A version of the Poisson equation that occurs in mechanics is the following model for the vertical deflection of a bar with a distributed load P(x):

where A_c = cross-sectional area, E = Young’s modulus, u = deflection, and x = distance measured along the bar’s length. If the bar is rigidly fixed (u = 0) at both ends, use the finite-element method to model its deflections for A_c = 0.1 m², E = 200 × 10⁹ N/m², L = 10 m, and P(x) = 1000 N/m. Employ a value of Δx = 2 m.

Transcribed Image Text:

AE_ = P(x) аґ