;Model for Monte Carlo testing 18-point cell with variable angles

;

;The cell is made of six triangles, each with one point toward the middle and the other two 

;on the same radius further out.  The triangles are joined together in pairs.  We model one 

;of these pairs with six separately placed points so that we can use Monte Carlo testing to 

;simulate the sorts of errors that might occur in construction. 

;

;The two triangles are labeled 'a' and 'b', and the points are '1' (on the inner radius), '2' and '3' 

;(on the outer radius).  That make a total of six points: 1a, 2a, 3a, and 1b, 2b, 3b.  

;

;Each point is positioned by specifying its radius (rXX) and angle (aXX).  There are six pairs of 

;coordinates: (r1a, a1a) through (r3b, a3b).  Each of these ordinates is allowed to vary 

;independently by an amount equivalent to plus or minus 1mm.  That leads to a total variation 

;of plus or minus 2mm on length of the sides of the triangles and plus or minus 1mm on the 

;placement.  In reality the effects might be reversed, with the dimensions being more accurate 

;than the placement, but the model was starting to get complex enough as it was without trying 

;to add in that factor.

;

;In addition, variables are used to simulate the sorts of force errors that might occur due to shifts 

;of plus or minus 1mm in the placement of the balance points on the bars and triangles. 'eba' 

;simulates the bar balance position error effect on triangle 'a' with 'ebb' being its mirror effect on 

;triangle 'b'.  Similarly 'eha' and 'ehb' simulate the effects of a radial (height) error on the balance 

;point placement on the triangles and 'ewa' and 'ewb' simulate the effects of an angular (width) 

;placement error.  Finally, the relative radial errors of points 2 and 3 for each triangle is used to 

;compute a skew error factor for each triangle 'ska' and 'skb' that in turn computes a net effect 

;for each point.

;

;All of the error factors are simply summed, due to the complex nature of doing mathematical 

;expressions within Plop, but the net error from this is minimal since (1+a)*(1+b) is approximately 

;equal to (1+a+b) for small a and b. The error factors were similarly computed separately in a 

;spreadsheet to help simplify the math.

;

;The net effect is that the Monte Carlo testing will approximate the effects of construction errors 

;of up to 2mm in triangle sizing and 1mm of net triangle and balance point placement in each 

;direction.  The downside is that we are actually testing the results of three sets of equally 

;misconstructed triangle pairs as opposed to six independently constructed triangles, but at 

;least it gives us a slightly more realistic effect than simply varying the parameters of the 

;original model.

var r1a  0.388119

var r1b  0.388119

var skewa  0

var skewb  0

var r2a  0.842417 + skewa

var r2b  0.842417 - skewa

var r3a  0.842417 + skewb

var r3b  0.842417 - skewb

var ska  r2a - r3a

var skb  r2b - r3b

var es2a  ska * 7.2261

var es2b  skb * 7.2261

var es3a  ska * -7.2261

var es3b  skb * -7.2261

var a1a  0

var a2a  15.1972

var a3a  -15.1972

var a1b  60

var a2b  75.1972

var a3b  44.8028

var f  1

var eba  0

var fba  1 + eba

var ebb  0 - eba

var fbb  1 + ebb

var eha  0

var ehb  0

var ewa  0

var ewb  0

var e1a  eha * -2

var e2ax  eha + ewa

var e2a  e2ax + es2a

var e3ax  eha - ewa

var e3a  e3ax + es2a

var e1b  ehb * -2

var e2bx  ehb + ewa

var e2b  e2bx + es2b

var e3bx  ehb - ewa

var e3b  e3bx + es3b

var f1ah  f + e1a

var f2ax  1 + e2a

var f3ax  1 + e3a

var f1bh  f + e1b

var f2bx  1 + e2b

var f3bx  1 + e3b

var f1a  fba * f1ah

var f1b  fbb * f1bh

var f2a  fba * f2ax

var f2b  fbb * f2bx

var f3a  fba * f3ax

var f3b  fbb * f3bx

diameter 406.4

thickness 18

density 2.45e-06

modulus 6000

poisson 0.22

f-ratio 5

n-mesh-rings 24

rel-support-radii r1a r2a r3a r1b r2b r3b

rel-force f1a f2a f3a f1b f2b f3b

num-support 3 3 3 3 3 3

support-angle a1a a2a a3a a1b a2b a3b

basis-ring-size 3

basis-ring-min 0

monte skewa 0.004921

monte skewb 0.004921

monte eba 0.014657

monte eha 0.017781

monte ehb 0.017781

monte ewa 0.024003

monte ewb 0.024003

part triangle 3 point 0 0 point 1 0 point 2 0

part triangle 3 point 3 0 point 4 0 point 5 0

part bar 3 part 0 0 part 1 0