The themomechanical calculations for CIRCE in two steps: the first calculations concerned the feasability study using estimated values for the position and weight of the mechanical elements; the second step uses values from the final mechanical CAD design.
The system is considered a cemented cantilever beam with null deflection or bending in the fixation. Two different loads are applied to the system: the internal and the external loads. The superposition theorem is used for each load and the total bent due to loads is equal to the sum of each one. The bent of the bench is due to torsion, tension and bending. All these effects are assumed no coupled and thus the coupledflexure coefficients were neglected. When the instrument moves the gravity angle in relation with the bench changes and the variation in the flexure of the bench creates a shift of the image into the detector.
Deflections, shear and moments were calculated using standard analytical solutions implemented in ITMAS. The feasability assumed that the bench is attached to the front of the instrument. This study showed deflections lower is in the order of the tolerances (25um) in the worth case of the bench parallel to the ground. The shift between mirrors is in the order of some microns.
We study the influence of the thickness of the bench in order to optimize the dimensions of the instrument. An increase of the thickness of the bench increases its stiffness but also its distributed weight participating in the deflection of the system. The study with ITMAS showed that the optimum value is about 40mm.
The second study the mechanical CAD design that consider the physical limitations from the telescope specifications. Values of the elements used for the thermomechanical calculations are shown in the following table.
Mechanical  Element X(cm)  Y(cm)  Z(cm)  Volume(liters)  Weight(kg) 
F1  17.53561314  0 15.6409  2.297628  6.226572 
F2  89.99548219  0.000001016  286.3503  2.78953  7.559625 
C1  703.0348439  0.013157454  283.372  4.836717  13.1075 
C2  140.9170908  0.01840738  93.41091  0.436713  1.183491 
IM1  1062.68148  0.132106416  211.091  2.843016  7.704575 
IM2  878.9555294  0.037731446  12.0942  0.191266  0.518332 
IM3  1051.71924  0.018615152  11.00891  0.172181  0.46661 
IM4  876.0236838  0.026206704  326.8984  3.065712  8.30808 
Filt Wheels  405.1460889  1.09913928  66.6649  1.193636  3.234755 
Filt Box  477.6064936  33.46281293  116.289  1.518762  4.115844 
Detector  1175.882949  42.89849078  2.539152  0.275213  0.745828 
Bracket 1  64.23266732  56.26286944  52.1246  1.032358  2.79769 
Bracket 2  128.4971514  49.37481489  324.3209  0.944301  2.559056 
Bracket 3  679.0453993  49.53429819  291.7184  2.234331  6.055038 
Bracket 4  118.1489204  84.52582003  95.34327  0.611058  1.655966 
Bracket 5  1146.165147  56.88742801  210.863  0.981754  2.660553 
Bracket 6  854.6161028  88.1876156  6.04431  0.538064  1.458153 
Bracket 7  1071.206688  88.43974032  1.83525  0.481806  1.305695 
Bracket 8  886.7877801  74.98995365  319.3113  1.837902  4.980715 
The deflection of the beam at X is given by
and the the resulting shifts of the mirrors are
We show the deflection of the bench(pink) and the deflection due to mirrors and distributed loads(Orange) and bracket (bleu) independently. Analytical results are over plotted with yellow. Using reinforced structures and lightning of the bench improve deflection by about 2030%.

DIMENTIONNING
ITMAS
Bench Flexures
Thermal Calculations
Assembling
Testing
CAD DESIGN
Bench
Optomechanics
Filter Box
Focal Plane
Other
