Reply To: How to calculate eigen frequencies using analytical approach?

[Rameez_ul_Haq]

,I am just mentioning a fishing rod, or maybe a very thin beam which can bend long way (which changes its stiffness during deformation) when subjected to forces, and still stay below the yield point. I should use Large deflection to take into account the varying stiffness of the structure. But the Stress-Strain relation can be derived from the Force-displacement relation, as I already have shown in the attached picture. However, the stress-strain relation is still kept linear (with constants like E and v) even when I am taking into account the change in stiffness of the structure during deformation. This thing confuses me. I mean for Large Deflection = ON, if we are not using a linear relation to calcuate the stresses from strains in FEM like ANSYS, then it is understandable. But still if we are, then it doesn't make any sense near me because it can be derived from the F = Kx (where K is changable) as written in various textbooks.
"Once you talk about nonlinear effects, then Hooke's law only applies during the initial linear elastic deformation, and not when the large deflection starts.", this statement appeals as if Large deformation should be used after the yield the point, and should not be used before it.