彈性力學(xué)仿真軟件：ADINA：非線性靜力分析進(jìn)階

彈性力學(xué)仿真軟件：ADINA：非線性靜力分析進(jìn)階1軟件介紹與安裝1.1ADINA軟件概述ADINA(AutomaticDynamicIncrementalNonlinearAnalysis)是一款由美國(guó)ADINAR&DInc.開發(fā)的高級(jí)有限元分析軟件，廣泛應(yīng)用于結(jié)構(gòu)、流體、熱力學(xué)和多物理場(chǎng)耦合分析。其非線性靜力分析功能特別強(qiáng)大，能夠處理復(fù)雜的材料非線性、幾何非線性以及接觸問題，是工程設(shè)計(jì)和研究中不可或缺的工具。1.2ADINA安裝與配置1.2.1系統(tǒng)要求操作系統(tǒng):Windows10/11,Linux處理器:多核處理器內(nèi)存:至少16GBRAM硬盤空間:至少10GB可用空間1.2.2安裝步驟下載軟件:從ADINA官方網(wǎng)站下載最新版本的安裝包。解壓:使用解壓軟件打開下載的安裝包。運(yùn)行安裝程序:找到并運(yùn)行安裝程序，通常為ADINA_Installer.exe。許可設(shè)置:輸入ADINA許可信息，通常包括許可服務(wù)器的IP地址和端口號(hào)。選擇組件:選擇需要安裝的組件，如ADINA結(jié)構(gòu)分析、流體分析等。安裝路徑:選擇軟件的安裝路徑。完成安裝:按照安裝向?qū)瓿砂惭b過程。1.2.3配置許可許可服務(wù)器:確保許可服務(wù)器已正確配置并運(yùn)行。環(huán)境變量:在系統(tǒng)中設(shè)置ADINA的環(huán)境變量，指向許可文件或服務(wù)器。測(cè)試連接:使用ADINA提供的許可測(cè)試工具檢查與許可服務(wù)器的連接。1.3用戶界面與基本操作1.3.1用戶界面ADINA的用戶界面直觀且功能豐富，主要分為以下幾個(gè)部分：-菜單欄:提供軟件的主要功能選項(xiàng)。-工具欄:快速訪問常用工具。-模型樹:顯示當(dāng)前模型的結(jié)構(gòu)和組件。-圖形窗口:顯示和操作模型的3D視圖。-狀態(tài)欄:顯示當(dāng)前操作狀態(tài)和提示信息。1.3.2基本操作1.3.2.1創(chuàng)建新模型啟動(dòng)ADINA:雙擊桌面圖標(biāo)或從開始菜單啟動(dòng)。選擇新模型:在菜單欄中選擇File>New。定義模型類型:選擇結(jié)構(gòu)分析、流體分析或耦合分析。1.3.2.2導(dǎo)入幾何模型選擇導(dǎo)入:在菜單欄中選擇File>Import。支持格式:ADINA支持多種格式，如IGES、STEP、STL等。導(dǎo)入模型:選擇幾何模型文件并導(dǎo)入。1.3.2.3材料屬性設(shè)置選擇材料:在模型樹中選擇需要設(shè)置材料的實(shí)體。定義材料屬性:在屬性面板中輸入材料的彈性模量、泊松比等參數(shù)。應(yīng)用材料:點(diǎn)擊應(yīng)用按鈕，將材料屬性應(yīng)用到所選實(shí)體。1.3.2.4網(wǎng)格劃分選擇網(wǎng)格類型:在菜單欄中選擇Mesh>MeshType。設(shè)置網(wǎng)格參數(shù):調(diào)整網(wǎng)格大小、精度等參數(shù)。生成網(wǎng)格:點(diǎn)擊Mesh>Generate生成網(wǎng)格。1.3.2.5邊界條件與載荷設(shè)置邊界條件:在模型樹中選擇實(shí)體，然后在菜單欄中選擇BoundaryConditions。應(yīng)用載荷:選擇實(shí)體，然后在菜單欄中選擇Loads，輸入載荷值。1.3.2.6運(yùn)行分析選擇分析類型:在菜單欄中選擇Analysis>NonlinearStatic。設(shè)置分析參數(shù):調(diào)整分析的步數(shù)、收斂準(zhǔn)則等。運(yùn)行分析:點(diǎn)擊Analysis>Run開始分析。1.3.2.7查看結(jié)果結(jié)果可視化:在菜單欄中選擇Results>Visualize。分析報(bào)告:選擇Results>Report生成分析報(bào)告。1.3.3示例：創(chuàng)建一個(gè)簡(jiǎn)單的梁模型并進(jìn)行非線性靜力分析1.3.3.1步驟1:創(chuàng)建新模型啟動(dòng)ADINA，選擇結(jié)構(gòu)分析。1.3.3.2步驟2:定義幾何使用內(nèi)置的幾何工具創(chuàng)建一個(gè)矩形梁。1.3.3.3步驟3:設(shè)置材料屬性選擇梁實(shí)體，定義材料為鋼，彈性模量200GPa，泊松比0.3。1.3.3.4步驟4:網(wǎng)格劃分選擇`Mesh`>`MeshType`，設(shè)置為四面體網(wǎng)格，然后生成網(wǎng)格。1.3.3.5步驟5:應(yīng)用邊界條件與載荷在梁的一端設(shè)置固定邊界條件，在另一端應(yīng)用垂直向下的載荷。1.3.3.6步驟6:運(yùn)行非線性靜力分析選擇`Analysis`>`NonlinearStatic`，設(shè)置分析步數(shù)為10，然后運(yùn)行分析。1.3.3.7步驟7:查看結(jié)果在`Results`>`Visualize`中查看梁的變形和應(yīng)力分布。通過以上步驟，用戶可以完成一個(gè)簡(jiǎn)單的梁模型的非線性靜力分析，理解ADINA的基本操作流程。2非線性靜力分析基礎(chǔ)2.1非線性力學(xué)概念在工程分析中，線性力學(xué)假設(shè)材料的應(yīng)力與應(yīng)變之間存在線性關(guān)系，且結(jié)構(gòu)的變形不會(huì)顯著影響其剛度。然而，在許多實(shí)際應(yīng)用中，這些假設(shè)可能不成立，導(dǎo)致需要進(jìn)行非線性分析。非線性力學(xué)涉及結(jié)構(gòu)響應(yīng)的復(fù)雜性，包括材料非線性、幾何非線性和邊界條件非線性。2.1.1材料非線性材料非線性指的是材料的應(yīng)力-應(yīng)變關(guān)系不再遵循線性比例。例如，金屬在塑性變形階段、混凝土在受壓時(shí)、橡膠在大變形時(shí)，都會(huì)表現(xiàn)出非線性特性。2.1.2幾何非線性幾何非線性考慮了結(jié)構(gòu)變形對(duì)分析結(jié)果的影響。當(dāng)結(jié)構(gòu)的變形足夠大，以至于不能忽略其對(duì)結(jié)構(gòu)剛度的影響時(shí)，就需要使用幾何非線性分析。這在大位移、大旋轉(zhuǎn)或接觸問題中尤為重要。2.2材料非線性介紹材料非線性分析在ADINA中通過定義材料屬性來實(shí)現(xiàn)。ADINA支持多種材料模型，包括彈性、塑性、粘彈性、超彈性等。2.2.1彈塑性材料模型彈塑性材料模型是ADINA中最常用的非線性材料模型之一。它描述了材料在彈性階段和塑性階段的行為。在彈性階段，應(yīng)力與應(yīng)變成正比；在塑性階段，材料繼續(xù)變形，但應(yīng)力可能保持不變或緩慢增加。2.2.1.1示例假設(shè)我們有一個(gè)簡(jiǎn)單的彈塑性材料模型，其彈性模量為200GPa，泊松比為0.3，屈服強(qiáng)度為250MPa。在ADINA中，可以使用以下輸入文件定義這種材料：MATERIAL1

TYPEELASTICPLASTIC

E200000

NU0.3

SIGY250

ENDMATERIAL2.3幾何非線性原理幾何非線性分析考慮了結(jié)構(gòu)變形對(duì)分析結(jié)果的影響。在ADINA中，當(dāng)結(jié)構(gòu)的位移或旋轉(zhuǎn)足夠大時(shí)，可以激活幾何非線性分析。這通常通過在分析設(shè)置中選擇適當(dāng)?shù)姆蔷€性選項(xiàng)來實(shí)現(xiàn)。2.3.1大位移和大旋轉(zhuǎn)大位移和大旋轉(zhuǎn)分析是幾何非線性分析的一部分，它考慮了結(jié)構(gòu)在大變形下的行為。在這些情況下，結(jié)構(gòu)的初始幾何和最終幾何之間的差異可能很大，不能簡(jiǎn)單地用小變形理論來描述。2.3.2接觸問題接觸分析是幾何非線性分析的另一個(gè)重要方面。當(dāng)兩個(gè)或多個(gè)物體接觸時(shí)，接觸面的變形和壓力分布可能非常復(fù)雜，需要使用非線性分析來準(zhǔn)確預(yù)測(cè)。2.3.2.1示例考慮一個(gè)簡(jiǎn)單的接觸問題，其中兩個(gè)物體在接觸面上相互作用。在ADINA中，可以使用以下輸入文件定義接觸條件：CONTACT

SURFACE1

TYPESLIDING

BODY1

SURFACE2

BODY2

ENDSURFACE

ENDCONTACT在這個(gè)例子中，SURFACE1和SURFACE2是接觸的兩個(gè)表面，BODY1和BODY2是與這些表面相關(guān)的物體。TYPESLIDING指定了接觸類型為滑動(dòng)接觸。2.4非線性靜力分析流程進(jìn)行非線性靜力分析時(shí)，通常遵循以下步驟：定義材料屬性：根據(jù)材料的非線性特性，選擇合適的材料模型并定義其參數(shù)。設(shè)置幾何非線性：如果結(jié)構(gòu)的變形足夠大，需要在分析設(shè)置中激活幾何非線性選項(xiàng)。定義接觸條件：對(duì)于涉及接觸的問題，需要定義接觸表面和接觸類型。施加載荷和邊界條件：根據(jù)問題的物理特性，施加適當(dāng)?shù)妮d荷和邊界條件。選擇求解器設(shè)置：非線性分析可能需要使用增量迭代求解器，以逐步逼近最終解。運(yùn)行分析：執(zhí)行非線性靜力分析，ADINA將計(jì)算結(jié)構(gòu)在非線性條件下的響應(yīng)。后處理和結(jié)果分析：分析結(jié)果，檢查應(yīng)力、應(yīng)變、位移等，確保分析的準(zhǔn)確性和合理性。通過以上步驟，可以使用ADINA進(jìn)行復(fù)雜的非線性靜力分析，為工程設(shè)計(jì)和優(yōu)化提供關(guān)鍵信息。3ADINA中的非線性靜力分析設(shè)置3.1定義非線性材料屬性在ADINA中進(jìn)行非線性靜力分析，首先需要定義材料的非線性屬性。非線性材料屬性可以包括塑性、蠕變、超彈性等特性。以塑性材料為例，我們可以通過定義材料的應(yīng)力-應(yīng)變關(guān)系來模擬材料在大應(yīng)力下的非線性行為。3.1.1示例：定義塑性材料假設(shè)我們正在分析一個(gè)結(jié)構(gòu)件，其材料為鋼，具有理想的彈塑性行為。在ADINA中，可以通過以下步驟定義這種材料：選擇材料類型：在材料屬性定義中選擇“塑性”。輸入彈性模量和泊松比：這是材料的線性彈性屬性。定義屈服強(qiáng)度：對(duì)于理想彈塑性材料，需要輸入材料的屈服強(qiáng)度。設(shè)置硬化類型：理想彈塑性材料通常假設(shè)為“理想硬化”或“完全硬化”。3.1.1.1數(shù)據(jù)樣例彈性模量：E泊松比：ν屈服強(qiáng)度：σ3.2設(shè)置幾何非線性條件幾何非線性分析考慮了結(jié)構(gòu)變形對(duì)分析結(jié)果的影響，尤其在大變形或大位移情況下。在ADINA中，幾何非線性可以通過選擇適當(dāng)?shù)姆治鲱愋蛠砑せ睢?.2.1激活幾何非線性在ADINA的分析設(shè)置中，選擇“非線性靜力分析”，并確保勾選“考慮幾何非線性”。3.3應(yīng)用非線性載荷與邊界條件非線性載荷與邊界條件的設(shè)置是確保分析準(zhǔn)確性的關(guān)鍵。在ADINA中，可以施加各種類型的載荷，包括力、壓力、溫度載荷等，并可以定義隨時(shí)間變化的載荷。3.3.1示例：應(yīng)用非線性載荷假設(shè)我們正在分析一個(gè)承受逐漸增加的力的結(jié)構(gòu)，可以按照以下步驟設(shè)置載荷：選擇載荷類型：在載荷定義中選擇“力”。定義載荷大小：輸入力的大小，例如F=設(shè)置載荷步：定義載荷隨時(shí)間的變化，例如，從0到1000N，分10步增加。3.3.1.1數(shù)據(jù)樣例初始力：F最終力：F載荷步數(shù)：N3.3.2示例代碼;ADINAScriptforNonlinearStaticAnalysis

;DefineMaterialProperties

MAT1

TYPEPLASTIC

E200e3

NU0.3

SIGY250

HARDENIDEAL

ENDMAT

;SetNonlinearGeometryOption

ANALYSISNONLINEAR

GEOMETRYNONLINEAR

;ApplyNonlinearLoad

LOAD1

TYPEFORCE

VALUE0

ENDLOAD

LOAD2

TYPEFORCE

VALUE1000

STEP10

ENDLOAD

;DefineBoundaryConditions

BC1

TYPEFIXED

NODES123

DOF123

ENDBC3.3.3代碼解釋MAT1：定義材料屬性，類型為塑性。E200e3：設(shè)置彈性模量為200GNU0.3：設(shè)置泊松比為0.3。SIGY250：定義屈服強(qiáng)度為250MHARDENIDEAL：設(shè)置硬化類型為理想硬化。ANALYSISNONLINEAR：選擇非線性靜力分析。GEOMETRYNONLINEAR：激活幾何非線性。LOAD1和LOAD2：定義載荷，從0N逐漸增加到1000N，共10步。BC1：定義邊界條件，固定節(jié)點(diǎn)1、2、3的所有自由度。通過以上步驟，我們可以在ADINA中設(shè)置一個(gè)非線性靜力分析，考慮材料的塑性行為、幾何非線性以及非線性載荷的影響。這將幫助我們更準(zhǔn)確地預(yù)測(cè)結(jié)構(gòu)在復(fù)雜載荷條件下的響應(yīng)。4非線性靜力分析案例研究4.1簡(jiǎn)單梁的非線性彎曲在非線性靜力分析中，簡(jiǎn)單梁的非線性彎曲是一個(gè)基礎(chǔ)但重要的案例。非線性行為可能由材料非線性、幾何非線性和接觸條件引起。對(duì)于簡(jiǎn)單梁，我們主要關(guān)注材料非線性和幾何非線性。4.1.1材料非線性材料非線性通常指材料的應(yīng)力-應(yīng)變關(guān)系不再遵循線性關(guān)系。例如，鋼材在超過屈服點(diǎn)后，其應(yīng)力-應(yīng)變曲線會(huì)表現(xiàn)出明顯的非線性特征。在ADINA中，可以通過定義材料屬性來模擬這種非線性行為。4.1.2幾何非線性幾何非線性發(fā)生在結(jié)構(gòu)的變形足夠大，以至于不能忽略變形對(duì)結(jié)構(gòu)剛度的影響。在簡(jiǎn)單梁的彎曲中，當(dāng)梁的撓度較大時(shí)，梁的中性軸會(huì)發(fā)生偏移，這將影響梁的剛度，從而導(dǎo)致非線性響應(yīng)。4.1.3案例描述假設(shè)我們有一根長(zhǎng)度為10米的簡(jiǎn)單梁，兩端固定，中間受到垂直向下的集中力作用。梁的截面為矩形，寬度為0.2米，高度為0.1米。材料為鋼材，彈性模量為200GPa，泊松比為0.3，屈服強(qiáng)度為250MPa。我們將使用ADINA進(jìn)行非線性靜力分析，以研究梁的非線性彎曲行為。4.1.4ADINA操作步驟建立模型：在ADINA中創(chuàng)建梁的幾何模型，定義材料屬性和邊界條件。網(wǎng)格劃分：對(duì)梁進(jìn)行網(wǎng)格劃分，確保網(wǎng)格足夠細(xì)以捕捉非線性行為。加載：在梁的中間位置施加垂直向下的集中力。求解：設(shè)置非線性靜力分析，求解梁的變形和應(yīng)力分布。4.2復(fù)合材料板的壓屈分析復(fù)合材料因其高比強(qiáng)度和比剛度，在航空航天、汽車和建筑領(lǐng)域得到廣泛應(yīng)用。然而，復(fù)合材料的非線性行為，特別是在壓縮載荷下的壓屈分析，是設(shè)計(jì)和分析中的關(guān)鍵問題。4.2.1壓屈分析原理壓屈分析（BucklingAnalysis）用于評(píng)估結(jié)構(gòu)在壓縮載荷作用下發(fā)生失穩(wěn)的臨界載荷。對(duì)于復(fù)合材料板，由于其各向異性，壓屈分析更為復(fù)雜，需要考慮材料的非線性以及層間效應(yīng)。4.2.2案例描述考慮一塊由多層復(fù)合材料組成的矩形板，尺寸為1米×1米，厚度為0.01米。板的材料為碳纖維增強(qiáng)塑料（CFRP），每層的彈性模量、泊松比和厚度不同。板的四周固定，受到垂直向下的均勻壓縮載荷。我們將使用ADINA進(jìn)行壓屈分析，以確定板的臨界壓縮載荷。4.2.3ADINA操作步驟建立模型：在ADINA中創(chuàng)建復(fù)合材料板的幾何模型，定義各層的材料屬性和厚度。網(wǎng)格劃分：對(duì)板進(jìn)行網(wǎng)格劃分，確保網(wǎng)格能夠準(zhǔn)確反映各層的材料特性。加載：在板的上表面施加垂直向下的均勻壓縮載荷。求解：設(shè)置壓屈分析，求解板的臨界壓縮載荷和失穩(wěn)模式。4.3混凝土結(jié)構(gòu)的非線性響應(yīng)混凝土是一種廣泛使用的建筑材料，其非線性行為在結(jié)構(gòu)分析中至關(guān)重要?；炷恋姆蔷€性響應(yīng)包括塑性、裂縫和損傷等現(xiàn)象，這些都會(huì)影響結(jié)構(gòu)的承載能力和安全性。4.3.1混凝土非線性響應(yīng)原理混凝土的非線性響應(yīng)主要由其復(fù)雜的材料性質(zhì)決定。在受壓時(shí)，混凝土表現(xiàn)出塑性行為；在受拉時(shí)，混凝土容易產(chǎn)生裂縫。此外，混凝土的損傷累積也會(huì)影響其長(zhǎng)期性能。4.3.2案例描述假設(shè)我們有一座混凝土橋梁，橋面寬度為10米，長(zhǎng)度為50米，橋墩高度為10米。橋梁受到車輛載荷和風(fēng)載荷的作用。我們將使用ADINA進(jìn)行非線性靜力分析，以研究橋梁在這些載荷作用下的非線性響應(yīng)。4.3.3ADINA操作步驟建立模型：在ADINA中創(chuàng)建橋梁的幾何模型，定義混凝土的材料屬性。網(wǎng)格劃分：對(duì)橋梁進(jìn)行網(wǎng)格劃分，確保網(wǎng)格能夠捕捉混凝土的裂縫和損傷行為。加載：在橋梁上施加車輛載荷和風(fēng)載荷。求解：設(shè)置非線性靜力分析，求解橋梁的變形、應(yīng)力分布和損傷累積。4.3.4注意事項(xiàng)在進(jìn)行混凝土結(jié)構(gòu)的非線性分析時(shí)，需要特別注意以下幾點(diǎn)：-材料模型：選擇合適的混凝土材料模型，如彈塑性模型或損傷模型。-裂縫模擬：使用裂縫追蹤技術(shù)來模擬混凝土的裂縫發(fā)展。-損傷累積：考慮損傷累積對(duì)結(jié)構(gòu)性能的影響，特別是在長(zhǎng)期載荷作用下。以上案例研究展示了ADINA在非線性靜力分析中的應(yīng)用，包括簡(jiǎn)單梁的非線性彎曲、復(fù)合材料板的壓屈分析和混凝土結(jié)構(gòu)的非線性響應(yīng)。通過這些案例，可以深入了解非線性行為對(duì)結(jié)構(gòu)性能的影響，以及如何使用ADINA進(jìn)行有效的非線性靜力分析。5高級(jí)非線性靜力分析技巧5.1接觸分析的設(shè)置與解讀在進(jìn)行非線性靜力分析時(shí)，接觸分析是關(guān)鍵的一部分，尤其是在處理結(jié)構(gòu)件之間的相互作用時(shí)。ADINA提供了強(qiáng)大的接觸分析功能，能夠模擬各種接觸條件，包括滑動(dòng)、摩擦、間隙等。5.1.1設(shè)置接觸分析在ADINA中設(shè)置接觸分析，首先需要定義接觸對(duì)，即哪些表面之間可能發(fā)生接觸。這通常在前處理階段完成，通過選擇主表面（MasterSurface）和從表面（SlaveSurface）來定義接觸對(duì)。主表面和從表面的選擇基于物理接觸的性質(zhì)和分析需求。5.1.1.1示例假設(shè)我們有一個(gè)簡(jiǎn)單的模型，包含一個(gè)壓板和一個(gè)底座，壓板將接觸并施力于底座上。在ADINA中，接觸分析的設(shè)置可能如下：```plaintext*CONTACT1,2,0.3,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0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