Large module depicted with force and fixtures
In order to find the minimum thickness for the modules, the worst case scenario was considered. This was determined to be the large module with 2 medium modules (or 8 extra-small modules) on top of it. For simplicity, the entire surface area was considered rather than account for the walls of the smaller modules. The weight of the modules were also neglected. This makes it an overestimate which is good for product quality.
A heavy metal pen was selected and it was assumed that the entire surface area (226mm x 144mm) within the top space space was filled with these pens. This was figured using the pen's bottom surface area of 11.938mm x 11.938mm. The pens were assumed to be perfect cylinders. The total number of pens was rounded up to 229 pens. The weight of the pens came up to value of 146.4799 Newtons. The bottom surface was fixed.
A design study was conducted to determine the optimal wall thickness for metal. The goal was to reduce weight in order to save costs. Reducing weight also increase storage capacity because of the thinner walls. The constraint used for this design study was a factor of safety of 1.5. The example below uses balsa wood.