// sphere.fe // Spherical tank. SYMMETRIC_CONTENT // natural for a sphere /* sphere radius */ #define R 1.00 /* cosine of contact angle */ PARAMETER WALLT = 0.707 /* density of body */ #define RHO 1.0 #define wstuff (R^2*z/(x^2 + y^2)/sqrt(x^2+y^2+z^2)) #define gstuff (G*RHO/8*R^4*z^4/(x^2 + y^2)/(x^2+y^2+z^2)^2) #define gapstuff (G*RHO*R^4/8*z^2/(x^2+y^2+z^2)^2) constraint 1 convex /* the sphere */ formula: x^2 + y^2 + z^2 = R^2 energy: e1: WALLT*wstuff*y - gstuff*y + G*RHO/8*y*z^2 + gapstuff*y e2: -WALLT*wstuff*x + gstuff*x - G*RHO/8*x*z^2 - gapstuff*x e3:0 content: c1: -wstuff*y/3 c2: wstuff*x/3 c3: 0 constraint 2 /* just for showing the sphere outline */ formula: x^2 + y^2 + z^2 = R^2 vertices: 1 1 0 0 constraint 1 2 0 1 0 constraint 1 3 -1 0 0 constraint 1 4 0 -1 0 constraint 1 5 0 0 1 constraint 2 FIXED // to show back hemisphere 6 0 0 -1 constraint 2 FIXED 7 0 1 0 constraint 2 FIXED 8 -1 0 0 constraint 2 FIXED 9 0 -1 0 constraint 2 FIXED edges: 1 1 2 constraint 1 2 2 3 constraint 1 3 3 4 constraint 1 4 4 1 constraint 1 5 5 9 constraint 2 FIXED // to show back hemisphere 6 9 6 constraint 2 FIXED 7 6 7 constraint 2 FIXED 8 7 5 constraint 2 FIXED 9 5 8 constraint 2 FIXED 10 9 8 constraint 2 FIXED 11 6 8 constraint 2 FIXED 12 7 8 constraint 2 FIXED faces: 1 1 2 3 4 2 5 10 -9 constraint 2 density 0 FIXED // to show back hemisphere 3 -10 6 11 constraint 2 density 0 FIXED 4 -11 7 12 constraint 2 density 0 FIXED 5 8 9 -12 constraint 2 density 0 FIXED bodies: // start with sphere half full 1 1 volume 2*pi*R^3/3 volconst 2*pi*R^3/3