Consider a simply supported beam with the deflection-dependent Young's modulus under the uniform load as shown...

   

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Consider a simply supported beam with the deflection-dependent Young's modulus under the uniform load as shown in Fig3 The left end of the beam is at x = 0, and the right end of the beam is at x = b. The deflection of the beam w(r) is the solution of the second-order differential equation w" (r) = (20 + aw(x))x(x - b), (2) where a and b are the last two non-zero integers, taken from your student ID. For example, if your ID is 103838497, then a = 9 and b = 7. If your ID is 103838407, then a = 4 and b = 7. The deflection w must vanish at x = 0 and at x=b, i.e. w(x = 0) = 0 and w(x = b) = 0. W W mar Figure 3: Shape of a simply supported beam under uniformly distributed load. The left end of the beam is at x = 0 the right end of the beam is at x = b. Consider a simply supported beam with the deflection-dependent Young's modulus under the uniform load as shown in Fig3 The left end of the beam is at x = 0, and the right end of the beam is at x = b. The deflection of the beam w(r) is the solution of the second-order differential equation w" (r) = (20 + aw(x))x(x - b), (2) where a and b are the last two non-zero integers, taken from your student ID. For example, if your ID is 103838497, then a = 9 and b = 7. If your ID is 103838407, then a = 4 and b = 7. The deflection w must vanish at x = 0 and at x=b, i.e. w(x = 0) = 0 and w(x = b) = 0. W W mar Figure 3: Shape of a simply supported beam under uniformly distributed load. The left end of the beam is at x = 0 the right end of the beam is at x = b.

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To solve the boundary value problem Eq 2 using finite differences we will discretize the equation by approximating the second derivative wr using a fi... View the full answer