Answer Happy

A round stepped rod is loaded as shown in Figure 2. The detailed specification of geometry, material and boundary conditions are also included in the figure. Using one linear 2-noded finite element for each section of the rod, calculate (a) the global/system stiffness matrix and load vector and hence (b) (c) (d) the nodal displacement vector. (6 Marks) Identify two prime sources of errors in the results you have obtained in part (b) above.. (2 Marks) If the exact displacement of a generic point in section [1] at a distance x from the fixed end is given by u(x)= [1] L₁ E₁A, 12 evaluate the magnitudes of the errors you have identified in part (c) above and make appropriate suggestions to reduce these errors if the number of elements is not to change. (6 Marks) Note: Units are intentionally not given. Work using given numerical values. Total (20 Marks) -450x² +20x10 20×10¹x]. T ts(x) = (900-x²) per unit length (6 Marks) [2] Figure 2 E₁ = E₂ = 30x105, P = 2x10³ A₁ = 4, A₂= 2, L₁= L₂ = 30