2010年我校参加全国大学生数学建模竞赛获全国二等奖论文A题

plot(hi,ti,x,y1); average=mean(ti); s=std(ti);

h2=0.1+0.4*tan(4.1*pi/180);

f=(b^2/2*asin((-y*tan(4.1*pi/180)+h2-b)/b)+((-y*tan(4.1*pi/180)+h2-b)/2)*sqrt(b^2-(-y*tan(4.1*pi/180)+h2-b)^2)+b^2*pi/4)*2*a/b; d=int(f,0,h2/tan(4.1*pi/180)); eval(d);

vv=[];

hii=0.15:0.01:1.17;

h11=hii+0.4*tan(4.1*pi/180); for i=1:length(h11)

f=(b^2/2*asin((-y*tan(4.1*pi/180)+h11(i)-b)/b)+((-y*tan(4.1*pi/180)+h11(i)-b)/2)*sqrt(b^2-(-y*tan(4.1*pi/180)+h11(i)-b)^2)+b^2*pi/4)*2*a/b;

d=int(f,0,2.45); vv=[vv eval(d)]; end

vv=vv*1000; vv'

vvv=[];

hiii=0:0.01:0.15;

h111=hiii+0.4*tan(4.1*pi/180); for i=1:length(h111)

f=(b^2/2*asin((-y*tan(4.1*pi/180)+h111(i)-b)/b)+((-y*tan(4.1*pi/180)+h111(i)-b)/2)*sqrt(b^2-(-y*tan(4.1*pi/180)+h111(i)-b)^2)+b^2*pi/4)*2*a/b;

d=int(f,0,h111(i)/tan(4.1*pi/180)); vvv=[vvv eval(d)]; end

vvv=vvv*1000; format long; vvv'

vvvv=[];

hiiii=1.18:0.01:1.2;

h1111=1.2-hiiii+2.05*tan(4.1*pi/180); for i=1:length(h1111)

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f=(b^2/2*asin((-y*tan(4.1*pi/180)+h1111(i)-b)/b)+((-y*tan(4.1*pi/180)+h1111(i)-b)/2)*sqrt(b^2-(-y*tan(4.1*pi/180)+h1111(i)-b)^2)+b^2*pi/4)*2*a/b;

d=int(f,0,h1111(i)/tan(4.1*pi/180)); vvvv=[vvvv eval(d)]; end

vvvv=pi*a*b*l*1000-vvvv*1000; format long; vvvv'

附录三：

用来求纵向倾斜时的体积：

syms y;

a=3;R=1.625;

%第一部分体积 h=0:0.1:0.3;

h1=h+2*tan(a*pi/180); y0=[];

for i=1:length(h1)

f1=(y-0.625)^2+(-y*tan(a*pi/180)+h1(i)-1.5)^2-1.625^2; x0=solve(f1);

y0=[y0 min(eval(x0))]; end y0'

v11=[]; v12=[];

for i=1:length(h1) %求左球冠体积

f2=((R^2-(0.625-y)^2)/2*asin((h1(i)-y*tan(a*pi/180)-1.5)/(sqrt(R^2-(0.625-y)^2)))+((h1(i)-y*tan(a*pi/180)-1.5)/2)*sqrt(R^2-(0.625-y)^2-(h1(i)-y*tan(a*pi/180)-1.5)^2)+pi*(R^2-(0.625-y)^2)/4)*2; t=y0(i);

d2=int(f2,t,0); v11=[v11 eval(d2)];

%求圆柱体积

f3=((1.5^2)/2*asin((-y*tan(a*pi/180)+h1(i)-1.5)/1.5)+((-y*tan(a*pi/180)+h1(i)-1.5)/2)*sqrt(1.5^2-(-y*tan(a*pi/180)+h1(i)-1.5)^2)+pi*1.5^2/4)*2;

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d3=int(f3,0,(h1(i))/(tan(a*pi/180))); v12=[v12 eval(d3)]; end

v1=v11+v12;

disp('第一部分的体积'); v1'

%第二部分体积 h=0.4:0.1:1.3;

h1=h+2*tan(a*pi/180); y0=[];

%求水平面与左球冠的交点 for i=1:length(h1)

f1=(y-0.625)^2+(-y*tan(a*pi/180)+h1(i)-1.5)^2-1.625^2; x0=solve(f1);

y0=[y0 min(eval(x0))]; end %y0

v21=[]; v22=[]; v23=[];

for i=1:length(h1) %求左球冠体积

f2=((R^2-(0.625-y)^2)/2*asin((h1(i)-y*tan(a*pi/180)-1.5)/(sqrt(R^2-(0.625-y)^2)))+((h1(i)-y*tan(a*pi/180)-1.5)/2)*sqrt(R^2-(0.625-y)^2-(h1(i)-y*tan(a*pi/180)-1.5)^2)+pi*(R^2-(0.625-y)^2)/4)*2; t=y0(i);

d2=int(f2,t,0); v21=[v21 eval(d2)];

%求圆柱体积

f3=((1.5^2)/2*asin((-y*tan(a*pi/180)+h1(i)-1.5)/1.5)+((-y*tan(a*pi/180)+h1(i)-1.5)/2)*sqrt(1.5^2-(-y*tan(a*pi/180)+h1(i)-1.5)^2)+pi*1.5^2/4)*2;

d3=int(f3,0,8); v22=[v22 eval(d3)];

%求水平面与右球冠的交点

f4=(y-7.375)^2+(-y*tan(a*pi/180)+h1(i)-1.5)^2-1.625^2; x00=solve(f4);

y00=max(eval(x00));

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%求右球冠体积

f5=((R^2-(y-7.375)^2)/2*asin((h1(i)-y*tan(a*pi/180)-1.5)/(sqrt(R^2-(y-7.375)^2)))+((h1(i)-y*tan(a*pi/180)-1.5)/2)*sqrt(R^2-(y-7.375)^2/2-(h1(i)-y*tan(a*pi/180)-1.5)^2)+pi*(R^2-(y-7.375)^2)/4)*2; y00

d4=int(f5,8,y00); v23=[v23 eval(d4)]; end

v2=v21+v22+v23;

disp('第二部分的体积'); v2'

%第三部分体积 h=1.4:0.1:1.8;

h1=h+2*tan(a*pi/180); y0=[];

%求水平面与左球冠的交点 for i=1:length(h1)

f1=(y-0.625)^2+(-y*tan(a*pi/180)+h1(i)-1.5)^2-1.625^2; x0=solve(f1);

y0=[y0 min(eval(x0))]; end y0'

v311=[]; v312=[]; v31=[]; v32=[]; v33=[]; v3=[];

for i=1:length(h1) %求左球冠体积

f2=((R^2-(0.625-y)^2)/2*asin((h1(i)-y*tan(a*pi/180)-1.5)/(sqrt(R^2-(0.625-y)^2)))+((h1(i)-y*tan(a*pi/180)-1.5)/2)*sqrt(R^2-(0.625-y)^2-(h1(i)-y*tan(a*pi/180)-1.5)^2)+pi*(R^2-(0.625-y)^2)/4)*2; t=y0(i);

d2=int(f2,t,0);

v311=[v311 eval(d2)];

f6=pi*(R^2-(0.625-y)^2); t=y0(i);

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