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1 Politecnico di Milano – Master Degree in Biomedical Engineering Computational Biomechanics Laboratory A.A. 2018-19 – Date 04/02/2019 Surname.........................................................................................Name............................................................................................. Person Code............................................ MARK……………./30 The written examination will last 120 minutes. FINITE ELEMENT MODELING AND STRUCTURAL MECHANICS 1) Consider a bar fixed at the left extremity and subjected to two concentrated loads P1 = 600·103 N and P2 = 100·103 N (see figure below). The bar is made of steel (Young modulus E = 200 GPa and Poisson coefficient ν =0.3) and is characterized by two portions with different length L and cross-sectional area A (L1 = 200 mm, A1 = 1000 mm2 and L2 = 500 mm, A2 = 500 mm2). The bar is discretized using two linear one-dimensional elements. 1a) Write the shape functions of a linear one -dimensional element r eferred to the natural reference system (2 pts) 1b) Derive the stiffness matrix of a linear one-dimensional element (3 pts) 1c) Determine the nodal displacements (use the elimination approach to handle the boundary conditions) (4 pts) 1d) Determine the stress in each portion of the bar (2 pts) 1e) Determine the reaction force at the support (2 pts) 2 2) Describe a possible alternative to the elimination approach to solve the previous problem (point 1c) (3 pts) FINITE VOLUME MODELING AND COMPUTATIONAL FLUID DYNAMICS 3) Consider a two -dimensional steady-state flow without body forces with the direction of flow as indicated in the figure below. 3a) Write the momentum equations in case of two-dimensional domain. (1 pts) 3b) Determine the contribution of each face of cell P to the…