机械优化设计课程作业.pdf

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1、 机械优化设计 课程作业 姓名：薛中玉 学号:s20066109 盖板问题 1 设有一箱形盖板,已知长度cml600 0 =，宽度mb60=，厚度cmts5 . 0=。翼板厚度为 f t)(cm，它承受最大的单位载荷MPaq01. 0=，要求在满足强度刚度和稳定性等条件 下，设计一个重量最轻的结构方案。 设计变量： 12 , T T f Xx xth= 目标函数： min. 21 120)(xxxf+= 设计约束：按照强度，刚度和稳定性要求建立如下的约束条件。 01 320 1 1/ )( 01 45 7 1/)( 01 45 7 1/ )( 0125. 01/ )( 0)( 0)( 2 2

2、16 2 3 1max5 21max4 2max3 22 11 = = = = = = xxffxg xxxg xxxg xxg xxg xxg k 程序运行结果分析： 1以下四次运行结果为设计变量 x0 发生变化时对结果的影响： 结果一： N KG KH -PRIMARY DATA- N= 2 KG= 6 KH= 0 X: .5000 10.0000 BL: .0000 .0000 BU: 20.0000 100.0000 EP: EPS: C: H0: R: .0000100 .0000100 .700 .010 3.000 -OPTIMUM SOLUTION- IRC= 35 IQU=

3、190 IXF= 1027 R = .162351E-04 F0= .855803E+02 X : .465418E+00 .296999E+02 FX= .855501E+02 GX: .465418E+00 .296999E+02 .642498E+01 .115022E+01 .752890 E-03 .277224E+00 HX: Stop - Program terminated. 结果二： N KG KH -PRIMARY DATA- N= 2 KG= 6 KH= 0 X: .7000 20.0000 BL: .0000 .0000 BU: 20.0000 100.0000 EP:

4、 EPS: C: H0: R: .0000100 .0000100 .700 .010 3.000 -OPTIMUM SOLUTION- IRC= 35 IQU= 190 IXF= 1027 R = .162351E-04 F0= .855803E+02 X : .465418E+00 .296999E+02 FX= .855501E+02 GX: .465418E+00 .296999E+02 .642498E+01 .115022E+01 .752890 E-03 .277224E+00 HX: Stop - Program terminated. 结果三： N KG KH -PRIMAR

5、Y DATA- N= 2 KG= 6 KH= 0 X: 2.0000 40.0000 BL: .0000 .0000 BU: 20.0000 100.0000 EP: EPS: C: H0: R: .0000100 .0000100 .700 .010 3.000 -OPTIMUM SOLUTION- IRC= 35 IQU= 181 IXF= 918 R = .162351E-04 F0= .855500E+02 X : .471100E+00 .289879E+02 FX= .855199E+02 GX: .471100E+00 .289879E+02 .624698E+01 .11243

6、0E+01 .757758 E-03 .231575E+00 HX: Stop - Program terminated. 结果四： N KG KH -PRIMARY DATA- N= 2 KG= 6 KH= 0 X: 3.0000 50.0000 BL: .0000 .0000 BU: 20.0000 100.0000 EP: EPS: C: H0: R: .0000100 .0000100 .700 .010 3.000 -OPTIMUM SOLUTION- IRC= 35 IQU= 199 IXF= 959 R = .162351E-04 F0= .939580E+02 X : .587

7、759E+00 .234186E+02 FX= .939497E+02 GX: .587759E+00 .234186E+02 .485464E+01 .114114E+01 .258475 E+00 .284427E-02 HX: Stop - Program terminated. 由运行结果可知：当初始值选的过大时，会出现一个较大的极值点。初始点的选取对循 环次数没有明显的影响，仅当选取较小时一维搜索次数有所增加。 2以下四次运行结果为惩罚因子 r 发生变化时对结果的影响： 结果一： N KG KH -PRIMARY DATA- N= 2 KG= 6 KH= 0 X: 1.0000 30

8、.0000 BL: .0000 .0000 BU: 20.0000 100.0000 EP: EPS: C: H0: R: .0000100 .0000100 .700 .010 1.000 -OPTIMUM SOLUTION- IRC= 34 IQU= 179 IXF= 868 R = .773099E-05 F0= .872718E+02 X : .519852E+00 .248794E+02 FX= .872616E+02 GX: .519852E+00 .248794E+02 .521986E+01 .101189E+01 .458866 E-01 .109153E-02 HX: St

9、op - Program terminated. 结果二： N KG KH -PRIMARY DATA- N= 2 KG= 6 KH= 0 X: 1.0000 30.0000 BL: .0000 .0000 BU: 20.0000 100.0000 EP: EPS: C: H0: R: .0000100 .0000100 .700 .010 2.000 -OPTIMUM SOLUTION- IRC= 32 IQU= 167 IXF= 831 R = .315551E-04 F0= .878807E+02 X : .404958E+00 .392512E+02 FX= .878462E+02 G

10、X: .404958E+00 .392512E+02 .881281E+01 .147257E+01 .128709 E-02 .941019E+00 HX: Stop - Program terminated. 结果三： N KG KH -PRIMARY DATA- N= 2 KG= 6 KH= 0 X: 1.0000 30.0000 BL: .0000 .0000 BU: 20.0000 100.0000 EP: EPS: C: H0: R: .0000100 .0000100 .700 .010 4.000 -OPTIMUM SOLUTION- IRC= 32 IQU= 180 IXF=

11、 1028 R = .631101E-04 F0= .857206E+02 X : .457385E+00 .307752E+02 FX= .856614E+02 GX: .457385E+00 .307752E+02 .669380E+01 .118962E+01 .149667 E-02 .347712E+00 HX: Stop - Program terminated. 结果四： N KG KH -PRIMARY DATA- N= 2 KG= 6 KH= 0 X: 1.0000 30.0000 BL: .0000 .0000 BU: 20.0000 100.0000 EP: EPS: C

12、: H0: R: .0000100 .0000100 .700 .010 5.000 -OPTIMUM SOLUTION- IRC= 34 IQU= 178 IXF= 886 R = .386549E-04 F0= .858978E+02 X : .446991E+00 .322125E+02 FX= .858513E+02 GX: .446991E+00 .322125E+02 .705312E+01 .123979E+01 .116676 E-02 .442979E+00 HX: Stop - Program terminated. 由运行结果可知：惩罚因子 r 对程序运行循环有一定的影响

13、，特别是变化较大时， 对循环次数，一维搜索次数影响都较大，对目标函数最优解也有较大的影响。 3以下四次运行结果为缩减系数 c 发生变化时对结果的影响： 结果一： N KG KH -PRIMARY DATA- N= 2 KG= 6 KH= 0 X: 1.0000 30.0000 BL: .0000 .0000 BU: 20.0000 100.0000 EP: EPS: C: H0: R: .0000100 .0000100 .500 .010 3.000 -OPTIMUM SOLUTION- IRC= 21 IQU= 134 IXF= 856 R = .286102E-05 F0= .85517

14、9E+02 X : .474699E+00 .285375E+02 FX= .855014E+02 GX: .474699E+00 .285375E+02 .613439E+01 .110727E+01 .319647 E-03 .202722E+00 HX: Stop - Program terminated. 结果二： N KG KH -PRIMARY DATA- N= 2 KG= 6 KH= 0 X: 1.0000 30.0000 BL: .0000 .0000 BU: 20.0000 100.0000 EP: EPS: C: H0: R: .0000100 .0000100 .600

15、.010 3.000 -OPTIMUM SOLUTION- IRC= 27 IQU= 143 IXF= 756 R = .511746E-05 F0= .855237E+02 X : .475628E+00 .284292E+02 FX= .855046E+02 GX: .475628E+00 .284292E+02 .610730E+01 .110338E+01 .427779 E-03 .195943E+00 HX: Stop - Program terminated. 结果三： N KG KH -PRIMARY DATA- N= 2 KG= 6 KH= 0 X: 1.0000 30.00

16、00 BL: .0000 .0000 BU: 20.0000 100.0000 EP: EPS: C: H0: R: .0000100 .0000100 .800 .010 3.000 -OPTIMUM SOLUTION- IRC= 47 IQU= 237 IXF= 1119 R = .104535E-03 F0= .858202E+02 X : .452736E+00 .314233E+02 FX= .857515E+02 GX: .452736E+00 .314233E+02 .685581E+01 .121300E+01 .190377 E-02 .390787E+00 HX: Stop

17、 - Program terminated. 结果四： N KG KH -PRIMARY DATA- N= 2 KG= 6 KH= 0 X: 1.0000 30.0000 BL: .0000 .0000 BU: 20.0000 100.0000 EP: EPS: C: H0: R: .0000100 .0000100 .900 .010 3.000 -OPTIMUM SOLUTION- IRC= 84 IQU= 424 IXF= 1918 R = .477803E-03 F0= .859303E+02 X : .453941E+00 .313239E+02 FX= .857969E+02 GX

18、: .453941E+00 .313239E+02 .683098E+01 .121188E+01 .406378 E-02 .385689E+00 HX: Stop - Program terminated. 由运行结果可知：当缩减系数 c 增大时，各种循环搜索次数都有明显的增加。目标 函数最优值值也有所增加。 综合分析，惩罚因子 r 过大、过小均不好， ，缩减系数 c 的取值范围建议 0.1 到 0.7 之间，x 的初值取值要求在可行域内，尽量不要靠近边界。 工程实际问题 一楼顶要上吊建筑材料，需在楼顶垂直墙面安装起重滑轮支架。结构如图：起重最 大质量为1万牛顿， 两杆均采用实心圆柱杆状优

19、质钢材， 许用抗压、 抗拉应力分别为300 兆帕、160兆帕，AD最大距离为1000mm。 要求：满足强度的条件下，通过对两杆直径d1,d2及2杆长度L2的优化设计使两杆 质量总和最小。 设计分析：由于C点受力，将力平移至B点，产生一瞬时针的附加力矩M，使AB 段受拉力，BD段受压力，AC杆上应力最大点在支撑点B点的上边，其大小为力F产 生的拉应力与力矩M产生的拉应力的最大值之和。约束函数共包括11个不等式约束， 1个等式约束。11个不等式约束包含几何形状约束及力学性能约束，等式约束即直角三 角形ABD应满足的勾股定理。 设计变量： 123451212 , , , TT Xx x x x xd

20、 d l l h= 目标函数：min. 322 124 ( )10f xxx x=+ 约束函数： 11 22 33 44 55 654 75 3 83 3 934 ( )0 ( )0 ( )0 ( )0 ( )0 ( )0 ( )8000 ( )100 ( )100 g xx gxx gxx gxx gxx gxxx gxx gxx gxxx = = = = = = = = = 10( ) gx = 4 4 2 2 4*10 3000 x x 11( ) gx = 434 33 23 151 4*10 (10)32*10 1600 xx x xx + 3222 1354 h (x)=(10 -

21、x ) +x -x =0 程序运行结果分析： 1以下三次运行结果为设计变量初值发生变化时对结果的影响： 结果一： N KG KH -PRIMARY DATA- N= 5 KG= 11 KH= 1 X: 30.0000 30.0000 500.0000 700.0000 300.0000 BL: 10.0000 10.0000 .0000 500.0000 200.0000 BU: 100.0000 100.0000 700.0000 1500.0000 1000.0000 EP: EPS: C: H0: R: .0000100 .0000100 .700 .010 3.000 -OPTIMUM

22、 SOLUTION- IRC= 4 IQU= 42 IXF= 253 R = .102900E+01 F0= .207259E+06 X : .107677E+02 .865420E+01 .426766E-02 .121379E+04 .687972E +03 FX= .206850E+06 GX: .107677E+02 .865420E+01 .426766E-02 .121379E+04 .687972E +03 .525822E+03 .112028E+03 .999996E+03 .626506E-01 .298418E- 01 .213798E+03 HX: .330369E+0

23、0 Stop - Program terminated. 结果二： N KG KH -PRIMARY DATA- N= 5 KG= 11 KH= 1 X: 50.0000 50.0000 300.0000 1000.0000 500.0000 BL: 10.0000 10.0000 .0000 500.0000 200.0000 BU: 100.0000 100.0000 700.0000 1500.0000 1000.0000 EP: EPS: C: H0: R: .0000100 .0000100 .700 .010 3.000 -OPTIMUM SOLUTION- IRC= 4 IQU=

24、 42 IXF= 253 R = .102900E+01 F0= .207259E+06 X : .107677E+02 .865420E+01 .426766E-02 .121379E+04 .687972E +03 FX= .206850E+06 GX: .107677E+02 .865420E+01 .426766E-02 .121379E+04 .687972E +03 .525822E+03 .112028E+03 .999996E+03 .626506E-01 .298418E- 01 .213798E+03 HX: .330369E+00 Stop - Program termi

25、nated. 结果三： N KG KH -PRIMARY DATA- N= 5 KG= 11 KH= 1 X: 60.0000 60.0000 200.0000 1200.0000 700.0000 BL: 10.0000 10.0000 .0000 500.0000 200.0000 BU: 100.0000 100.0000 700.0000 1500.0000 1000.0000 EP: EPS: C: H0: R: .0000100 .0000100 .700 .010 3.000 -OPTIMUM SOLUTION- IRC= 2 IQU= 54 IXF= 356 R = .2100

26、00E+01 F0= .540659E+06 X : .212135E+02 .860380E+01 .147847E-01 .122064E+04 .699989E +03 FX= .540372E+06 GX: .212135E+02 .860380E+01 .147847E-01 .122064E+04 .699989E +03 .520650E+03 .100011E+03 .999985E+03 .658747E-01 .119423E +03 .220653E+03 HX: -.384646E+01 Stop - Program terminated. 由三套结果可知： 当第三次初

27、始点取的较大时， 目标函数值出现一个较大的极值点， 循环次数也增加了。 2以下三次运行结果为惩罚因子r发生变化时对结果的影响： 结果一： N KG KH -PRIMARY DATA- N= 5 KG= 11 KH= 1 X: 50.0000 50.0000 300.0000 1000.0000 500.0000 BL: 10.0000 10.0000 .0000 500.0000 200.0000 BU: 100.0000 100.0000 700.0000 1500.0000 1000.0000 EP: EPS: C: H0: R: .0000100 .0000100 .700 .010 2

28、.000 -OPTIMUM SOLUTION- IRC= 3 IQU= 31 IXF= 234 R = .980000E+00 F0= .207241E+06 X : .107676E+02 .865403E+01 .406750E-02 .121379E+04 .687971E +03 FX= .206846E+06 GX: .107676E+02 .865403E+01 .406750E-02 .121379E+04 .687971E +03 .525823E+03 .112029E+03 .999996E+03 .503437E-01 .443668E- 01 .213798E+03 H

29、X: .271189E+00 Stop - Program terminated. 结果二： N KG KH -PRIMARY DATA- N= 5 KG= 11 KH= 1 X: 50.0000 50.0000 300.0000 1000.0000 500.0000 BL: 10.0000 10.0000 .0000 500.0000 200.0000 BU: 100.0000 100.0000 700.0000 1500.0000 1000.0000 EP: EPS: C: H0: R: .0000100 .0000100 .700 .010 3.000 -OPTIMUM SOLUTION

30、- IRC= 4 IQU= 42 IXF= 253 R = .102900E+01 F0= .207259E+06 X : .107677E+02 .865420E+01 .426766E-02 .121379E+04 .687972E +03 FX= .206850E+06 GX: .107677E+02 .865420E+01 .426766E-02 .121379E+04 .687972E +03 .525822E+03 .112028E+03 .999996E+03 .626506E-01 .298418E- 01 .213798E+03 HX: .330369E+00 Stop -

31、Program terminated. 结果三： N KG KH -PRIMARY DATA- N= 5 KG= 11 KH= 1 X: 50.0000 50.0000 300.0000 1000.0000 500.0000 BL: 10.0000 10.0000 .0000 500.0000 200.0000 BU: 100.0000 100.0000 700.0000 1500.0000 1000.0000 EP: EPS: C: H0: R: .0000100 .0000100 .700 .010 4.000 -OPTIMUM SOLUTION- IRC= 3 IQU= 41 IXF=

32、293 R = .196000E+01 F0= .207562E+06 X : .107784E+02 .865439E+01 .593869E-02 .121380E+04 .687978E +03 FX= .207086E+06 GX: .107784E+02 .865439E+01 .593869E-02 .121380E+04 .687978E +03 .525818E+03 .112022E+03 .999994E+03 .775801E-01 .214822E +00 .213802E+03 HX: .817821E+00 Stop - Program terminated. 由运

33、行结果可看出： 对本题而言惩罚因子的大小变化对目标函数的最优点没有产生 较大的影响，但太小时对循环次数有一定的影响。 3以下三次运行结果是缩减系数c发生变化对结果的影响： 结果一： N KG KH -PRIMARY DATA- N= 5 KG= 11 KH= 1 X: 50.0000 50.0000 300.0000 1000.0000 500.0000 BL: 10.0000 10.0000 .0000 500.0000 200.0000 BU: 100.0000 100.0000 700.0000 1500.0000 1000.0000 EP: EPS: C: H0: R: .000010

34、0 .0000100 .500 .010 3.000 -OPTIMUM SOLUTION- IRC= 4 IQU= 42 IXF= 263 R = .375000E+00 F0= .207057E+06 X : .107635E+02 .865409E+01 .293958E-02 .121380E+04 .687971E +03 FX= .206757E+06 GX: .107635E+02 .865409E+01 .293958E-02 .121380E+04 .687971E +03 .525824E+03 .112029E+03 .999997E+03 .548493E-01 .124

35、129E- 01 .213798E+03 HX: .324293E+00 Stop - Program terminated. 结果二： N KG KH -PRIMARY DATA- N= 5 KG= 11 KH= 1 X: 50.0000 50.0000 300.0000 1000.0000 500.0000 BL: 10.0000 10.0000 .0000 500.0000 200.0000 BU: 100.0000 100.0000 700.0000 1500.0000 1000.0000 EP: EPS: C: H0: R: .0000100 .0000100 .700 .010 3

36、.000 -OPTIMUM SOLUTION- IRC= 4 IQU= 42 IXF= 253 R = .102900E+01 F0= .207259E+06 X : .107677E+02 .865420E+01 .426766E-02 .121379E+04 .687972E +03 FX= .206850E+06 GX: .107677E+02 .865420E+01 .426766E-02 .121379E+04 .687972E +03 .525822E+03 .112028E+03 .999996E+03 .626506E-01 .298418E- 01 .213798E+03 H

37、X: .330369E+00 Stop - Program terminated. 结果三： N KG KH -PRIMARY DATA- N= 5 KG= 11 KH= 1 X: 50.0000 50.0000 300.0000 1000.0000 500.0000 BL: 10.0000 10.0000 .0000 500.0000 200.0000 BU: 100.0000 100.0000 700.0000 1500.0000 1000.0000 EP: EPS: C: H0: R: .0000100 .0000100 .800 .010 3.000 -OPTIMUM SOLUTION

38、- IRC= 3 IQU= 31 IXF= 210 R = .192000E+01 F0= .207453E+06 X : .107725E+02 .865424E+01 .564897E-02 .121379E+04 .687972E +03 FX= .206956E+06 GX: .107725E+02 .865424E+01 .564897E-02 .121379E+04 .687972E +03 .525821E+03 .112028E+03 .999994E+03 .655436E-01 .618371E- 01 .213799E+03 HX: .185578E+00 Stop - Program terminated. 由输出结果可知：当降低系数c提高时，循环次数有所下降。目标函数的极值点没 有发生大的变化。 综上分析结果：无论改变任何初始参数，对运行结果的最优点和最优值均没有太大 的影响，因此我们可以称本程序的运行最优解为： T 6 10.7635, 8.65409, 0.03, 1213.80, 687.971 f(x)=0.206757*10 X =