4942.sagews

modes = ['等间距模式','任意间距模式']
@interact
def _(f_x = float(0.6),f_y = float(0.26) ,a = float(1.48),b= float(8.25),sigma= float(0.025),lamda = float(0.11),dx= float(0.1),l_1 = float(0.8),aspectRatio = [[1,1,1],'automatic'],place_mode=selector(modes, buttons=True),t=input_box(default=None,label='安放位置'),symmetry=("对称排列", True)):
    dataFile=open(DATA+'result.txt','w')
    dataFile.write('计算条件：\n')
    dataFile.write('fx=%f,fy=%f,a=%f,b=%f,sigma=%f,lamba=%f,dx=%f,l1=%f\n'%(f_x,f_y,a,b,sigma,lamda,dx,l_1))
    x,y,z = var('x,y,z')
    z2_1(x,y)=f_x*(x/a)**2-f_y*(y/b)**2+sigma/2
    z2_2(x,y)=f_x-f_y*(y/b)**2
    p1=plot3d(z2_1, (x,-a,a), (y,-b,b),opacity=0.3)
    p2=plot3d(z2_2, (x,a,a+lamda), (y,-b,b),color="yellow")
    p3=plot3d(z2_2, (x,-a-lamda,-a), (y,-b,b),color="yellow")
    p4=plot3d(z2_1-sigma, (x,-a,a), (y,-b,b),color="red",opacity=0.3)

    u = var('u')
    u_1= u*(x*(sqrt(f_x)/a)-y*(sqrt(f_y)/b))==z
    u_2=x*(sqrt(f_x)/a)+y*(sqrt(f_y)/b)==u
    
    tmax = (sqrt(f_x)-sqrt(f_y))/(sqrt(f_x)/a)
    if(place_mode == '等间距模式'):
        kmax = int(tmax/dx)
        print '计算模式：等间距模式'
        print 'k的取值范围:' + str(range(-kmax,kmax+1))
        print '钢筋的间距为%.3f时,单侧的钢筋条数为%d,总共%d条'%(dx,kmax*2+1,kmax*4+2)
        dataFile.write('计算模式：等间距模式')
        dataFile.write('钢筋的间距为%.3f时,单侧的钢筋条数为%d,总共%d条'%(dx,kmax*2+1,kmax*4+2))
        dataFile.write('k的取值范围:\n' + str(range(-kmax,kmax+1)) + '\n')
    
    p51 = None
    p52 = None
    
    generatrix_u = []
    generatrix_v = []
    p91 = None
    p92 = None
    
    generatrix_fomula_u =[]
    generatrix_fomula_v =[]
    ts = []
    ts = []
    if(place_mode =='等间距模式'):
        for k in range(-kmax,kmax+1):
            ts.append(k*dx)
    elif(t == None and place_mode =='任意间距模式'):
        print '请输入间距'
        return
    elif(type(t) is int or type(t) is float or type(t)==type(1) or type(t) == type(0.1)):
        ts.append(t)
        print '请最少输入2个点'
        return
    else:
        for tx in t:
            if(type(tx) == type(1) or type(tx) is float or type(tx) == type(0.1)):
                if(not tx in ts and (tx<tmax and tx>-tmax)):
                    ts.append(tx)
                    if(symmetry and tx!=0):
                        ts.append(-tx)
    if(place_mode =='任意间距模式'):                
        print '计算模式：任意间距模式'              
        print 't的范围为[%.2f,%.2f],您输入的有效的钢筋位置:%s'%(-tmax,tmax,str(ts))
    
    dataFile.write('计算模式：任意间距模式')
    dataFile.write('t的范围为[%.2f,%.2f],您输入的有效的钢筋位置:%s'%(-tmax,tmax,str(ts)) +'\n')
    if(len(ts)==0):
        print '请输入钢筋的位置'
        return
    for tx in ts:
        if(not (type(tx) == type(1) or type(tx) is float or type(tx) == type(0.1))):
            continue
        solns = solve([u_1,u_2],x,y,u)
        solns2 = solve([u_1,u_2,u==tx*sqrt(f_x)/a ],x,z,u,solution_dict=True)
        #show(solns)
        #show(solns2)
        ####################绘制u族母线#######################
        p51= p51 + parametric_plot3d([solns2[0][x],y,solns2[0][z]],(y,-b-l_1,b+l_1),color='blue')
        ####################绘制v族母线#######################
        p52= p52 + parametric_plot3d([-solns2[0][x],y,solns2[0][z]],(y,-b-l_1,b+l_1),color='blue')
        
        
        generatrix_fomula_u.append([x==solns2[0][x], z==solns2[0][z]])
        generatrix_fomula_v.append([x==-solns2[0][x], z==solns2[0][z]])

        
        #直母线上任取两点算坐标
        solns10 = solve([solns2[0][x]==x,solns2[0][z]==z,y==0],x,y,z,solution_dict=True)
        solns11 = solve([solns2[0][x]==x,solns2[0][z]==z,y==1],x,y,z,solution_dict=True)
        
        u10 = vector([solns10[0][x],solns10[0][y],solns10[0][z]])
        u11 = vector([solns11[0][x],solns11[0][y],solns11[0][z]])
        
        u20 = u10 -u11 #直母线的方向向量
        generatrix_u.append(u20)
        #p91 +=arrow3d(u10,u11)
        
        #直母线上任取两点算坐标
        solns10 = solve([-solns2[0][x]==x,solns2[0][z]==z,y==0],x,y,z,solution_dict=True)
        solns11 = solve([-solns2[0][x]==x,solns2[0][z]==z,y==1],x,y,z,solution_dict=True)
        
        v10 = vector([solns10[0][x],solns10[0][y],solns10[0][z]])
        v11 = vector([solns11[0][x],solns11[0][y],solns11[0][z]])
        
        v20 = v10 -v11 #直母线的方向向量
        #p92 +=arrow3d(v10,v11)
        generatrix_v.append(v20) 

       
    plane1 = y==b+l_1
    u_3=z==0
    u_4=x*(sqrt(f_x)/a)+y*(sqrt(f_y)/b)==0
    
    solns3 = solve([u_3,u_4,plane1],x,y,z,solution_dict=True) 
    html('过（0，0，0）的母线与平面y=b+l1的交点坐标：$%s$'%latex(solns3))
    dataFile.write('过（0，0，0）的母线与平面y=b+l1的交点坐标：\n%s\n'%solns3)
    P1 = point((solns3[0][x],solns3[0][y],solns3[0][z]) )
    A = vector([solns3[0][x],solns3[0][y],solns3[0][z] ]) #过（0，0，0）的母线与平面y=b+l1的交点
    #p333 = point3d([solns3[0][x],solns3[0][y],solns3[0][z] ])
    B = vector([0,0,0])
    AB = B -A;  # 锚固面法向  
    
    p45 = None   
    ###############第1象限############################
    P = vector([x, y, z])
    AP = P - A;  
    grapple = AB.dot_product(AP)
    #grapple = (-sqrt(f_y)/b) *(x+( a*(b+l_1) * sqrt(f_y)/(b*sqrt(f_x))  )) + (sqrt(f_x)*(y-b-l_1)/a)
    p61 = implicit_plot3d(grapple,(x,-a-l_1,0),(y,b,b+2*l_1),(z,f_y-f_x,f_x-f_y+l_1),opacity=0.7)

    dataFile.write('第1象限中母线与锚固法线夹角:\n')
    for gener in generatrix_u:
        costheta1 = abs(gener.dot_product(AB))/( sqrt(gener.dot_product(gener)) * sqrt(AB.dot_product(AB)) )
        theta1 = arccos(costheta1)*180/ pi
        #print 'theta1=%f'%(theta1.n(30))
        dataFile.write('%.2f\t'%(theta1.n(30)))
    dataFile.write('\n第1象限中母线与锚固面的交点坐标:\n')
    for gener in generatrix_fomula_u:
        solns45 = solve([grapple==0,gener[0],gener[1]],x,y,z,solution_dict=True)
        #show(solns45)
        p45 +=point3d([solns45[0][x],solns45[0][y],solns45[0][z] ],color = 'yellow',size=7)
        dataFile.write('%.2f,%.2f,%.2f\n'%(solns45[0][x].n(30),solns45[0][y].n(30),solns45[0][z].n(30)))
    ###############第2象限############################
    P = vector([-x, y, z])
    AP = P - A;  
    grapple = AB.dot_product(AP)
    p62 = implicit_plot3d(grapple,(x,0,a+l_1),(y,b,b+2*l_1),(z,f_y-f_x,f_x-f_y+l_1),opacity=0.7)

    dataFile.write('第2象限中母线与锚固法线夹角:\n')
    for gener in generatrix_v:
        costheta2 = abs(gener.dot_product(AB))/( sqrt(gener.dot_product(gener)) * sqrt(AB.dot_product(AB)) )
        theta2 = arccos(costheta2)*180/ pi
        #print 'theta2=%f'%(theta2.n(30))
        dataFile.write('%.2f\t'%(theta2.n(30)))
    dataFile.write('\n第2象限中母线与锚固面的交点坐标:\n')
    for gener in generatrix_fomula_v:
        solns45 = solve([grapple==0,gener[0],gener[1]],x,y,z,solution_dict=True)
        #show(solns45)
        p45 +=point3d([solns45[0][x],solns45[0][y],solns45[0][z] ],color = 'yellow',size=7)
        dataFile.write('%.2f,%.2f,%.2f\n'%(solns45[0][x].n(30),solns45[0][y].n(30),solns45[0][z].n(30)))
    ###############第3象限############################
    P = vector([x, -y, z])
    AP = P - A;  
    grapple = AB.dot_product(AP)
    p63 = implicit_plot3d(grapple,(x,-a-l_1,0),(y,-b-2*l_1,-b),(z,f_y-f_x,f_x-f_y+l_1),opacity=0.7)    

    dataFile.write('第3象限中母线与锚固法线夹角:\n')
    for gener in generatrix_v:
        costheta3 = abs(gener.dot_product(AB))/( sqrt(gener.dot_product(gener)) * sqrt(AB.dot_product(AB)) )
        theta3 = arccos(costheta3)*180/ pi
        #print 'theta3=%f'%(theta3.n(30))
        dataFile.write('%.2f\t'%(theta3.n(30)))
    dataFile.write('\n第3象限中母线与锚固面的交点坐标:\n')
    for gener in generatrix_fomula_v:
        solns45 = solve([grapple==0,gener[0],gener[1]],x,y,z,solution_dict=True)
        #show(solns45)
        p45 +=point3d([solns45[0][x],solns45[0][y],solns45[0][z] ],color = 'yellow',size=7)
        dataFile.write('%.2f,%.2f,%.2f\n'%(solns45[0][x].n(30),solns45[0][y].n(30),solns45[0][z].n(30)))
    ###############第4象限############################
    P = vector([-x, -y, z])
    AP = P - A;  
    grapple = AB.dot_product(AP)
    p64 = implicit_plot3d(grapple,(x,0,a+l_1),(y,-b-2*l_1,-b),(z,f_y-f_x,f_x-f_y+l_1),opacity=0.7)
    
    dataFile.write('第4象限中母线与锚固法线夹角:\n')
    for gener in generatrix_u:
        costheta4 = abs(gener.dot_product(AB))/( sqrt(gener.dot_product(gener)) * sqrt(AB.dot_product(AB)) )
        theta4 = arccos(costheta4)*180/ pi
        #print 'theta4=%f'%(theta4.n(30))
        dataFile.write('%.2f\t'%(theta4.n(30)))
    dataFile.write('\n第4象限中母线与锚固面的交点坐标:\n')
    for gener in generatrix_fomula_u:
        solns45 = solve([grapple==0,gener[0],gener[1]],x,y,z,solution_dict=True)
        #show(solns45)
        p45 +=point3d([solns45[0][x],solns45[0][y],solns45[0][z] ],color = 'yellow',size=7)
        dataFile.write('%.2f,%.2f,%.2f\n'%(solns45[0][x].n(30),solns45[0][y].n(30),solns45[0][z].n(30)))
    ####################各母线间的交点############################
    dataFile.write('各母线间的交点：\nu-v')
    p77 = None
    for j in xrange(len(generatrix_fomula_v)):
        dataFile.write('\tv%d'%(j))
    for i in xrange(len(generatrix_fomula_u)):
        dataFile.write('\nu%d\t'%(i))
        for j in xrange(len(generatrix_fomula_v)):
            #求母线间的交点
            solns88=solve([generatrix_fomula_u[i][0],generatrix_fomula_u[i][1],generatrix_fomula_v[j][0]],x,y,z,solution_dict=True)
            #show(solns88)
            p77 +=point3d([solns88[0][x],solns88[0][y],solns88[0][z] ],color = 'yellow',size=7)
            dataFile.write('(%f,%f,%f)\t'%(round(solns88[0][x].n(30),2),round(solns88[0][y].n(30),2),round(solns88[0][z].n(30),2)) )

    p7 = point3d((0,0,0),color = 'yellow')   
        
    show(p1+p2+p3+p4+p51+p52+p61+p62+p63+p64+p7+p77+p45,aspect_ratio=aspectRatio, figsize=5)
    dataFile.close()

f= open(DATA + 'result.txt','r')
for line in f:
    print line

WARNING: Output truncated!

full_output.txt

计算条件： fx=0.600000,fy=0.260000,a=1.480000,b=8.250000,sigma=0.025000,lamba=0.110000,dx=0.100000,l1=0.800000 计算模式：等间距模式钢筋的间距为0.100时,单侧的钢筋条数为11,总共22条k的取值范围: [-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5] 计算模式：任意间距模式t的范围为[-0.51,0.51],您输入的有效的钢筋位置:[-0.5, -0.40000000000000002, -0.30000000000000004, -0.20000000000000001, -0.10000000000000001, 0.0, 0.10000000000000001, 0.20000000000000001, 0.30000000000000004, 0.40000000000000002, 0.5] 过（0，0，0）的母线与平面y=b+l1的交点坐标： [{z: 0, y: 181/20, x: -277293991/259461588}] 第1象限中母线与锚固法线夹角: 1.839978 1.472166 1.104229 0.736208 0.368115 0.000000 0.368115 0.736208 1.104229 1.472166 1.839978 第1象限中母线与锚固面的交点坐标: [-1.5618516, 8.9917663, 0.35934577] [-1.4632270, 9.0034131, 0.27682111] [-1.3646023, 9.0150598, 0.19962420] [-1.2659777, 9.0267065, 0.12775505] [-1.1673531, 9.0383533, 0.061213649] [-1.0687285, 9.0500000, 0.00000000] [-0.97010387, 9.0616467, -0.055885897] [-0.87147925, 9.0732935, -0.10644404] [-0.77285464, 9.0849402, -0.15167443] [-0.67423002, 9.0965869, -0.19157707] [-0.57560539, 9.1082337, -0.22615196] 第2象限中母线与锚固法线夹角: 13.592696 13.548641 13.514261 13.489643 13.474846 13.469910 13.474846 13.489643 13.514261 13.548641 13.592696 第2象限中母线与锚固面的交点坐标: [1.5618516, 8.9917663, 0.35934577] [1.4632270, 9.0034131, 0.27682111] [1.3646023, 9.0150598, 0.19962420] [1.2659777, 9.0267065, 0.12775505] [1.1673531, 9.0383533, 0.061213649] [1.0687285, 9.0500000, 0.00000000] ... [-1.3646023, -9.0150598, 0.19962420] [-1.4632270, -9.0034131, 0.27682111] [-1.5618516, -8.9917663, 0.35934577] 第4象限中母线与锚固法线夹角: 1.839978 1.472166 1.104229 0.736208 0.368115 0.000000 0.368115 0.736208 1.104229 1.472166 1.839978 第4象限中母线与锚固面的交点坐标: [0.57560539, -9.1082337, -0.22615196] [0.67423002, -9.0965869, -0.19157707] [0.77285464, -9.0849402, -0.15167443] [0.87147925, -9.0732935, -0.10644404] [0.97010387, -9.0616467, -0.055885897] [1.0687285, -9.0500000, 0.00000000] [1.1673531, -9.0383533, 0.061213649] [1.2659777, -9.0267065, 0.12775505] [1.3646023, -9.0150598, 0.19962420] [1.4632270, -9.0034131, 0.27682111] [1.5618516, -8.9917663, 0.35934577] 各母线间的交点： u-v v0 v1 v2 v3 v4 v5 v6 v7 v8 v9 v10 u0 (0.000000,-4.234003,-0.068481) (-0.050000,-3.810603,-0.054785) (-0.100000,-3.387203,-0.041088) (-0.150000,-2.963802,-0.027392) (-0.200000,-2.540402,-0.013696) (-0.250000,-2.117002,0.000000) (-0.300000,-1.693601,0.013696) (-0.350000,-1.270201,0.027392) (-0.400000,-0.846801,0.041088) (-0.450000,-0.423400,0.054785) (-0.500000,0.000000,0.068481) u1 (0.050000,-3.810603,-0.054785) (0.000000,-3.387203,-0.043828) (-0.050000,-2.963802,-0.032871) (-0.100000,-2.540402,-0.021914) (-0.150000,-2.117002,-0.010957) (-0.200000,-1.693601,0.000000) (-0.250000,-1.270201,0.010957) (-0.300000,-0.846801,0.021914) (-0.350000,-0.423400,0.032871) (-0.400000,0.000000,0.043828) (-0.450000,0.423400,0.054785) u2 (0.100000,-3.387203,-0.041088) (0.050000,-2.963802,-0.032871) (0.000000,-2.540402,-0.024653) (-0.050000,-2.117002,-0.016435) (-0.100000,-1.693601,-0.008218) (-0.150000,-1.270201,0.000000) (-0.200000,-0.846801,0.008218) (-0.250000,-0.423400,0.016435) (-0.300000,0.000000,0.024653) (-0.350000,0.423400,0.032871) (-0.400000,0.846801,0.041088) u3 (0.150000,-2.963802,-0.027392) (0.100000,-2.540402,-0.021914) (0.050000,-2.117002,-0.016435) (0.000000,-1.693601,-0.010957) (-0.050000,-1.270201,-0.005478) (-0.100000,-0.846801,0.000000) (-0.150000,-0.423400,0.005478) (-0.200000,0.000000,0.010957) (-0.250000,0.423400,0.016435) (-0.300000,0.846801,0.021914) (-0.350000,1.270201,0.027392) u4 (0.200000,-2.540402,-0.013696) (0.150000,-2.117002,-0.010957) (0.100000,-1.693601,-0.008218) (0.050000,-1.270201,-0.005478) (0.000000,-0.846801,-0.002739) (-0.050000,-0.423400,0.000000) (-0.100000,0.000000,0.002739) (-0.150000,0.423400,0.005478) (-0.200000,0.846801,0.008218) (-0.250000,1.270201,0.010957) (-0.300000,1.693601,0.013696) u5 (0.250000,-2.117002,0.000000) (0.200000,-1.693601,0.000000) (0.150000,-1.270201,0.000000) (0.100000,-0.846801,0.000000) (0.050000,-0.423400,0.000000) (0.000000,0.000000,0.000000) (-0.050000,0.423400,0.000000) (-0.100000,0.846801,0.000000) (-0.150000,1.270201,0.000000) (-0.200000,1.693601,0.000000) (-0.250000,2.117002,0.000000) u6 (0.300000,-1.693601,0.013696) (0.250000,-1.270201,0.010957) (0.200000,-0.846801,0.008218) (0.150000,-0.423400,0.005478) (0.100000,0.000000,0.002739) (0.050000,0.423400,0.000000) (0.000000,0.846801,-0.002739) (-0.050000,1.270201,-0.005478) (-0.100000,1.693601,-0.008218) (-0.150000,2.117002,-0.010957) (-0.200000,2.540402,-0.013696) u7 (0.350000,-1.270201,0.027392) (0.300000,-0.846801,0.021914) (0.250000,-0.423400,0.016435) (0.200000,0.000000,0.010957) (0.150000,0.423400,0.005478) (0.100000,0.846801,0.000000) (0.050000,1.270201,-0.005478) (0.000000,1.693601,-0.010957) (-0.050000,2.117002,-0.016435) (-0.100000,2.540402,-0.021914) (-0.150000,2.963802,-0.027392) u8 (0.400000,-0.846801,0.041088) (0.350000,-0.423400,0.032871) (0.300000,0.000000,0.024653) (0.250000,0.423400,0.016435) (0.200000,0.846801,0.008218) (0.150000,1.270201,0.000000) (0.100000,1.693601,-0.008218) (0.050000,2.117002,-0.016435) (0.000000,2.540402,-0.024653) (-0.050000,2.963802,-0.032871) (-0.100000,3.387203,-0.041088) u9 (0.450000,-0.423400,0.054785) (0.400000,0.000000,0.043828) (0.350000,0.423400,0.032871) (0.300000,0.846801,0.021914) (0.250000,1.270201,0.010957) (0.200000,1.693601,0.000000) (0.150000,2.117002,-0.010957) (0.100000,2.540402,-0.021914) (0.050000,2.963802,-0.032871) (0.000000,3.387203,-0.043828) (-0.050000,3.810603,-0.054785) u10 (0.500000,0.000000,0.068481) (0.450000,0.423400,0.054785) (0.400000,0.846801,0.041088) (0.350000,1.270201,0.027392) (0.300000,1.693601,0.013696) (0.250000,2.117002,0.000000) (0.200000,2.540402,-0.013696) (0.150000,2.963802,-0.027392) (0.100000,3.387203,-0.041088) (0.050000,3.810603,-0.054785) (0.000000,4.234003,-0.068481)

a =vector([1,2,3])
print a.inner_product(a)
print a.dot_product(a)

14 14

round(1.020334,2)

1.02