1. A rod of unit cross section area, elastic modulus E and density pis suspended in a vertical plane such that it deform

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1 A Rod Of Unit Cross Section Area Elastic Modulus E And Density Pis Suspended In A Vertical Plane Such That It Deform 1 (30.23 KiB) Viewed 105 times

1. A rod of unit cross section area, elastic modulus E and density pis suspended in a vertical plane such that it deforms under its own weight: 8 u(x) E H The governing differential equation and boundary conditions for the axial displacement u(x) are d'u dx² 12(0)=0, 0(H)=E ++pg=0, 0≤x≤H (1) where g is the acceleration due to gravity. By analogy with the 1-D model problem, the total potential energy functional for the unit cross-section rod can be written as 11(u) = (6) - [5 (da) * - Pg 1 (x) dx dx (2) a) Assuming an approximate solution of the form u(x) = Ax(x-2H), determine the displacement at the end x = H using the Rayleigh-Ritz Method. (10 points) b) If you were to solve the governing differential equation BVP in Equation (1) to obtain the exact solution for u(x), would it be the same as your Rayleigh-Riz solution? Clearly explain why or why not. Note: you do not need to solve Equation (1) to answer this. (5 points)