泊松比ν=0.2建模過程Part打開ABAQUS使用功能模塊，彈出窗口CreatePart，參數為：Name：beam；ModelingSpace：2D；Type：Deformable；BaseFeature─Shell；Approximatesize：2000。點擊Continue進入Sketch二維繪圖區。由于該梁關于Y軸對稱，建模的時候取沿X軸的一半作為模擬對象。使用功能模塊，分別鍵入獨立點(0,0),(1600,0),(1600,406),(406,0),(0,0)并按下下方提示區的Done，完成草圖。圖2.1beam部件二維幾何模型相同的方法建立混凝土墊塊：圖2.2plate部件二維幾何模型所選用的點有(0,0),(40,0),(40,10),(0,10)受壓區鋼筋：在選擇鋼筋的basefeature的時候選擇wire，即線模型。圖2.3compressionbar部件二維幾何模型選取的點(0,0),(1575,0)受拉區鋼筋：圖2.4tensionbar部件二維幾何模型選取的點(0,0),(1575,0)箍筋：圖2.5stirrup部件二維幾何模型選取的點為(0,0),(0,330)另外，此文里面為了作對比，部分的模型輸入尺寸的時候為m，下面無特別說明尺寸都為mm。PropertyModule中選擇property，然后選擇功能模塊對不同的材料進行賦值，下面是各種材料輸入時候的數據：混凝土本構關系：模型一：（該模型的尺寸單位為m）在彈出的對話框中命名為beam，在Mechanical選項中點擊Elastic，在Young’sModulus中輸入28020000000，Poisson’sRatio為0.2；類似的方法找到ConcreteDamagedPlasticity，按混凝土結構設計規范對受壓取點8個，受拉取點7個。下面是計算過程：由規范中附錄C中C2混凝土本構關系：混凝土單軸受拉的應力-應變曲線公式：，所用參數可以參考規范（混凝土結構設計規范GB50010-2010）混凝土單軸受壓的應力-應變曲線公式：，所用參數可以參考規范以及塑性應變與總應變的關系：，其中以及塑性應變與總應變的關系：，與上式相同借助matlab軟件計算受壓、拉時的本構關系方程，其中塑性應變分別取0、0.0005、0.001、0.002、0.003、0.004、0.005、0.008得對應應力為23171225.88、35072364.4、32320980.31、24236963.88、17763125.96、13340141.18、10334750.06、5892086.123；開裂應變分別取0、0.001、0.003、0.005、0.008、0.01、0.05得對應應力2721000、2648625.968、875761.085、511922.937、334706.391、50489.31、16333.482。由于水平限制，算得的受拉損傷因子未能通過abaqus的算前檢測，這里沒有輸入。模型二：（該模型單元尺寸為m）Elastic中的設置與模型一相同，計算其本構關系的時候按照文獻Finite-ElementModelingofIntermediateCrackDebondinginFRP-PlatedRCBeams，G.M.Chen中的公式：單軸受壓：，所用參數可見于引用的文獻；受壓的時候為了尋找輸入塑性應變的起始點，令abaqus中提供的應力--應變輸入方式的名義值與真實值關系公式為0，有：解之得：22.76652048MPa，0.00081284，0。從點0.00081284開始以步長0.0002得到83個點。在輸入到abaqus前使用公式進行轉換，輸入的具體值可見附錄。單軸受拉：，所用參數可見于引用文獻；由于hc為裂縫帶寬（上面提到的文獻中也命名為平面四節點單元的特征裂縫長度），取，其中e為單元網格長度，這里取10mm，即hc為14mm。在清華江見鯨或者J.G.ROTS撰寫的文獻中都能找到其他單元類型的hc與e的換算公式，這里提到的hc也可稱為Lcr，這提供了把本文中的開裂位移轉化為開裂應變的方法：對wt進行離散是采用前密后疏的方法，一開始的10個點步長為0.00012，中間,28個點步長為0.0012，最后13個點步長為0.006，加上零點一共53個點。把位移轉換成應變以后，同樣地，使用名義值--真實值的轉換公式得到數據，具體數值可見于附錄。由于水平問題，算得的受拉損傷因子未能通過abaqus的算前檢測，這里沒有輸入。模型三：該模型使用的尺寸單位為mm，受壓時的取值只需在模型二的取值基礎上進行單位換算即可。本構關系的輸入方式為應力--位移的方法，在輸入類型中選擇Displacement單軸受拉：對wt進行離散，取等步長0.0012，共51個點。這里還進行了受拉損傷因子dt的計算，按公式：，具體數據可見附錄。鋼筋本構關系：類似的，把鋼筋的楊氏模量輸入到Elastic中，三個模型的受拉受壓鋼筋都是200GPa，在Plastic中按照名義值--真實值得方法，取得兩個點：屈服強度440MPa，塑性應變為0；屈服強度448.8MPa，塑性應變為0.02。箍筋的屈服強度取596MPa，塑性應變為0。墊塊的本構關系：這里墊塊的本構可以按混凝土的本構輸入，也可以按鋼筋的輸入，為了方便計算取鋼筋的本構關系作為其材料屬性。建立完本構關系后需對混凝土等截面屬性進行賦值，點擊，彈出CreateSection對話框，將Category設為solid，Type設為Homogeneous，其余參數保持默認，點擊Continue，material為beam，thickness為203mm，墊塊也是類似的輸入方式；對于鋼筋，Category設為beam，Type設為truss，如受拉鋼筋，由文獻得直徑為16mm，面積為200.96（mm2），由于同一水平面上有兩根，取值402；受壓鋼筋和箍筋分別按直徑9.5mm和7mm計算。然后再同一個環境欄中使用，提示區要求用戶選擇賦予截面的部件，分別對上述創建過的部件賦予材料屬性，完成操作。Assembly進入Assembly模塊，如圖2.6裝配完畢的模型所示進行裝配。圖2.6裝配完畢的模型墊塊的位置和鋼筋的布置嚴格按照文獻Finite-ElementModelingofIntermediateCrackDebondinginFRP-PlatedRCBeams，G.M.Chen進行。為了后期布置網格時候的方便，使用對所有鋼筋進行組合，然后對組合后的鋼筋在模型樹中的instance進行操作‘makeindependent’。Step在環境欄的Module列表中進入Step模塊。點擊如下圖進行設置：圖2.7Step-1的Basic選項圖2.8Step-1的Incrementation選項圖中，Minimum不需要設置很小，Maximumnumberofincrements也不需要設置很大，當模型真的不收斂的時候這兩項的影響比較小，Maximun的設置回影響到Job中計算時的總增量步數目。Interaction圖2.9約束管理器圖2.10加載點coupling約束圖2.11鋼筋與混凝土的embededregion約束圖2.12墊塊與混凝土梁的tie約束按照上述圖示的對象設置相關約束，完畢后結束該操作。Load如下圖所示，在環境欄的Module列表中選擇Load模塊，進行荷載與邊界條件的定義。定義邊界條件點擊，彈出對話框createboundarycondition，step選擇initial，category選擇mechanical，typesforselectedstep選擇symmetry/antisymmetry/encastre，點擊continue，選擇對稱軸，邊界類型選擇XSYMM（鎖定轉角是因為對稱的位置需要承受彎矩）。對于墊塊上的邊界條件，step選擇initial，category選擇mechanical，typesforselectedstep選擇displacement/rotation，點擊continue，然后選擇左下角墊塊下部的最左邊角點（這里選擇下部的邊上一點就可以，具體的位置對模擬影響不大）上約束類型限制U2。圖2.13梁的約束示意圖施加荷載這里采用的是位移加載法，設置見圖2.14。圖2.14位移和在的施加上圖中，U2是施加在Y軸方向上的位移，負號指向向下，模型一為-0.02（單位為米）、模型二為-0.02（單位為米）、模型三為-3（單位為毫米）Mesh首先使用工具對鋼筋單元默認的beam單元更改為truss單元。然后使用對整個模型進行撒種，撒種之前可以使用控制網格類型。撒種以后點擊對整個模型進行網格劃分，效果如下：圖2.15網格單元30mm×30mm效果圖（模型一）圖2.16網格單元10mm×10mm效果圖（模型二、模型三）計算結果Job在環境欄的Module列表中選擇Job功能模塊進行作業提交創建分析作業點擊工具，彈出createjob對話框，source分別選擇模型Model-1（模型一）、Model-lcr（模型二）、Model-mm（模型三），建立的JobName，對應為num-1、11-19、11-16costom，完成作業生成。提交分析點擊工具（JobManager），分別對三個模型submit，可以再status中看到經歷的submitted--running--completed的過程。Visualization在住菜單JobManager，中點擊Results，如下圖方法查看裂縫效果圖：該界面下編號①中可更改為LE（對數應變）；②進入云圖顯示，旁邊的管理器可以對輸入的云圖參數進行設置；③則為具體輸出的模擬結果曲線圖等的操作工具。分析：從圖3.2中可見網格較大的時候，裂縫也顯示得比較大，選取的點數較少，也可能是導致裂縫出現的數目比較少的原因；模型二在加載處左端的裂縫都基本能沿450發展，中軸到加載點之間的水平空間，裂縫呈豎直，很好的反應了該位置不受剪力，只是受到彎矩導致裂縫開裂的效果；模型三位移荷載只能加載到3mm，裂縫出現，但并不明顯，可見于圖3.4，圖3.5在元模型的基礎上修改粘結系數為0.0005（原為0），裂縫出現，但裂縫開展與理論有差距，從圖上看可發現和模型二的差別很大，零剪力區裂縫歪曲發展，加載處左端圖3.1visualization模塊使用了的工具位置示意圖圖3.2模型一的裂縫模擬圖圖3.3模型二的裂縫模擬圖圖3.4模型三不帶粘性系數的裂縫模擬圖圖3.5模型三粘結系數為0.0005的裂縫模擬圖裂縫分布不規則，這是由于所輸入粘結系數后對損傷值的影響而不能真實模擬開裂，其使用在以后的模擬中有待研究。荷載--位移曲線在圖3.1所示的編號③的位置點擊該工具，彈出對話框CreateXYData，選擇ODBfieldoutput，點擊continue，然后position選擇uniquenodal，選中RF與U作為場輸出變量，selection選項中拾取參考點，選中以后點擊plot，此后出現以時間為變量的荷載--位移曲線；再次點擊編號③的位置的工具，彈出對話框CreateXYData，選擇operateonxydata，點擊continue，使用combine操作對輸出的數據進行重新布置，下方xydata欄中有剛才輸出的數據，雙擊的一個數據會成為x軸上的數據，第二個則為y軸上的數據，結束后點擊plotexpression，這一步更好的做法是在模型樹中找到，把對應的數據復制到excel中進行表哥的繪制。下面是excel表示的曲線圖：受拉區混凝土應力--應變曲線類似上一小節的方法得到其曲線圖：受壓區混凝土應力--應變曲線類似上一小節的方法得到其曲線圖：受拉區鋼筋應力--應變曲線類似上一小節的方法得到其曲線圖：附錄模型二混凝土本構取值：*Material,name=beam*Elastic2.802e+10,0.2*ConcreteDamagedPlasticity35.,0.1,1.16,0.667,0.*ConcreteCompressionHardening2.27665e+07,0.2.70001e+07,4.87e-053.02955e+07,0.0001313.26542e+07,0.0002463.41623e+07,0.0003923.49521e+07,0.0005643.51697e+07,0.0007563.49536e+07,0.0009633.44232e+07,0.001183.36758e+07,0.001413.27869e+07,0.001643.18134e+07,0.001873.0797e+07,0.002112.97674e+07,0.002342.87453e+07,0.002582.77447e+07,0.002822.67749e+07,0.003052.58415e+07,0.003282.49476e+07,0.003512.40945e+07,0.003742.32824e+07,0.003972.25106e+07,0.00422.17779e+07,0.004422.10827e+07,0.004652.04233e+07,0.004871.97978e+07,0.005091.92044e+07,0.005311.86412e+07,0.005531.81065e+07,0.005751.75984e+07,0.005961.71153e+07,0.006181.66558e+07,0.006391.62183e+07,0.006611.58014e+07,0.006821.5404e+07,0.007031.50247e+07,0.007251.46626e+07,0.007461.43165e+07,0.007671.39854e+07,0.007881.36686e+07,0.008091.33652e+07,0.00831.30743e+07,0.008511.27953e+07,0.008711.25275e+07,0.008921.22702e+07,0.009131.2023e+07,0.009341.17852e+07,0.009541.15563e+07,0.009751.13359e+07,0.009951.11235e+07,0.01021.09187e+07,0.01041.07212e+07,0.01061.05305e+07,0.01081.03463e+07,0.0111.01683e+07,0.01129.99628e+06,0.01149.82985e+06,0.01169.66877e+06,0.01189.51282e+06,0.0129.36174e+06,0.01229.21532e+06,0.01249.07336e+06,0.01268.93565e+06,0.01288.80203e+06,0.0138.6723e+06,0.01328.5463e+06,0.01348.42389e+06,0.01368.30491e+06,0.01388.18923e+06,0.0148.0767e+06,0.01427.96721e+06,0.01447.86064e+06,0.01467.75687e+06,0.01487.6558e+06,0.0157.55732e+06,0.01527.46134e+06,0.01547.36777e+06,0.01567.27651e+06,0.01587.18748e+06,0.0167.10061e+06,0.01627.01582e+06,0.01646.93303e+06,0.01666.85218e+06,0.0168*ConcreteTensionStiffening2.72126e+06,0.2.7069e+06,8.55431e-062.69288e+06,1.71134e-052.67893e+06,2.56725e-052.66504e+06,3.42317e-052.65124e+06,4.2791e-052.6375e+06,5.13503e-052.62384e+06,5.99096e-052.61024e+06,6.8469e-052.59672e+06,7.70285e-052.58327e+06,8.5588e-052.45263e+06,0.0001711862.32886e+06,0.0002567872.21176e+06,0.0003423912.10108e+06,0.0004279981.99659e+06,0.0005136051.89805e+06,0.0005992131.80521e+06,0.0006848211.71782e+06,0.0007704281.63563e+06,0.0008560321.5584e+06,0.0009416351.48589e+06,0.001027241.41785e+06,0.001112831.35405e+06,0.001198421.29426e+06,0.001284011.23826e+06,0.00136961.18584e+06,0.001455181.13679e+06,0.001540751.09091e+06,0.001626321.04799e+06,0.001711881.00787e+06,0.00179743970351.,0.00188298935276.,0.00196853902480.,0.00205406871807.,0.00213959843113.,0.00222512816256.,0.00231063791107.,0.00239614767539.,0.00248164669549.,0.00290904596170.,0.00333626538552.,0.0037633490607.,0.00419016448335.,0.00461685409265.,0.00504336371992.,0.00546971335828.,0.00589588300538.,0.00632189266152.,0.00674773232837.,0.00717339200804.,0.00759888170262.,0.0080242模型三混凝土本構取值：*Material,name=beam*Elastic28020.,0.2*ConcreteDamagedPlasticity35.,0.1,1.16,0.667,0.*ConcreteCompressionHardening22.7665,0.27.0001,4.87e-0530.2955,0.00013132.6542,0.00024634.1623,0.00039235.,0.00056435.2,0.00075634.9536,0.00096334.4232,0.0011833.6758,0.0014132.7869,0.0016431.8134,0.0018730.797,0.0021129.7674,0.0023428.7453,0.0025827.7447,0.0028226.7749,0.0030525.8415,0.0032824.9476,0.0035124.0945,0.0037423.2824,0.0039722.5106,0.004221.7779,0.0044221.0827,0.0046520.4233,0.0048719.7978,0.0050919.2044,0.0053118.6412,0.0055318.1065,0.0057517.5984,0.0059617.1153,0.0061816.6558,0.0063916.2183,0.0066115.8014,0.0068215.404,0.0070315.0247,0.0072514.6626,0.0074614.3165,0.0076713.9854,0.0078813.6686,0.0080913.3652,0.008313.0743,0.0085112.7953,0.0087112.5275,0.0089212.2702,0.0091312.023,0.0093411.7852,0.0095411.5563,0.0097511.3359,0.0099511.1235,0.010210.9187,0.010410.7212,0.010610.5305,0.010810.3463,0.01110.1683,0.01129.99628,0.01149.82985,0.01169.66877,0.01189.51282,0.0129.36174,0.01229.21532,0.01249.07336,0.01268.93565,0.01288.80203,0.0138.6723,0.01328.5463,0.01348.42389,0.01368.30491,0.01388.18923,0.0148.0767,0.01427.96721,0.01447.86064,0.01467.75687,0.01487.6558,0.0157.55732,0.01527.46134,0.01547.36777,0.01567.27651,0.01587.18748,0.0167.10061,0.01627.01582,0.01646.93303,0.01666.85218,0.0168*ConcreteTensionStiffening,type=DISPLACEMENT2.721,0.2.58017,0.00122.44675,0.00242.32051,0.00362.20119,0.00482.08855,0.0061.98232,0.00721.88224,0.00841.78805,0.00961.69947,0.01081.61624,0.0121.5381,0.01321.46479,0.01441.39607,0.01561.33168,0.01681.27138,0.0181.21494,0.01921.16214,0.02041.11276,0.02161.06659,0.02281.02343,0.0240.983093,0.02520.945393,0.02640.910156,0.02760.877216,0.02880.846415,0.030.817603,0.03120.79064,0.03240.76539,0.03360.741727,0.03480.719533,0.0360.698696,0.03720.679109,0.03840.660676