After looking at some of the analytical expressions for analyzing beams, I noticed that none of the equations depend on the material's Poisson ratio. Some analytical expressions can be found in https://www.linsgroup.com/MECHANICAL_DESIGN/Beam/beam_formula.htm
I believe these equations are derived from the Euler Bernoulli equations and not from 3-D Linear elasticity, and Poisson's ratio isn't included in Euler Bernoulli. What underlying assumption in Euler Bernoulli allows for the exclusion of the Poisson's ratio?
If I want to model a beam under the Euler Bernoulli assumptions in a 3-D linear elasticity code, where the Poisson's ratio is required as an input, how can this be done? Essentially, I am trying to perform a one to one comparison of the linear elasticity code I am using with the analytical beam expressions. To do this, I need to figure out what value to input for the Poisson's ratio in the code. When I model the beam with the code and vary the Poisson's ratio, the deflection changes as a function of the poisson's ratio. However, the analytical beam expressions do not depend on the Poisson's ratio, so it is not clear to me how this comparison can be performed.