易拉罐形状和尺寸的最优设计(3)

[]20070518;[]20070813第25卷第6期大学数学Vol.25,.62009年12月COLLEGEMATHEMATICSDec.2009王博1,李若超1,樊爱军2(1.,400038;2.,400038)[].,,,.,,.,,.[];;[]O172.1[]B[]16721454(2009)060138051,2006C,.21.(355ml);2.,;3.rb;4..3r:(,d=2r).h:.V:.b:.:.S:.SV:.4,.,,.,,.,1[1].,,(2).a,a2,4a2,78.5%.(2)21.5%.,,,.2,.,,().[2],..34,,.:S(r,h)=2rh+r2+r2=2[r2+rh],V=r2h.,((r+b)2-r2)(h+(1+)b)=2rhb+2r(1+)b2+hb2+(1+)b3.abr2.br2.,SVVSV(r,h)=2rhb+(1+)r2b+2r(1+)b2+hb2+(1+)b3,V(r,h)=r2h.br,b2,b3,SV(r,h)SV(r,h)S(r,h)=2rhb+r2(1+)b.g(r,h)=r2h-V,,:minS(r,h)=2rhb+r2(1+)b,g(r,h)=r2h-V=0,r0,h0.3,4.,,,.h1,h2,r1,r2,((r2+b)2-r22)(h2+(1+)b).abr21;br22;b(r1+r2)h21+(r22-r21).139第6期王博,等:易拉罐形状和尺寸的最优设计:minS(r1,r2,h1,h2)=2r2h2b+r22b+r21b+b(r1+r2)h21+(r22-r21),g(r1,r2,h1,h2)=r22h2+h1(r21+r22+r1r2)3-V=0,r0,h0.51.,1.1(:)12.2681.25211.0165.4626.5940.0160.04815,370,380.3,hr1.86.2.V,,r,h,r,h.Lagrange.h=h(r),S(r,h)S(r,h(r)),gr+ghdhdr=0.,(r0,h0)S(r,h)dSdrr=r0h=h0=Sr+Shdhdr=Sr-Shgrgh=0.LagrangeL(r,h,)=S(r,h)-g(r,h),,(r0,h0):Lr=Sr-gr=0,Lh=Sh-gh=0,L=g=0.2,0,L(r,h,)=b[2rh+(1+)r2]-[r2h-V],Lr=b[2(1+)r+2h]-2rh=0,(1)Lh=2br-r2=r(2b-r)=0,(2)L=-(r2h-V)=0.(3)(2),(3)h=Vr2,=2br,(1)h=(1+)r.=3,h=4r=2d,2,1.86.3.3,,Matlab7.01,,.,=3,b=0.016,V=355;,115,0.2,:r1=2.8,r2=3.3,h1=1.3,h2=10.8.,,.4.,,.,,,.140大学数学第25卷,.,,.,,.,,,,,,..,,(0.6181)..,.,5.,10.C25,A35.,355,B.Br1,r2,Ar3,Bh.B,,6,x2r21-y2r21-h224(r22-r21)=1.V=h2-h2f2(y)dx.V=h2-h2r21+4(r22-r21)y2h2=355,(4)2r2=0.618h.(5)10,8[3],36,18,5.732,2.866.,2.866r15.732.MATLAB7.01,r10.1(4),(5),,2.2r12.8662.9663.066r23.5813.5053.428h11.58911.34411.095141第6期王博,等:易拉罐形状和尺寸的最优设计.baf(x)dxb-a6n[(y0+y2n)+4(y1+y3++y2n-1)+2(y2+y4++y2n-2)],2.866r15.73224,MATLAB7.01.(r1+r2)l,,2rh,:S1=369,S2=335,S3=331.,.,3.3(:)11.0953.0663.4283.09511.664,:,,,,[1].,.,.,,,,,[5].,.,.,,,,,.,,,,.,,.[][1],.[J].,2004,(4):17-20.[2].[R].[3].[M].:,2003.[4].[J].,2001,25(12):35.[5].[M].:,2004:184-192.OptimalDesignforShapeandSizeofCanWANGBo1,LIRuochao1,FANAijun2(1.TeamSeven,Studentbrigade,CollegeofMedicine,ThirdMilitaryUniversity,Chongqing400038,China;2.DepartmentofMathematics,CollegeofBiomedicalEngineeringandMedicalImagine,ThirdMilitaryUniversity,Chongqing400038,China)Abstract:Thepaperfocusesontheoptimaldesignfortheshapeandsizeofcan.First,basedontherealdataforthecaninmarket,usingthemethodofLagrangemultiplicator,weverifieditsshapeandsizeisreasonable.Secondly,inordertosavemorematerialthanthenormalcanandeasytouse,aninnovativespecialdesignisprovided.Thirdly,basedontheSimpsonsformula,thesizeofthenewprojectisobtained.Keywords:optimizedmodel;Lagrangemultiplicatormethod;Simpsonsformula142大学数学第25卷