
Re: URES result in Simulation
Mike Pogue Dec 4, 2014 10:03 AM (in response to David Grigg)The results are based on Hook's law. As shown on the Wikipedia page, it relates a force vector to a stress displacement vector via a stiffness tensor for some differential unit of volume. This equation is discretized using Galerkins method into a linear system of equations which the computer can solve. The property most closely related to displacement is the Young's modulus, a measure of the stiffness of the material, with second order effects from Poisson's ratio. From these two properties, you can compute any elastic property for an orthotropic material.
The math behind FEA is very, very complicated. You can conceptualize Hooke's law by it's most common, high school form: F = K*x, where F is the applied force, K is the spring constant (a function of the Young's modulus and the geometry), and x is the resultant displacement (Ures, the diagonal of the vector displacement). The solution is x = K*F^1, which, in some sense, is the matrix equation that every FEA solver solves. This means that if you pull on a spring of stiffness K with a force F, you get a displacement x = K/F when it settles down.

Re: URES result in Simulation
David Grigg Dec 3, 2014 4:16 PM (in response to Mike Pogue)Thanks. That's straight forward enough. That also reminds me that I should be able to use this to determine the effective stiffness of the assembly, and should likely correspond to the modal analysis results in a subsequent frequency analysis. Correct?


Re: URES result in Simulation
Jared Conway Dec 4, 2014 4:29 AM (in response to David Grigg)most common questions relative to ures
1. what is it? sqrt (x^2+y^2+z^2)
2. does it include displacement from strain only or also displacement from "moving". > both
3. how is it calculated, as mike noted, F=kx
i'm not sure what you mean about stiffness calculations and static matching frequency? the stiffness matrix is the same regardless of the type of analysis so yes, it should be the same, but displacements have no meaning in frequency.

Re: URES result in Simulation
David Grigg Dec 4, 2014 12:24 PM (in response to Jared Conway)k=F/x (x from Static Analysis, URES)
w(est.)=sqrt(k/m) (estimation of 1st fundamental resonance)
Mode Shape 1 value [w(modeled)], from frequency analysis.
I was simply stating that the an effective k, recognized by the use of Hook's Law, as Mike mentioned, should at least to first order match the first fundamental mode results from a frequency analysis, if you use the simple w=sqrt(k/m).
I modeled a simple spring mass system and validated that it was very close, just as a confidence builder.

Re: URES result in Simulation
Jared Conway Dec 4, 2014 7:01 PM (in response to David Grigg)the k is one and the same in both analyses

Re: URES result in Simulation
David Grigg Dec 4, 2014 7:04 PM (in response to Jared Conway)Exactly.


