# Flexible vegetation

by czarnm
Tags: flexible, vegetation
 Sci Advisor P: 5,524 Sure- you could use the cantilever equation (with caveats): EI$$\frac{\partial^{4}y}{\partial s^4} = 0$$ Where E is the Young's modulus, I the moment of inertia, 's' the coordinate that deforms with the beam, etc. etc. You probably want to start with a free end and a built-in end for the boundary conditions- the fixed end position and slope are zero, the bending moment at the free end vanishes, and the force 'F' is applied at the free end as well: $$y(0) =\frac{\partial y}{\partial s}\right)_{s=0} = 0$$ $$\frac{\partial^{2} y}{\partial s^{2}}\right)_{s=L} = 0$$ $$\frac{\partial^{3} y}{\partial s^{3}}\right)_{s=L} = F$$ If you are applying a force at different locations, your boundary conditions will change as well. In order to extract out the shear stress, I think you need to be careful- one could calculate the bending energy by calculating the curvature along the length, for example. In any case, you need to know Young's modulus which is experimentally determined. Basically, this is why engineers have moved to finite element analysis software platforms to calculate all this stuff for them.