機(jī)械優(yōu)化設(shè)計(jì)作業(yè)

1、機(jī)械優(yōu)化設(shè)計(jì)作業(yè)在MATLAB下編程如下：在MATLAB下編程如下：先編寫M文件，建立目標(biāo)函數(shù)function f=zuoye2(x)f=-x(1)*x(2)*x(3); 主程序如下： x0=1;1;1;A=-1,-2 ,-2;1,2,2;b=0;72;lb=zeros(3,1);x,fval,exitflag,output=fmincon(zuoye2,x0,A,b,lb)Warning: Trust-region-reflective algorithm does not solve this type of problem, using active-setalgorithm. You

2、could also try the interior-point or sqp algorithms: set the Algorithm option tointerior-point or sqp and rerun. For more help, see Choosing the Algorithm in the documentation. In fmincon at 472Local minimum possible. Constraints satisfied.fmincon stopped because the predicted change in the objectiv

3、e functionis less than the default value of the function tolerance and constraints were satisfied to within the default value of the constraint tolerance.Active inequalities (to within options.TolCon = 1e-006): lower upper ineqlin ineqnonlin 2 x = 23.9997 12.0001 12.0001fval = -3.4560e+003exitflag =

4、 5output = iterations: 9 funcCount: 42 lssteplength: 1 stepsize: 3.3708e-004 algorithm: medium-scale: SQP, Quasi-Newton, line-search firstorderopt: 0.0025 constrviolation: 0 message: 1x777 char 由題，先選取設(shè)計(jì)變量。一、設(shè)計(jì)變量由于材料已經(jīng)給定，其質(zhì)量只是內(nèi)徑d、外徑D、跨距L及外伸端a的函數(shù)。因此設(shè)計(jì)變量為X=x1,x2,x2T=l,D,aT (1)二、目標(biāo)函數(shù)依據(jù)題意，以主軸自身質(zhì)量最小為設(shè)計(jì)目標(biāo)，

5、即Fx=14x1+x3x22-d2 (2)為材料密度。三、約束條件1）撓度要求y=Fa2(l+a)3EIy0 (3)上式中慣性矩I=(D4-d4)64,E為主軸彈性模量。將I、E代入得：64Fx32(x1+x3)3E(x24-d4)y0 (4)2)強(qiáng)度要求max=MmaxWz (5)Wz=(D4-d4)32D (6)由(5)(6)式可得：32Fx2x3(x24-d4) (7)3)邊界約束條件300x1650,60x2110,90x3150 (8)四、將物理模型轉(zhuǎn)化為數(shù)學(xué)模型minfx=14x1+x3x22-d2 (9)S.t.(10)在MATLAB中先建立目標(biāo)函數(shù)M文件function f=m

6、yfun(x)f=6.16225*(x(1)+x(3)*(x(2)2-900)/1000000;因?yàn)榧s束為非線性，所以同樣建立非線性約束M文件function c,ceq=mycon(x)F=15000;y0=0.05;c(1)=9.71*x(3)2*(x(1)+x(3)/(x(2)4-304)-1;c(2)=32*F*x(2)*x(3)/(3.14*(x(2)4-304)*180)-1;ceq=;在MATLAB命令窗口給出初始搜索值和線性約束，并調(diào)用優(yōu)化程序：a=-1/300 0 0 0 -1/60 0 0 1/110 0 0 0 -1/90; 注：相比較式（10）的約束作了一個(gè)變形b=-1

7、;-1;1;-1; x0=300;100;100; lb=zeros(3,1);x,fval,exitflag,output=fmincon(myfun,x0,a,b,lb,mycon)Warning: Trust-region-reflective algorithm does not solve this type of problem, using active-setalgorithm. You could also try the interior-point or sqp algorithms: set the Algorithm option tointerior-point o

8、r sqp and rerun. For more help, see Choosing the Algorithm in the documentation. In fmincon at 472Local minimum found that satisfies the constraints.Optimization completed because the objective function is non-decreasing in feasible directions, to within the default value of the function tolerance,a

9、nd constraints were satisfied to within the default value of the constraint tolerance.Active inequalities (to within options.TolCon = 1e-006): lower upper ineqlin ineqnonlin 1 1 4 x = 300.0000 74.9069 90.0000fval = 11.3220exitflag = 1output = iterations: 7 funcCount: 33 lssteplength: 1 stepsize: 2.9

10、587e-005 algorithm: medium-scale: SQP, Quasi-Newton, line-search firstorderopt: 1.1603e-009 constrviolation: 1.6105e-012 message: 1x788 char經(jīng)比較可發(fā)現(xiàn)和此前的結(jié)果一致。同上，先建立目標(biāo)函數(shù)M文件function f=fun(x)f=(x(1)-3)2+x(2)2;再建立非線性約束M文件function c,ceq=funcon(x)c(1)=x(1)2+x(2)-4;ceq=;在MATLAB命令窗口給出初始搜索值和線性約束，并調(diào)用優(yōu)化程序： x0=1,1; a=-1 0;0 -1 b=-0.5;0 lb=zeros(2,1) x,fval,exitflag,output=fmincon(fun,x0,a,b,lb,funcon)Active inequalities (to within options.TolCon = 1e-006): lower upper ineqlin ineqnonlin 2 2 1x = 2.0000 0fval = 1.0000exitflag = 1output = iterations: 4 funcCount: 1