I have a practical problem related to the design of a monochromator for a neutron beam. This device basically consists of an elastic metallic plate carrying the diffracting crystals, which is curved mechanically to achieve proper focusing conditions. Assuming it can be schematically represented by a homogeneous blade supported on two fulcrums at points A and B at (distance d), which is deformed by applying a vertical force at the middle point M, is there a simple mathematical expression giving the shape of the resulting profile as a function of the vertical displacement h of point M? Does it depend on the elastic constants of the material or is it universal provided the material is homogeneous?
I thought It would be easy to find this problem discussed somewhere but Google did not return any relevant reference.