;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  0.388063

var r1b  0.388063

var r2a  0.84244

var r2b  0.84244

var r3a  0.84244

var r3b  0.84244

var ska  r2a - r3a

var skb  r2b - r3b

var es2a  ska * 7.2686

var es2b  skb * 7.2686

var es3a  ska * -7.2686

var es3b  skb * -7.2686

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 r1a 0.004921

monte r1b 0.004921

monte r2a 0.004921

monte r2b 0.004921

monte r3a 0.004921

monte r3b 0.004921

monte a1a 0.726602

monte a2a 0.334703

monte a3a 0.334703

monte a1b 0.726602

monte a2b 0.334703

monte a3b 0.334703

monte eba 0.014613

monte eha 0.017885

monte ehb 0.017885

monte ewa 0.021843

monte ewb 0.021843

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