复合材料结构力学作业.docx

1、复合材料结构力学作业复合材料结构力学作业时可以删除ferejfce only-rar21 year.March对材料AS4/3501-6进行设计已知 el = 147.2MP。屛=965MPq、G = 6.86GPa,u = 0.3, r = 0.134 mw, P = 1.61X1 =2356MPgX=1468MPgF =49AMPa,Yc =186 MPa,S = 105 MPg2d、50 nun1STEP I Special Stacking Sequence (SSS)(一) 在Task I载荷作用下已知 Longitudinal Load =100 kN, Transverse Lo

2、ad =-5 kN, Shear Load =30 kN 外加载荷可等效为 N = N“ N22 Nj =2000 - 50 600SN/？对0,丄度铺设层合板，b = 14925 -373 4478 7 MPa，带入最大正应力准则得N=max6.3349,2.0054,42.6476=42.6476,所以0”$ 所需的最小层数为 42.6 层, 且52先破坏对90,丄度铺设层合板b = - 373 14925 - 4478 f MPaN=max0.2541/302.1255/42.6476=302.1255,所以90,丄所需的最小层数为 302.1255层，且2先破坏对(45),丄度铺设层合

3、板45 度b= 5496.1 180.5 -1912 .3 MPa ,N=max2.3328,3.6538,18.2124)=18.2124-45 度b= 1218.8 380.7 1912.3MPa,N=max0.51732,7.70658.2124)=18.2124所以对(45),丄度铺设层合板，共需要18.21*4=72.84层，且先破坏对(0/60)Js度铺设层合板0度b=6366.5 -6.2 2T!.1 MPa , N=max2.7022,0.0333,2.1686)=2.7022 +60 度b= 2267 185.7 - 450.87 MPt/, N二max0.9622,3.75

4、91,4.2933 =4.2933-60 度b= 1918 .5 381.7 223 1 MPa , N=max 1.3069,7.7267,2.1248)=7.37267 所以对(0/土60),丄度铺设层合板，共需要7.37*6=44.22层，且。的先破坏 绘制在表格中，如下所示：层合板铺层层合板层数层合板厚 度(mm)层合板质(g)取整数层取整后 每层厚 度(mm)最先破 坏层0,丄42.65.708447.4628440.129712叽302.1340.485325.90433020.1341(45)丄72.849.760678.5728740.131962(。/土60)”44.225.

5、925547.7003480.1234。22从上表中可以看到，0”、所需的层数最少，即质量最轻对08x/90% /(45。/- 45。铺层，设+45度和-45度的层数相同(1)当0度铺层占10%,90度铺层占0%时，则45度和-45度各占45%时0 度a = 30809 - 870 439MP, N= 13.08+45 度b = 9050.4 148.9 一2489.6MPa , N=23.71-45 度b = - 268.5 585.1 2489 .6 MPa , N=23.71代入最大正应力准则进行校核，经比较得,N=23.71,所以共需要23.71*2=47.42层当0度铺层占10%,9

6、0度铺层占10%时，则45度和-45度各占40%时0 度,b = 27954 一433 482 7 MPa , N=max 11.865232&4.5905 二11.86590 度，b = 14524 1555 482 MPa , N=max9.8937,31.48,4.5905)=31.4845 度,a = 11831 322 2002 丫 MPa , N二max5.0216,6.5182,19.07=19.07-45 度，b = 1598.5 800.7 2001 .6MP,N=max 0.6783,16.2085,19.0629 )=19.0629代入最大正应力准则进行校核，经比较得,N

7、=31.48,所以共需要31.48*2=62.96层当0度铺层占10%,90度铺层占20%时，则45度和-45度各占35%时0 度b = 27248 -183 535 7 , N=11.5790 度b = - 10498 1583 -5341 MPa , N=32.04+45度o- = 14048 434 1779 MP, N= 16.94-45 度b = 2702.2 965.5 1778 7 MPa, N=19.53经比较得,N=32.04,所以共需32.04*2=64.08层当0度铺层占10%,90度铺层占25%时,45度和-45度各占32.5%0 度,b = 27327 - 90 56

8、5 MPa , N= 11.690 度，b = 9092 1614.5 一 565.3MPa , N= 32.682245 度,7)= 15117 481 1716 MP, N 二 16.3429-45 度,b = 3118 .7 1042.9 1716.1.7 MPa , N= 21.1113经比较得,N=32.68,所以共需要32.68*2=65.36层(5)当0度铺层占10%,90度铺层占30%时，则45度和-45度各占30%时0 度(t = 27618 - 9 606/MP, N=11.7290 度b = -7933 1655 599.8 ，N= 15.95+45 度 Q = 1620

9、7 525 -1675 z MPa , N=22.67-45 度b = 3477 .2 1120.6 1675 / MPa , N=33.49经比较得,N=33.49,所以共需要33.49*2=66.98层当0度铺层占10%,90度铺层占40%时，则45度和-45度各占25%时90度b = _6107.8 1760.9 683MPa, N=15.64+45 度b = 18561 606 一 1642MP , N=26045 度b = 4062 1285 1642 MP, N=3565经比较得,N=3565,所以共需要35.65*2=71.3层当0度铺层占10%,90度铺层占50%时,45度和-

10、45度各占20%0, 7 = 30507 255 793皿，N= 12.9590 度,cr = -4691 .8 1902.6 一793.5，MP , N= 3&545 度,b = 21327 685 -1659MPa , N= 15.8-45 度,b = 4888 1472.9 1658 .6 MPa , N=14.3经比较得,N=38.5,所以共需要38.5*2=77层当0度铺层占10%,90度铺层占60%时,则45度和-45度各占15%时0 度b = 32990 378 946MP , N= 1490 度(7 = -3607 2086 .3 - 946.2 MPa , N=42.2+45

11、 度b = 24781 762 -1720 MPa , N=16.3-45 度b = 4701 1702 1720 MPa , N=34.46经比较得,N=42.2,所以共需要42.2*2=84.4层(9)当0度铺层占10%,90度铺层占75%时，则45度和-45度各占6.25%时0 度r = 39942 622 1450 7 MA/, N= 16.9590 度b = -1729.6 2572 -1449 .87 MPa , N=52.07+45 度cr = 34490 877 一 1964 MPa , N=1 &7-45 度b = 3722 2317 1963 .51 MPa , N=46.

12、9经比较得,N=52.07,所以共需要52.07*2=104.14层(10)当0度铺层占25%,90度铺层占0%时，则45度和-45度各占37.5%时0 度b = 20231 -568 507 ，N=8.5883+45 度 Q = 8284.7 - 9.1 一 1632 MPa, N= 15.55经比较得,N=1555,所以共需要15.55*2=31.10层(11)当0度铺层占25%,90度铺层占10%时，则45度和-45度各占32.5%时0度t) = 19118 -265 565MP“，N=8.1190 度b = 9458.5 1072 .5 一 563.5MPa , N=21.71+45

13、度b = 10829 126 一 1347 MPa , N=13.85-45 度b = 1169.4 684.5 1346.5MP , N= 12.83经比较得,N=21.71，所以共需要21.71 *2=43.42层(12)当0度铺层占25%,90度铺层占25%时，则45度和-45度各占25%时0 度,b = 19099 -18 683MP, N= 8.190 度,b = 5669.7 1141 -683.27 MPd , N=23.0945 度,b = 13964 222 -1167 7 MPa , N=max5.93,4.5,11.1)=11.1-45 度,b = 534.6 900.6

14、 11677 MPa , N=max(0.36,18.23,11.1 =18.23经比较得,N=23.09,所以共需要23.09*2=46.18层(13)当0度铺层占25%,90度铺层占50%时，则45度和-45度各占12.5%时0 度b = 21050 227 1047 y MPa , N=9.9790 度b = - 2452.1 1327 .3 -1047 7 MPa , N=26.8+45 度 Q = 20408 257 一 1107 MPa , N= 10.54-45 度b = 1809.8 1297 1107 MPa , N=26.21经比较得,N=26.8,所以共需要26.8*2=

15、53.6层(14)当0度铺层占50%,90度铺层占0%时，则45度和-45度各占25%时0 度b = 12870 - 357 683，N=6.590 度cr = -9106.8 471.7 一683.2MP , N=9.55+45 度b = 9131.3 -182.1 一 1035 .6MPa , N=9.86-45 度b = - 5367 .7 496.6 1035 .61 MPa , N= 11.05经比较得,N=11.05,所以共需要11.05*2=22层(15)当0度铺层占50%,90度铺层占10%时，则45度和-45度各占20%时90 度b = 5492.7 718.4 - 793.

16、5 MP“，N=1454+45 度 Q = 11957 -98 - 851MP, N=8.145 度b = 4882 689.8 851MPa, N=13.96经比较得,N=14.54,所以共需要14.54*2=29.08层(16)当0度铺层占50%,90度铺层占25%时,则45度和45度各占12.5%时0 度b = 12812 52 1047 J MPa , N=9.9790 度b = 2819.9 783.4 -1047 z MPr/, N= 15.85+45 度b = 16105 -102 -737MP“，N=701-45 度b = 6112.9 937.6 736.6，N=1 &97经

17、比较得,N=1&97,所以共需要18.97*2=37.94层在图表中表示如下:0度铺层 比例90度铺 层比例层合板 层数层合板 厚度 (mm)层合板 质量(g)取整数 层取整后 每层厚 度(mm)最先破 坏层10%0%47.426.354352.6010480.1342%10%10%62.968.436667.9145640.1318a 2210%20%64.088.586769.1230640.1342。2210%25%65.368.758270.5075660.1368。2210%30%66.988.975372.2510680.1360a 2210%40%71.39.554276.911

18、57201327。2210%50%7710.318083.06780.1323。2210%60%84.411.309691.0425840.1346。2210%75%104.1413.9548112.33610401342。2225%0%31.104.167433.4671320.13021225%10%43.425.818346.8373440.1322。2225%25%46.18688149.8142460.134525%50%53.67.182457.8183540.1330。2250%0%22.12.94829.3189220.134。2250%10%29.083.896731.368

19、4300.1299。2250%25%37.945.08440.9262380.1338。22从上表中可以看岀，当0度铺层占50%,90度铺层占0%时，则45度和-45度各占25%时所需的层数最少，为22层，此时的重量最轻。（二） 在Task II载荷作用下已知 Longitudinal Load =-50 kN, Transverse Load =10 kN, Shear Load =10 kN外加载荷可等效为 N = J n22 nJ =-1000 100 200Sn/？对0,丄度铺设层合板o- = -7462 .7 746.3 -1492.5Z M滞入最大正应力准则得：N二max5.0&1

20、5.1.3,14.2=15.1,所以0,丄所需的最小层数为15.1层对90,丄度铺设层合板b = 746.3 - 7462 .7 1492 .57 MPaN=max0.32,40.1,14.2 =40.1,所以90$所需的最小层数为40层对(45),丄度铺设层合板45 度r = - 2262.5 一961026 MPa , N=max 1.54,0.52,9.7)=9.7-45 度a =-836.7 -162.9 -1026. if A/Pti, N=max0.57,0.88,9.7)=9.7 所以对(45),丄度铺设层合板，共需要9.7*4=38.8层，且先破坏 对(0/ 60),丄度铺设层

21、合板，0 度a = - 3248 .2 17.3 -15.91 MPa , N=max2.21,0.35,2.08)=2.21+60 度b = -623.1 -105.5 218.77 / , N=max0.42,0.57,2.08)=2.08-60 度b=772.08 -170.8 -142.SrMPa , N=max0.33,0.92,1.36)=1.36 所以对(0/60)J .度铺设层合板，共需要2.21*6=13.26层，且先破坏 比较上述四种情况，可得采用0lts度铺层所需的层数最少，为13.26层在表中可表示为:层合板铺层层和板层 数层合板厚 度(mm)层合板质 量取整数层取整后

22、 每层厚 度(mm)最先破 坏层15.12.023416.2884160.126512叽40.15.373443.24624201279O22(45)丄3&85.132241.3142400.128302(0/60)丄13.261.776814.3032140.1269%从表中可以得出：选用(0/60)”铺层时，厚度最小对0/90/(45。/-45。)铺层，设+45度和-45度的层数相同 (1)当0度铺层占10%,90度铺层占0%时，则45度和-45度各占45%时90 度cr = 12512 - 825 146MPa , N=5.31+45 度a = -3390 -80.8 1352.3丫MP

23、a , N= 12.88-45 度a = - 283.8 一 226.2 -1352 MPa , N=12.88经比较得,N=12.88,所以共需要12.88*2=25.76层(2)当0度铺层占10%,90度铺层占10%时，则45度和-45度各占40%时0 度a =-14496 274 -161 z MPa , N=max9.87,5.55,1.53 =9.8790 度a =8297.5 -792.5 160.77 , N=max3.5,4.26,1.53)=4.26+45 度cr = -4804.7 -179.2 1074 MPa , N=max 3.27,0.96,10.2=10.2-45

24、 度a=-1393 .7 - 338.9 -1074 7 MPa , N=max 0.94,1.82,10.2 =10.2 经比较得,N=10.2,所以共需要10.2*2=20.4层当0度铺层占10%,90度铺层占25%时,45度和-45度各占32.5%0 度a =-13993 85 -188 7 MPa , N=max 9.5,1.72,1.79 =9.590 度a = 5254.8 - 815.7 188.4MPa , N二max2.23,4.38,1.8 =4.38+45 度o- = - 6368 .7 - 271.6 907MPa , N二max4.3,1.46,8.6=8.6-45

25、度cr = -2369.4 - 458.8 - 9(X7 T MPa , N=max 1.6,2.5,8.6 )=8.6经比较得,N=9.5,所以共需要9.5*2=19层当0度铺层占10%,90度铺层占50%时,45度和-45度各占20%0 度cr=-15431 -100 - 264rAfPa, N=max 10.5,0.54,2.5)=10.590 度o- = 2813一954.3 264.5MPa , N二max 19,5.13,2.5二2.5+45 度a = -9115 .4 - 395.9 859.77 , N=max(6.2,2.12,8.18(=8.18-45 度 & = -350

26、2.4 - 658.7 - 859.7r MPa, N=max 2.39,3.54,8.18= 8.18 经比较得,N=10.5,所以共需要10.5*2=21层（5）当0度铺层占25%,90度铺层占0%时，则45度和45度各占37.5%时0 度a = 一 10607 368 一 169 MPa , N=7.4690 度o- = 8642.2 - 532.7 169MPa , N=3.67+45 度a = -2776 1.8 907 7 A/Pn , N=8.64-45 度o- = 810.88 -166 一907 MPa , N=8.64经比较得,N=8.64,所以共需要&64*2=17.28

27、层当0度铺层占25%,90度铺层占10%时,45度和-45度各占32.5%0 度a = -9882 192.9 -188.4MPd , N=max6.7,3.9,1.8=6.790 度a = 5745 .8 - 538.6 188.47 , N=max2.4,2.9,1.8)=2.9+45 度a = -4067 .8 79.3 736.4MPa , N二max2.8,1.6,7.0 =7.0-45 度a= -68.47 - 266.47 一736.4MPa , N=max0.05,l.43,7.0=7.0经比较得,N=7.0,所以共需要7*2=14层当0度铺层占25%,90度铺层占25%时,4

28、5度和-45度各占25%0 度a =-9744.5 52 一 227.7MPa , N二max6.6,1.05,2.2 =6.690 度a = 3546.2 - 570.1 227 J7 MPa, N=max1.5,3.1,2.2)=3.1+45 度a = -5515 .7 -145.9 626.37 , N=max 3.8,0.8,5.96)=5.96-45 度a =-682.7 一372一626.3 MPa , N二max0.5,2,5.96=5.96经比较得,N=6.6,所以共需要6.6*2=13.2层当0度铺层占25%,90度铺层占50%时,45度和-45度各占12.5%0 度a = -10611 -84 -3497 MPa , N=max7.2,0.45,3.3 =7.290 度a = 1704.5 - 660.5 349MPa , N二max0.7,3.6,3.3=3.6