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{ HELIX_OBJIMPORT.PDE

 

 This sample demonstrates the import of a bounding mesh in OBJ file format.

 It uses the MATERIALS and BOUNDARY CONDITIONS sections to tie names stated

 in the OBJ file to FlexPDE properties.

 

 The OBJ file contains :

   one object named 'helix' that will be bound to a material property set.

   two groups named 'top', and 'bottom' that will be bound to BC sets.

}

title 'Import OBJ Helix'

 

coordinates cartesian3

 

select order=2

 

variables U V W

 

definitions

   E           { Young's Modulus }

   nu = 0.3   { Poisson's Ratio }

 

  { define the constitutive relations }

   G = E/((1+nu)*(1-2*nu))

   C11 = G*(1-nu)

   C12 = G*nu

   C13 = G*nu

   C22 = G*(1-nu)

   C23 = G*nu

   C33 = G*(1-nu)

   C44 = G*(1-2*nu)/2

 

  { Strains }

   ex = dx(U)

   ey = dy(V)

   ez = dz(W)

   gxy = dy(U) + dx(V)

   gyz = dz(V) + dy(W)

   gzx = dx(W) + dz(U)

 

  { Stresses }

   Sx  =  C11*ex + C12*ey + C13*ez

   Sy  =  C12*ex + C22*ey + C23*ez

   Sz  =  C13*ex + C23*ey + C33*ez

   Txy =  C44*gxy

   Tyz =  C44*gyz

   Tzx =  C44*gzx

 

  { find mean translation and rotation }

   Vol = Integral(1)

   Tx = integral(U)/Vol                   { X-motion }

   Ty = integral(V)/Vol                   { Y-motion }

   Tz = integral(W)/Vol                   { Z-motion }

   Rz = 0.5*integral(dx(V) - dy(U))/Vol   { Z-rotation }

   Rx = 0.5*integral(dy(W) - dz(V))/Vol   { X-rotation }

   Ry = 0.5*integral(dz(U) - dx(W))/Vol   { Y-rotation }

 

  { displacements with translation and rotation removed }

  { This is necessary only if all boundaries are free }

   Up = U - Tx + Rz*y - Ry*z

   Vp = V - Ty + Rx*z - Rz*x

   Wp = W - Tz + Ry*x - Rx*y

 

  { scaling factors for displacement plots }

   Mx = 0.1*globalmax(magnitude(y,z))/globalmax(magnitude(Vp,Wp))

   My = 0.1*globalmax(magnitude(x,z))/globalmax(magnitude(Up,Wp))

   Mz = 0.1*globalmax(magnitude(x,y))/globalmax(magnitude(Up,Vp))

   Mt = 0.2*globalmax(magnitude(x,y,z))/globalmax(magnitude(Up,Vp,Wp))

 

equations

   U:  dx(Sx) + dy(Txy) + dz(Tzx) = 0   { the U-displacement equation }

   V:  dx(Txy) + dy(Sy) + dz(Tyz) = 0   { the V-displacement equation }

   W:  dx(Tzx) + dy(Tyz) + dz(Sz) = 0   { the W-displacement equation }

 

materials 'helix' : E  = 2.0e11 { Young's Modulus for Steel (N/M^2) }

 

boundary conditions

  'top'    : natural(w) = -1e-3

  'bottom' : natural(w) = 1e-3

 

boundaries import OBJ 'helix.obj'

 

plots

  contour(Up) on y=0 as "X-displacement"

  contour(Vp) on x=0 as "Y-displacement"

  contour(Wp) on y=0 as "Z-displacement"

  grid(x+Mt*Up,y+Mt*Vp,z+Mt*Wp) as "Shape"

  grid(x+My*Up,z+My*Wp) on y=0 as "XZ Shape"

  grid(y+Mx*Vp,z+Mx*Wp) on x=0 as "YZ Shape"

  contour(Sx) on y=0 as "X-stress"

  contour(Sy) on y=0 as "Y-stress"

  contour(Sz) on y=0 as "Z-stress"

  contour(Txy) on y=0 as "XY Shear stress"

  contour(Tyz) on y=0 as "YZ Shear stress"

  contour(Tzx) on y=0 as "ZX Shear stress"

 

end