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1 Politecnico di Milano – Master Degree in Biomedical Engineering Computational Biomechanics Laboratory A.A. 2018-19 – Date 14/01/2019 Surname.........................................................................................Name............................................................................................. Person Code............................................ MARK……………./30 The written examination will last 120 minutes. FINITE ELEMENT MODELING AND STRUCTURAL MECHANICS 1) Consider the following bar with constant cross-section A (0.05 m2), length L (0.4 m), subjected to a distributed load fx (2 N/m) and characterized by an isotropic linear elastic material (E = 50 MPa, v= 0.3). The bar is discretized using one quadratic one-dimensional element, as shown in the figure. 1a) Determine the element shape functions referred to the natural reference system centered at the node 3. (5 pts) 1b) Define the Jacobian matrix by considering the sub -parametric function for the geometry approximation: 𝑥𝑒 = 1 2(1 − 𝑟)𝑥1 𝑒 + 1 2 (1 + 𝑟)𝑥2 𝑒 (1 pts) 1c) Compute the stiffness matrix of the element (4 pts) 1d) Compute the load vector (3 pts) 2) What are the main properties of the stiffness matrix? (3 pts) 2 FINITE VOLUME MODELING AND COMPUTATIONAL FLUID DYNAMICS 3) A straight thermally insulated rod of length L = 0.3 m and constant cross -sectional area A = 0.01 m2 is modeled using 3 one -dimensional elements with same length Δx, as shown in the figure below. The ends of the rod are maintained at constant temperature (T 1=30°C and T 4=15°C for the left and right ends, respectively). The thermal conductivity of t he domain is equal to 400 W/(m·K) and its s pecific heat is 0.39 kJ/(kg K). 3a) Write the energy conservation equation in its conservative form, defining all…