應力狀態(tài)分析、壓桿穩(wěn)定性分析

1、Harbin Institute of Technology 材料力學上機報告 設(shè)計題目： 應力狀態(tài)分析、壓桿穩(wěn)定性分析 院 系： 機電工程學院 班 級： 設(shè) 計 者： 學 號： 指導教師： 張桂蓮 設(shè)計時間： 哈爾濱工業(yè)大學材料力學上機報告一、 問題描述應力狀態(tài)分析：輸入：1.平面應力狀態(tài)輸入：（x、y、xy）；某截面方位角2.空間應力狀態(tài)輸入：（x、y、z、xy、yz、zx）輸出：1.輸出主應力（1、2、3）2.最大切應力（max=13=）3.如為平面應力狀態(tài)則需輸出方位角斜截面上的應力、及主方位角4.畫出應力圓示意圖壓桿穩(wěn)定分析輸入:1.截面參數(shù)輸入圓截面d圓環(huán)截面D，d矩形截面h，b工

2、字型截面對形心軸的慣性矩Iy、Iz及截面面積A2.相當長度系數(shù)、長度l3.材料參數(shù)：E、,p、s;線性經(jīng)驗公式系數(shù)a、b4.工作壓力P及穩(wěn)定安全系數(shù)nw輸出：1. 繪制臨界應力總圖（圖示）2. 臨界壓力Pcr或臨界應力cr3. 穩(wěn)定安全校核結(jié)果二、程序源代碼本程序采用Visual Basic 6.0編寫平面應力狀態(tài)分析Private Sub Timer1_Timer()End SubPrivate Sub Command1_Click()Dim x As Double, y As Double, xy As Double, As Double, X As Double, Y As Double

3、, z As Double'輸入數(shù)據(jù)（x , y ,xy ）；某截面方位角"x = Val(Text1.Text)y = Val(Text2.Text)xy = Val(Text3.Text) = Val(Text4.Text) / 180 * 4 * Atn(1)'計算主應力X = 0Y = (x + y) / 2 + (x - y) 2 / 4 + xy 2) 0.5z = (x + y) / 2 - (x - y) 2 / 4 + xy 2) 0.5'比較大小,輸出主應力（1 , 2 , 3 ）和最大剪應力max =13 =（1 - 3）/2If X &

4、gt;= Y And X >= z ThenText5.Text = Str(X)Text6.Text = Str(Y)Text7.Text = Str(z)Text8.Text = Str(X - z) / 2) Else If X <= Y And X <= z ThenText5.Text = Str(Y)Text6.Text = Str(z)Text7.Text = Str(X)Text8.Text = Str(Y - X) / 2) ElseText5.Text = Str(Y)Text6.Text = Str(X)Text7.Text = Str(z)Text8.

5、Text = Str(Y - z) / 2)End IfEnd If'計算并輸出,Text9.Text = Str(x + y) / 2 + (x - y) / 2 * Cos(2 * ) + xy * Sin(2 * )Text10.Text = Str(-(x - y) / 2 * Sin(2 * ) + xy * Cos(2 * )If x = y ThenText11.Text = Str(45) Else Text11.Text = Str(Atn(xy * 2 / (x - y) / 2) / (4 * Atn(1) * 180)End If'輸出應力圓Pictur

6、e1.ScaleMode = 3k = Text8.TextPicture1.Scale (-130 - Abs(x + y) - 2 * k, 100 + 5 * k)-(130 + Abs(x + y) + 2 * k, -100 - 5 * k)Picture1.Line (-130 - Abs(x + y) - 2 * k, 0)-(130 + Abs(x + y) + 2 * k, 0)Picture1.Line (0, -100 - 5 * k)-(0, 100 + 5 * k)Picture1.Circle (x + y) / 2, 0), (x - y) 2 / 4 + xy

7、2) 0.5, QBColor(12)End SubPrivate Sub Command2_Click()'清空文本框Text1.Text = "0"Text2.Text = "0"Text3.Text = "0"Text4.Text = "0"Text5.Text = ""Text6.Text = ""Text7.Text = ""Text8.Text = ""Text9.Text = ""Text10.

8、Text = ""Text11.Text = ""'清除圖片框Picture1.Cls'返回光標Text1.SetFocusEnd SubPrivate Sub Command3_Click()Me.HideForm10.Visible = TrueEnd SubPrivate Sub Command4_Click() Me.Hide Form4.Visible = TrueEnd SubPrivate Sub Label18_Click()End SubPrivate Sub Form_Load()End Sub二向應力狀態(tài)效果圖空間應

9、力狀態(tài)分析Private Sub Command1_Click()Dim x As Double, y As Double, z As Double, xy As Double, yz As Double, zx As Double'輸入數(shù)據(jù)（x ,y ,z ,xy ,yz ,zx ）x = Val(Text13.Text)y = Val(Text14.Text)z = Val(Text15.Text)xy = Val(Text16.Text)yz = Val(Text17.Text)zx = Val(Text18.Text) '計算I1,I2,I3;得到方程"x3-

10、I1*x2+I2*x-I3=0" I1 = x + y + z I2 = x * y - xy 2 + y * z - yz 2 + z * x - zx 2 I3 = (y * z - yz 2) * x - (xy * z - yz * zx) * xy + (xy * yz - zx * y) * zx'用盛金公式求解方程"x3-I1*x2+I2*x-I3=0"的根X1,X2,X3a = I1 2 - 3 * 1 * I2b = -I1 * I2 + 9 * 1 * I3c = I2 2 - 3 * I1 * I3d = b 2 - 4 * a *

11、c'當有三個相等實根時If (a = 0 And b = 0) ThenX1 = I1 / 3X2 = I1 / 3X3 = I1 / 3End If'當有兩個相等實根時If (a <> 0 And d = 0) ThenX1 = I1 + b / aX2 = -b / (2 * a)X3 = -b / (2 * a)End If'當有三個互不相等實根時If (d < 0 And a > 0) Then t = (-2 * a * I1 - 3 * b) / (2 * a (3 / 2) If (t = 0) Then u = 3.1415926

12、5357979 / 2 X1 = (I1 - 2 * a (1 / 2) * Cos(u / 3) / 3 X2 = (I1 + a (1 / 2) * (Cos(u / 3) + 3 (1 / 2) * Sin(u / 3) / 3 X3 = (I1 + a (1 / 2) * (Cos(u / 3) - 3 (1 / 2) * Sin(u / 3) / 3 Else If (-1 < t And t < 1 And t <> 0) Then u = Atn(1 - t 2) / t) X1 = (I1 - 2 * a (1 / 2) * Cos(u / 3) / 3

13、 X2 = (I1 + a (1 / 2) * (Cos(u / 3) + 3 (1 / 2) * Sin(u / 3) / 3 X3 = (I1 + a (1 / 2) * (Cos(u / 3) - 3 (1 / 2) * Sin(u / 3) / 3 End If End IfEnd If'當不全是實根時If (d > 0 Or d < 0 And a <= 0) ThenMsgBox "方程可能不全是實根,無法比較根的大小,請重新輸入", vbOKOnly, "溫馨提示"Text13.Text = ""

14、;Text14.Text = ""Text15.Text = ""Text16.Text = ""Text17.Text = ""Text18.Text = ""Text13.SetFocusEnd If'比較大小,輸出主應力（1 , 2 , 3 ）和最大剪應力max =13 =（1 - 3）/2以及應力圓 If (X1 >= X2 And X2 >= X3) Then Text19.Text = Str(X1) Text20.Text = Str(X2) Text21.Te

15、xt = Str(X3) Text22.Text = Str(X1 - X3) / 2) End If If (X1 >= X3 And X3 >= X2) Then Text19.Text = Str(X1) Text20.Text = Str(X3) Text21.Text = Str(X2) Text22.Text = Str(X1 - X2) / 2) Picture2.ScaleMode = 3 End If If (X2 >= X1 And X1 >= X3) Then Text19.Text = Str(X2) Text20.Text = Str(X1)

16、Text21.Text = Str(X3) Text22.Text = Str(X2 - X3) / 2) End If If (X2 >= X3 And X3 >= X1) Then Text19.Text = Str(X2) Text20.Text = Str(X3) Text21.Text = Str(X1) Text22.Text = Str(X2 - X1) / 2) End If If (X3 >= X1 And X1 >= X2) Then Text19.Text = Str(X3) Text20.Text = Str(X1) Text21.Text =

17、Str(X2) Text22.Text = Str(X3 - X1) / 2) End If If (X3 >= X2 And X2 >= X1) Then Text19.Text = Str(X3) Text20.Text = Str(X2) Text21.Text = Str(X1) Text22.Text = Str(X3 - X1) / 2) End If '輸出應力圓 A1 = Val(Text19.Text) B1 = Val(Text20.Text) C1 = Val(Text21.Text) E1 = Val(Text22.Text) Picture2.Sc

18、aleMode = 3 Picture2.Scale (-100 + C1 - (A1 - C1), 80 + (A1 - C1)-(100 + C1 + (A1 - C1), -80 - (A1 - C1) Picture2.Line (-100 + C1 - (A1 - C1), 0)-(100 + C1 + (A1 - C1), 0) Picture2.Line (0, -80 - (A1 - C1)-(0, 80 + (A1 - C1) Picture2.Circle (A1 + C1) / 2, 0), (A1 - C1) / 2, QBColor(12) Picture2.Circ

19、le (A1 + B1) / 2, 0), (A1 - B1) / 2, QBColor(12) Picture2.Circle (B1 + C1) / 2, 0), (B1 - C1) / 2, QBColor(12) End SubPrivate Sub Command2_Click()'清空文本框Text13.Text = ""Text14.Text = ""Text15.Text = ""Text16.Text = ""Text17.Text = ""Text18.Text =

20、""Text19.Text = ""Text20.Text = ""Text21.Text = ""Text22.Text = ""'清除圖片框Picture2.Cls'返回光標Text13.SetFocusEnd SubPrivate Sub Command3_Click() Me.Hide Form10.Visible = TrueEnd SubPrivate Sub Command4_Click()Me.HideForm4.Visible = TrueEnd SubPriv

21、ate Sub Form_Load()End Sub 空間應力狀態(tài)分析圓形截面壓桿穩(wěn)定性分析Private Sub Command1_Click()Dim d, u, l, e, tp, ts, a, b, p, n, t As DoubleDim i, s As DoubleDim r, rp, rs As DoubleConst pi = 3.1415d = Val(Text1.Text)u = Val(Text2.Text)l = Val(Text3.Text)e = Val(Text4.Text)tp = Val(Text5.Text)ts = Val(Text6.Text)a = V

22、al(Text7.Text)b = Val(Text8.Text)p = Val(Text9.Text)n = Val(Text10.Text)i = pi * d 4 / 64s = pi * d * d / 4r = 1000 * u * l / Sqr(i / s)rp = pi * Sqr(e / tp)rs = (a - ts) / bIf r >= rp Thent = pi 2 * e / (r 2 * n)Text11.Text = tIf p / s <= t ThenText12.Text = "滿足穩(wěn)定條件"ElseText12.Text

23、= "不滿足穩(wěn)定條件"End IfElseIf r >= rs Thent = (a - b * r) / nText11.Text = tIf p / s <= t ThenText12.Text = "滿足穩(wěn)定條件"ElseText12.Text = "不滿足穩(wěn)定條件"End IfElseText11.Text = ""Text12.Text = "這是一個強度問題"End IfDim Y As DoublePicture1.ClsPicture1.ScaleMode = 0Pi

24、cture1.Scale (-10, 300)-(200, -10)Picture1.DrawWidth = 1Picture1.Line (0, 0)-(200, 0), RGB(0, 0, 255)Picture1.Line (0, 0)-(0, 300), RGB(0, 0, 255)For X = 0 To rs Step 0.01Y = tsPicture1.PSet (X, Y), RGB(255, 0, 0)Next XFor X = rs To rp Step 0.01Y = a - b * XPicture1.PSet (X, Y), RGB(255, 0, 0)Next X

25、For X = rp To 300 Step 0.01Y = pi 2 * e / X 2Picture1.PSet (X, Y), RGB(255, 0, 0)Next XEnd SubPrivate Sub Command2_Click()Me.HideForm1.Visible = TrueEnd SubPrivate Sub Command3_Click()Me.HideForm4.Visible = TrueEnd SubPrivate Sub Frame1_DragDrop(Source As Control, X As Single, Y As Single)End Sub圖3

26、圓形截面壓桿穩(wěn)定性分析輸出結(jié)果例4利用程序進行圓環(huán)形截面壓桿穩(wěn)定性分析，外徑D=200mm，內(nèi)徑d=50mm，長度系數(shù)=1，桿長l=2000mm，彈性模量E=50000MPa，比例極限p=240MPa，屈服極限s=320MPa，系數(shù)a=234，系數(shù)b=1234，工作壓力P=30000N，安全系數(shù)n=4.5。輸出結(jié)果如圖4所示。圓環(huán)形壓桿穩(wěn)定性分析Private Sub Command1_Click()Dim d1, d2, u, l, e, tp, ts, a, b, p, n, t As DoubleDim i, s As DoubleDim r, rp, rs As DoubleConst

27、 pi = 3.1415d1 = Text1.Textd2 = Text13.Textu = Text2.Textl = Text3.Texte = Text4.Texttp = Text5.Textts = Text6.Texta = Text7.Textb = Text8.Textp = Text9.Textn = Text10.Texti = pi * (d1 4 - d2 4) / 64s = pi * (d1 2 - d2 2) / 4r = 1000 * u * l / Sqr(i / s)rp = pi * Sqr(e / tp)rs = (a - ts) / bIf r >

28、;= rp Thent = pi 2 * e / (r 2 * n)Text11.Text = tIf p / s <= t ThenText12.Text = "滿足穩(wěn)定條件"ElseText12.Text = "不滿足穩(wěn)定條件"End IfElseIf r >= rs Thent = (a - b * r) / nText11.Text = tIf p / s <= t ThenText12.Text = "滿足穩(wěn)定條件"ElseText12.Text = "不滿足穩(wěn)定條件"End IfEls

29、eText11.Text = ""Text12.Text = "這是一個強度問題"End IfDim Y As DoublePicture1.ClsPicture1.ScaleMode = 0Picture1.Scale (-10, 300)-(200, -10)Picture1.DrawWidth = 1Picture1.Line (0, 0)-(200, 0), RGB(0, 0, 255)Picture1.Line (0, 0)-(0, 300), RGB(0, 0, 255)For X = 0 To rs Step 0.01Y = tsPictu

30、re1.PSet (X, Y), RGB(255, 0, 0)Next XFor X = rs To rp Step 0.01Y = a - b * XPicture1.PSet (X, Y), RGB(255, 0, 0)Next XFor X = rp To 300 Step 0.01Y = pi 2 * e / X 2Picture1.PSet (X, Y), RGB(255, 0, 0)Next XEnd SubPrivate Sub Command2_Click()Me.HideForm1.Visible = TrueEnd SubPrivate Sub Command3_Click

31、()Me.HideForm4.Visible = TrueEnd SubPrivate Sub Frame2_DragDrop(Source As Control, X As Single, Y As Single)End Sub圖4 圓環(huán)形截面壓桿穩(wěn)定性分析輸出結(jié)果例5利用程序進行矩形截面壓桿穩(wěn)定性分析，高度h=250mm，寬度b=120mm，長度系數(shù)=1，桿長l=12mm，彈性模量E=300000MPa，比例極限p=240MPa，屈服極限s=320MPa，系數(shù)a=341，系數(shù)b=2658，工作壓力P=30000N，安全系數(shù)n=4.5。輸出結(jié)果如圖5所示。矩形截面壓桿穩(wěn)定性分析Private

32、 Sub Command1_Click()Dim h, d, u, l, e, tp, ts, a, b, p, n, t As DoubleDim i, s As DoubleDim r, rp, rs As DoubleConst pi = 3.1415h = Text1.Textd = Text13.Textu = Text2.Textl = Text3.Texte = Text4.Texttp = Text5.Textts = Text6.Texta = Text7.Textb = Text8.Textp = Text9.Textn = Text10.Texti = h * d 3 /

33、 12s = h * dr = 1000 * u * l / Sqr(i / s)rp = pi * Sqr(e / tp)rs = (a - ts) / bIf r >= rp Thent = pi 2 * e / (r 2 * n)Text11.Text = tIf p / s <= t ThenText12.Text = "滿足穩(wěn)定條件"ElseText12.Text = "不滿足穩(wěn)定條件"End IfElseIf r >= rs Thent = (a - b * r) / nText11.Text = tIf p / s <

34、;= t ThenText12.Text = "滿足穩(wěn)定條件"ElseText12.Text = "不滿足穩(wěn)定條件"End IfElseText11.Text = ""Text12.Text = "這是一個強度問題"End IfDim Y As DoublePicture1.ClsPicture1.ScaleMode = 0Picture1.Scale (-10, 300)-(200, -10)Picture1.DrawWidth = 1Picture1.Line (0, 0)-(200, 0), RGB(0, 0

35、, 255)Picture1.Line (0, 0)-(0, 300), RGB(0, 0, 255)For X = 0 To rs Step 0.01Y = tsPicture1.PSet (X, Y), RGB(255, 0, 0)Next XFor X = rs To rp Step 0.01Y = a - b * XPicture1.PSet (X, Y), RGB(255, 0, 0)Next XFor X = rp To 300 Step 0.01Y = pi 2 * e / X 2Picture1.PSet (X, Y), RGB(255, 0, 0)Next XEnd SubP

36、rivate Sub Command2_Click()Me.HideForm1.Visible = TrueEnd SubPrivate Sub Command3_Click()Me.HideForm4.Visible = TrueEnd SubPrivate Sub Frame1_DragDrop(Source As Control, X As Single, Y As Single)End Sub圖5 矩形截面壓桿穩(wěn)定性分析輸出結(jié)果例6利用程序進行工字形截面壓桿穩(wěn)定性分析，Iy=4215cm4，Iz=3135cm4，A=1223mm2，長度系數(shù)=1，桿長l=450mm，彈性模量E=3000

37、0MPa，比例極限p=240MPa，屈服極限s=320MPa，系數(shù)a=461，系數(shù)b=2561，工作壓力P=30000N，安全系數(shù)n=4.5。輸出結(jié)果如圖6所示。工字形截面壓桿穩(wěn)定性分析Private Sub Command1_Click()Dim iy, iz, s, u, l, e, tp, ts, a, b, p, n, t As DoubleDim i As DoubleDim r, rp, rs As DoubleConst pi = 3.1415iy = Text1.Textiz = Text13.Texts = Text14.Textu = Text2.Textl = Text3.Texte = Text4.Texttp = Text5.Textts = Text6.Texta = Text7.Textb = Text8.Textp = Text9.Textn = Text10.TextIf iz < iy Theni = izElsei = iyEnd Ifr = 1000 * u * l / Sqr(i / s)r