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(Course Numerical methods)
Q2. A version of the one-dimensional elliptic equation that occurs in Mechanics is the following model for the vertical deflection of a bar with a uniformly distributed load P(x): au AE дх2 = P(x) Where A = 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 = 0.19 m2, E = 110x10' N/m2, L = 9 m, P(x)} = 700 N/m, and P(x)2 = 0 N/m. P(x), is the uniformly distributed load on element 1. Element 3 has linearly varying load shown in the figure below. Obtain the expression for the linear load distribution of element 3 as a
function of the distance x and then use it in the element equation of element 3. The nodes are at equal distances. Use the dimensions indicated; the figure below being not according to scale. Use Thomas Algorithm to solve the final matrix equation. P(x) = 700 N/m Pa = 450 N/m (1) (2) (4) 2 3 k 9 m Elements Grid nodes