Chapter 5, Problem 5.2DOEP

Consider the bar, shown in Figure 1 that undergoes axial displacement due to both a distributed load and a point force. The bar is of cross-sectional area A = 1.10-3 m², and has a modulus of elasticity E = 100 GPa. 1(x) = 5 kN/m x=0.0 x=2.0 2.0m 10 kN Figure 1: Bar domain with varying distributed forces. a) The general form of the governing equations describing the bar's displacement, u(x), is given by, d (AE du(x)) -) +1(x) = 0. d.x dx What are the accompanying boundary conditions for this bar? b) Using the mesh in Figure 2, form the basis functions associated with element 2 and write the FEM approximation over the element. 1 2 3 1 2 1m 1m Figure 2: Mesh of 2 elements. Elements are numbered with underlines. c) The general form of the element stiffness matrix system, with nodes indexed by i and j, is, AE Uj N;(x)l(x)dx – Ng(0)f(0) ¥ [4]}]{{}}={{{}\(\\+} + {N(2)f(2) = N (0)5() }, (1) 0, respectively. L = (2) where f(2) and f(0) denote the boundary forces at positions x 2 and x Evaluate…

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amination) Question 1 Consider the bar, shown in Figure 1, that undergoes axial displacement due to both a distributed load and a point force. The bar is of cross-sectional area A = 1.103 m2, and has a modulus of elasticity E = 100 GPa. 1(x) = 5 kN/m 10 kN X x=0.0 x=2.0 2.0m Figure 1: Bar domain with varying distributed forces. a) The general form of the governing equations describing the bar's displacement, u(x), is given by, d (AE du(x)) + 1(x) = 0. dx dx What are the accompanying boundary conditions for this bar? MacBook Air a 会 DII F5 F6 F7 F8 80 F3 F4 0/ 20 [8 marksl 8 FO