计算机在材料科学中的应用上机指导书1.doc

计算机在材料科学中的应用上机指导书材料学院实验目录实验一 方程求根 （2学时）3实验二 线性方程组求解（2学时）6实验三 最小二乘法曲线拟合及回归分析数值计算 （4学时）10实验四 插值计算（2学时）15实验五 传热学计算机分析 （2学时）17实验六 相图热力学计算 （4学时）19实验七 互联网在材料科学中的应用 （2学时）21实验八 常用软件学习（2学时）23实验一 方程求根 2学时一、实验目的及任务要求1、实验目的：1）熟悉程序设计语言，了解简单的程序设计方法；2）熟悉迭代法求方程根及牛顿法求方程的算法设计；3）熟悉简单算法程序编写及调试方法。2、任务要求：1）熟悉机房环境；2）理解算法原理及程序编译过程。二、实验操作过程1、熟悉VB（或C语言）编译软件界面VB语言是一种面向对象的高级程序设计语言，目前应用较多的是Visual Basic6.0版本。界面如图所示：属性代码窗口窗体2、熟悉算法1）二分法求方程根11 2）牛顿法求方程根3、程序设计1）例题分析：以二分迭代法求解方程x3-x-1=0在区间0，2中的根（精度为e=10-6）f(x)= x3-x-1。程序设计（VB）：Private Sub cmdjisuan_Click()Dim x1 As Single, x2 As Single, x3 As Singlex1 = 0x2 = 2Dox3 = (x1 + x2) / 2If (x1 * x1 * x1 - x1 - 1) * (x3 * x3 * x3 - x3 - 1) 0 Thenx1 = x3Elsex2 = x3End IfLoop Until Abs(x2 - x1) 0.00001x = x - F(x) / dF(x)n = n + 1If n 1000 Thentxtroot.Text = 迭代发散Exit SubEnd IfLooptxtroot.Text = xEnd SubPrivate Function F(x0 As Single) As SingleF = x0 * x0 * x0 + 4 * x0 * x0 - 10End FunctionPrivate Function dF(x1 As Single) As SingledF = 3 * x1 * x1 + 8 * x1End Function实验二 线性方程组求解 2学时一、实验目的及任务要求1、实验目的：1）熟悉雅可比迭代法及其算法设计；2）熟悉追赶法解线性方程组及其算法设计；3）熟悉简单算法程序编写及调试方法。2、任务要求：1）熟悉线性方程组常用数值解法；2）理解算法原理及程序编译过程。二、实验操作过程1、雅可比迭代法算法设计线性方程组的矩阵表达式为AX=b，其一般形式为：Aijxj=bi (i=1,2, n j=1,2, n)将此式改写为迭代格式： （i=1, 2, ., n）程序设计：计算例题：给定初始值 x(0)=0,0,0T选代求解为 x*=3,2,1T程序设计(VB)：Option ExplicitOption Base 1Private a(3, 3) As Single, b(3) As Single, x(3) As Single, y(3) As SinglePrivate Sub cmdjisuan_Click()a(1, 1) = 8: a(1, 2) = -3: a(1, 3) = 2a(2, 1) = 4: a(2, 2) = 11: a(2, 3) = -1a(3, 1) = 6: a(3, 2) = 3: a(3, 3) = 12b(1) = 20: b(2) = 33: b(3) = 36y(1) = txtx1.Text: y(2) = txtx2.Text: y(3) = txtx3.TextDim i As Integer, j As Integer, N As Single, M(3) As Single, t As SingleDoFor i = 1 To 3t = 0For j = 1 To 3If i j Thent = t + a(i, j) * y(j) End IfNext jx(i) = (b(i) - t) / a(i, i)Next iFor i = 1 To 3M(i) = Abs(x(i) - y(i)NextN = M(1)For i = 2 To 3If N 0.00000001txtroot1.Text = x(1): txtroot2.Text = x(2): txtroot3.Text = x(3)End Sub2、追赶法解线性方程组三对角方程组的形式如下：追赶法程序框图：计算例题：VB程序：Option ExplicitOption Base 1Private Sub cmdjisuan_Click()Dim a(5) As Single, b(5) As Single, c(5) As Single, d(5) As Singlea(2) = -1: a(3) = -1: a(4) = -1: a(5) = -1b(1) = 4: b(2) = 4: b(3) = 4: b(4) = 4: b(5) = 4c(1) = -1: c(2) = -1: c(3) = -1: c(4) = -1d(1) = 100: d(2) = 200: d(3) = 200: d(4) = 200: d(5) = 100Dim i As Integerd(1) = d(1) / b(1): c(1) = c(1) / b(1)Dim t As SingleFor i = 2 To 4t = b(i) - a(i) * c(i - 1)c(i) = c(i) / td(i) = (d(i) - a(i) * d(i - 1) / tNextd(5) = (d(5) - a(5) * d(4) / (b(5) - a(5) * c(4)For i = 4 To 1 Step -1d(i) = d(i) - c(i) * d(i + 1)Nexttxtx1.Text = d(1): txtx2.Text = d(2): txtx3.Text = d(3): txtx4.Text = d(4): txtx5.Text = d(5)End SubPrivate Sub Command1_Click()txtx1.Text = : txtx2.Text = : txtx3.Text = : txtx4.Text = : txtx5.Text = 界面设计：实验三 最小二乘法曲线拟合及回归分析数值计算 4学时一、实验目的及任务要求1、实验目的：1）熟悉最小二乘法曲线拟合算法设计；2）熟悉该算法程序编写及调试方法。2、任务要求：1）熟悉一元及多元线性回归数值解法；2）理解算法原理及程序编译过程。二、实验操作过程1、一元线性回归已知现场的一组实测数据如下：选用直线方程，其形式为：y=a+bx一元线性回归的计算步骤： 1）输入原始数据输入原始数据主要包括，实测点的个数n，n组实测点值xi及函数值yi。 2）循环求和计算计算x, y, x2, y2, xy 3）构造正则方程组：a11=N a12=x b1=y a21=x a22=x2 b2=xy 4）求解二元一次线性方程组利用克拉姆法则计算： 程序设计：Option ExplicitOption Base 1Private Sub Command1_Click()Dim n As IntegerDim x(4) As Single, y(4) As Single, b(2) As Singlex(1) = 2: x(2) = 4: x(3) = 6: x(4) = 8: y(1) = 2: y(2) = 11: y(3) = 28: y(4) = 40Dim a(2, 2) As Singlea(1, 1) = 4Dim i As Integer, x1 As Single, x2 As Single, t(3) As SingleFor i = 1 To 4a(1, 2) = a(1, 2) + x(i)a(2, 2) = a(2, 2) + x(i) * x(i)b(1) = b(1) + y(i)b(2) = b(2) + x(i) * y(i)Nexta(2, 1) = a(1, 2)t(1) = a(1, 1) * a(2, 2) - a(1, 2) * a(2, 1)t(2) = b(1) * a(2, 2) - b(2) * a(1, 2)t(3) = a(1, 1) * b(2) - a(2, 1) * b(1)x1 = t(2) / t(1): x2 = t(3) / t(1)txta.Text = x1: txtb.Text = x2End SubPrivate Sub Command2_Click()txta.Text = : txtb.Text = End Sub2、多元线性回归P17 例2分析：求y对x1, x2, x3的线性回归方程。表22 去碳量y与天然矿石和烧结矿石的加入量x1, x2 及熔化时间x3实测数据 n=49，此题是三元线性回归，其回归系数a1、a2、a3满足三元正规方程：l11a1+l12a2+l13a3=l1yl21a1+l22a2+l23a3=l2yl31a1+l32a2+l33a3=l3yl11 = x12-(x1)2 l12=l21=x1x2-(x1)(x2) l13=l31=x1x3-(x1)(x3) l22=x22-(x2)2 l23=l32=x2x3-(x2)(x3) l33=x32-(x3)2l1y=x1y-(x1)(y) l2y=x2y-(x2)(y) l3y=x3y-(x3)(y)计算步骤：1）输入数据：N49，x1i, x2i, x3i, yi (i=1,2, , 49)2) 计算：x12、x22、x32、x1、x2、x3、x1x2、x2x3、x1x3、x1y、x2y、x3y、y3)计算线性方程组系数lij并解线性方程组4）计算a0，求出三元线性回归方程式。程序设计（VB）：Option ExplicitOption Base 1Private Sub cmdjisuan_Click()Dim x1(49) As Double, x2(49) As Double, x3(49) As Double, y(49) As Doublex1(1) = 2: x1(2) = 7: x1(3) = 5: x1(4) = 12: x1(5) = 1x1(6) = 3: x1(7) = 3: x1(8) = 6: x1(9) = 7: x1(10) = 0x1(11) = 3: x1(12) = 0: x1(13) = 8: x1(14) = 6: x1(15) = 0x1(16) = 3: x1(17) = 7: x1(18) = 16: x1(19) = 6: x1(20) = 0x1(21) = 9: x1(22) = 4: x1(23) = 0: x1(24) = 9: x1(25) = 2x1(26) = 9: x1(27) = 12: x1(28) = 6: x1(29) = 12: x1(30) = 0x1(31) = 5: x1(32) = 4: x1(33) = 0: x1(34) = 6: x1(35) = 4x1(36) = 10: x1(37) = 4: x1(38) = 5: x1(39) = 9: x1(40) = 6x1(41) = 5: x1(42) = 5: x1(43) = 8: x1(44) = 2: x1(45) = 7x1(46) = 4: x1(47) = 10: x1(48) = 3: x1(49) = 4x2(1) = 18: x2(2) = 9: x2(3) = 14: x2(4) = 3: x2(5) = 20x2(6) = 12: x2(7) = 17: x2(8) = 5: x2(9) = 8: x2(10) = 23x2(11) = 16: x2(12) = 18: x2(13) = 4: x2(14) = 14: x2(15) = 21x2(16) = 14: x2(17) = 12: x2(18) = 0: x2(19) = 16: x2(20) = 15x2(21) = 0: x2(22) = 6: x2(23) = 17: x2(24) = 0: x2(25) = 16x2(26) = 6: x2(27) = 5: x2(28) = 13: x2(29) = 7: x2(30) = 24x2(31) = 12: x2(32) = 15: x2(33) = 20: x2(34) = 16: x2(35) = 17x2(36) = 4: x2(37) = 14: x2(38) = 13: x2(39) = 8: x2(40) = 13x2(41) = 8: x2(42) = 11: x2(43) = 6: x2(44) = 13: x2(45) = 8x2(46) = 10: x2(47) = 5: x2(48) = 17: x2(49) = 15x3(1) = 50: x3(2) = 40: x3(3) = 46: x3(4) = 43: x3(5) = 64x3(6) = 40: x3(7) = 64: x3(8) = 39: x3(9) = 37: x3(10) = 55x3(11) = 60: x3(12) = 49: x3(13) = 50: x3(14) = 51: x3(15) = 51x3(16) = 51: x3(17) = 56: x3(18) = 48: x3(19) = 45: x3(20) = 52x3(21) = 40: x3(22) = 32: x3(23) = 47: x3(24) = 44: x3(25) = 39x3(26) = 39: x3(27) = 51: x3(28) = 41: x3(29) = 47: x3(30) = 61x3(31) = 37: x3(32) = 49: x3(33) = 45: x3(34) = 42: x3(35) = 48x3(36) = 48: x3(37) = 36: x3(38) = 36: x3(39) = 51: x3(40) = 54x3(41) = 100: x3(42) = 44: x3(43) = 63: x3(44) = 55: x3(45) = 50x3(46) = 45: x3(47) = 40: x3(48) = 64: x3(49) = 72y(1) = 4.3302: y(2) = 3.6485: y(3) = 4.483: y(4) = 5.5468: y(5) = 5.497y(6) = 3.1125: y(7) = 5.1182: y(8) = 3.8759: y(9) = 4.67: y(10) = 4.9536y(11) = 5.006: y(12) = 5.2701: y(13) = 5.3772: y(14) = 5.4849: y(15) = 4.596y(16) = 5.6645: y(17) = 6.0795: y(18) = 3.2194: y(19) = 5.8075: y(20) = 4.7306y(21) = 4.6805: y(22) = 3.1272: y(23) = 2.6104: y(24) = 3.7174: y(25) = 3.8946y(26) = 2.7066: y(27) = 5.6314: y(28) = 5.8152: y(29) = 5.1302: y(30) = 5.391y(31) = 4.4583: y(32) = 4.6569: y(33) = 4.5212: y(34) = 4.865: y(35) = 5.3566y(36) = 4.6098: y(37) = 2.3815: y(38) = 3.8746: y(39) = 4.5915: y(40) = 5.1588y(41) = 5.4372: y(42) = 3.996: y(43) = 4.397: y(44) = 4.0622: y(45) = 2.2905y(46) = 4.7115: y(47) = 4.531: y(48) = 5.3637: y(49) = 6.0771Dim i As Integer, x1x1 As Single, x11 As Single, x22 As Single, x2x2 As Single, x33 As Single, x3x3 As SingleDim x1x2 As Single, x2x3 As Single, x1x3 As Single, x1y As Single, x2y As Single, x3y As Single, yy As SingleFor i = 1 To 49x11 = x11 + x1(i)NextFor i = 1 To 49x1x1 = x1x1 + x1(i) * x1(i)x1x2 = x1x2 + x1(i) * x2(i)x1x3 = x1x3 + x1(i) * x3(i)x22 = x22 + x2(i)x2x2 = x2x2 + x2(i) * x2(i)x2x3 = x2x3 + x2(i) * x3(i)x33 = x33 + x3(i)x3x3 = x3x3 + x3(i) * x3(i)x1y = x1y + x1(i) * y(i)x2y = x2y + x2(i) * y(i)x3y = x3y + x3(i) * y(i)yy = yy + y(i)NextDim a(3, 3) As Single, b(3) As Singlea(1, 1) = x1x1 - (x11 / 49) * x11a(1, 2) = x1x2 - (x11 / 49) * x22a(1, 3) = x1x3 - (x11 / 49) * x33a(2, 2) = x2x2 - x22 * (x22 / 49)a(2, 3) = x2x3 - x22 * (x33 / 49)a(3, 3) = x3x3 - x33 * (x33 / 49)a(2, 1) = a(1, 2): a(3, 2) = a(2, 3): a(3, 1) = a(1, 3)b(1) = x1y - x11 * (yy / 49)b(2) = x2y - x22 * (yy / 49)b(3) = x3y - x33 * (yy / 49)txt11.Text = a(1, 1)txt12.Text = a(1, 2)txt13.Text = a(1, 3)txt22.Text = a(2, 2)txt23.Text = a(2, 3)txt33.Text = a(3, 3)txt1y.Text = b(1)txt2y.Text = b(2)txt3y.Text = b(3)a(2, 1) = a(1, 2): a(3, 1) = a(1, 3): a(3, 2) = a(2, 3)y(1) = 0.1: y(2) = 0.1: y(3) = 0Dim j As Integer, N As Single, M(3) As Single, t As Single, x(3) As SingleDoFor i = 1 To 3t = 0For j = 1 To 3If i j Thent = t + a(i, j) * y(j)End IfNext jx(i) = (b(i) - t) / a(i, i)Next iFor i = 1 To 3M(i) = Abs(x(i) - y(i)NextN = M(1)For i = 2 To 3If N 0.000001txta1.Text = x(1): txta2.Text = x(2): txta3.Text = x(3)Dim a0 As Singlea0 = yy / 49 - x(1) * x11 / 49 - x(2) * x22 / 49 - x(3) * x33 / 49txta0.Text = a0End SubPrivate Sub Command2_Click()txt11.Text = :txt12.Text = :txt13.Text = :txt22.Text = txt23.Text = :txt33.Text = :txt1y.Text = :txt2y.Text = txt3y.Text = :txta1.Text = : txta2.Text = : txta3.Text = :txta0.Text = End Sub实验四 插值计算 2学时一、实验目的及任务要求1、实验目的：1）熟悉拉格朗日算法流程；2）掌握三次样条插值计算方法；2）熟悉该算法程序编写及调试方法。2、任务要求：1）熟悉插值计算方法；2）理解算法原理及程序编译过程。二、实验操作过程1、拉格朗日插值法程序程序流程图：读该流程图并试编写程序。2、三次样条插值函数计算步骤：（1）按所给边界条件及所给节点（xi, yi）计算i，i，di；（2）在所给边界条件下解方程组计算出Mi（i=0, 1, 2, n）；（3）将所求得的Mi代入分段插值公式，求出各小区间xi, xi-1上的样条函数Si(x)；程序设计： 设给定函数表及边界条件S”（x0）=S”(x2)=0，求三次样条插值函数，并求f(x)在x=3, 4, 5处的近似值。根据上述计算思路编写程序并上机调试。实验五 传热学计算机分析 2学时一、实验目的及任务要求1、实验目的：1）熟悉传热学基本理论；2）掌握导热问题的数值解法；2、任务要求：1）编写程序实现简单导热问题的数值求解。二、实验操作过程1、导热问题的数值解法（1）有限差分法向前差商：向后差商：中心差商：一阶差商仍然是x的函数，可以继续对它求差商：2、有限差分法的求解步骤（1）根据问题的性质确定导热微分方程式、初始条件和边界条件；（2）对区域进行离散化，确定计算节点；（3）建立离散方程，对每一个节点写出表达式；（4）求解线性方程组；（5）对解进行分析。3、实例分析例题：设有一炉墙，厚度为，已知内壁温度为t0为500，外壁温度t4为100，求厚度方向的温度分布。 该问题属于一维稳态导热问题，导热微分方程：A：采用积分方法求解：炉墙的温度分布：B：采用有限差分法求解： 首先将区域离散化，对于稳态导热问题，只需要将空间区域离散。把要求解的空间区域0以间距x划分成m等分，这些等分线为网格线，以每一网格线为中心，宽度为x组成一系列子区间，称为元体。元体的中心称为节点。计算时，以节点的温度作为元体的平均温度，如将节点i的温度作为i元体的平均温度，记为ti；边界节点0和m则为半个元体的平均温度，记为t0和tm。常物性、一维、无内热源、稳定导热的微分方程为：代入差分方程：当m=4时建立差分方程如下：t0=500t2-2t1+t0=0t3-2t2+t1=0t4-2t3+t2=0t4=100根据上述计算方法编写程序并上机调试。实验六 相图热力学计算 4学时一、实验目的及任务要求1、实验目的：1）熟悉在线相图查询网站；2）熟悉相图的热力学计算方法；3）熟悉简单相图计算程序。2、任务要求：1）熟悉相图热力学数值计算方法。二、实验操作过程1、在线相图计算：FACT是世界排名数一数二的热力学计算软件，提供在线热力学据计算，二元三元相图计算等等强大功能。下面的网址提供在线常用相图查询 http:/www.crct.polymtl.ca/FACT/documentation/试访问该网站并查询相图，以下为在线查得Al2O3SiO2相图。For an equilibrium point calculation, point and click on the figure OR enter manually the coordinates (IE only): Y: Error! Reference source not found.X: Error! Reference source not found. Error! Reference source not found.2、NiOMgO完全固溶体相图绘制NiOMgO为液、固相连续互溶二元体系，液相和固相均为理想溶液。已知NiO和MgO的熔点分别为1960和2800，熔化热分别为52.3kJ/Mol和77.4kJ/Mol。以纯液态NiO作为NiO的标准态，纯固态MgO作为MgO的标准态，则和近似计算公式为：=77400(1-=52300(1-设1为NiO，2为MgO，则有又因为1 1所以：1=(1) 求得：即可计算出NiOMgO完全固溶相图。试采用VB语言实现上述计算。实验七 互联网在材料科学中的应用 2学时一、实验目的及任务要求1、实验目的：1）熟悉材料专业网站；2）熟悉通用及专用搜索引擎的使用；3）熟悉数据库资源的使用。2、任务要求：1）熟悉利用互联网查阅专业资料。二、实验操作过程1、访问材料专业网站1）协会网站利用专业学会网站是获取专题信息的一个捷径，它除了提供学会介绍、论文征集启事外，还提供与专题有关的电子出版物、热门话题、标准信息以及专业数据库等。国际材料研究学会联合会（International Union of MRS）的网址：中国材料研究学会：中国材料网： , 该网站是在科技部、国家自然科学基金委员会、教育部和中国科学院的支持下，在全国各个材料科研单位和高等院校的协助下，依托于中国材料研究学会和清华大学材料科学与工程研究院，由国家现代材料科技信息中心承办的。中心作为国际互联网上专门建立的首家国家级材料专业信息网络，为我国材料科技界和材料工业界的大范围交流、合作和服务提供了新的手段。服务群体主要是各科研院所、企事业单位有关材料行业科研人员和高等院校材料专业广大师生，主要服务内容有：免费浏览、会员之家及交流栏目等。比较著名的与材料研究相关的协会网站如下：材料研究协会 金属矿石和材料协会（TMS）国际晶体学联合会http:/www.iucr.ac.uk/welocme.html2)专业综合网站关于某个学科专业的综合信息网站，对该学科作综合性的介绍，使人们对该学科有一个全面的了解并可以方便的找到所需要的信息资源。陶瓷材料：中国陶瓷信息资源网：中国陶瓷网：21世纪陶瓷网：中华陶瓷在线：以上是国内有名气的陶瓷综合信息网站。金属材料：中国钢铁网： 全面准确地介绍国内外钢铁工业的面貌以及每日最新的钢铁动态。中国金属网： 钢铁信息网 中国联合钢铁网 等均是国内比较著名的金属综合信息网站。3）研究机构网站材料研究所http:/www.instmat.co.uk材料预备中心/mat-ref/mpc.html安大略材料研究中心：http:/www.queensu.ca/ocmr哥德堡材料学中心：http:/www.cms.fy.chalmers.se 等。2、数据库资源1）专利数据库IBM知识产权网IPN（The IBM Intellectual Property Network）于1997年推出，网址为，具有数据库容量大、数据更新及时、检索性能优异、开放性好等特点。1974年后公布的美国专利提供全文图像。中国专利信息网：英国德温特专利库：http:/www.derwent.co.uk日本专利信息组织：http:/www.japio.or.jp中国专利文献数据库：http:/www.bEI2）材料性能数据库Http://性能数据库：这是一个有关材料的综合数据库，包括热塑性树脂和热固性树脂等高分子材料，铝和铜等高分子材料，铝和铜等金属材料，陶瓷、半导体以及其他一些工程材料的性能。3）论文数据库Springer全文电子期刊、美国化学学会（ACS）会刊、英国皇家化学学会（RSC）全文电子期刊及数据库、Science全文、Nature全文、IEEE全文数据库以及国内的中国期刊网和维普、万方数据库、超星图书馆等。3、搜索引擎1） 2）4、材料科学文献检索1）工程索引（EI）美国工程索引（The Engineering Index），简称EI，在