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1 Politecnico di Milano – Master Degree in Biomedical Engineering Computational Biomechanics Laboratory Prof. D. Gastaldi A.A. 2020-21 – Date 10/02/2021 Surname.........................................................................................Name............................................................................................. Person Code............................................ MARK………………. The written examination will last 120 minutes. FINITE ELEMENT MODELING AND STRUCTURAL MECHANICS Consider the FEM structure in the Figure composed by 2D plane stress isoparametric 4-node elements with full integration. 1) Define the basics of the isoparametric element formulation and determine the shape functions. [4 pts] 2) Determine the Jacobian matrix for all the elements. [4 pts] 3) Determine the nodal force vector equivalent to reaction forces and to external loads: distributed traction (q) and concentrated forces F=qL. [6 pts] 4) Make a graphical representation of the nodal forces acting on the structure. [2 pts] 2 FINITE VOLUME MODELING AND COMPUTATIONAL FLUID DYNAMICS 5) Write the general transport equation with comments about the different terms. Then, apply the general transport equation to the energy conservation defining the physical parameters. [3 pts] 6) Write the integral form of the general transport equation. Assuming the finite volume scheme in a general 2D case what does it mean mid-point approximation? [3 pts] 7) Assuming the finite volume approach in 1D, describe a general advective term considering the 1st order upwind scheme. [3 pts] 8) Assuming the finite volume scheme in a general 2D case write the discretized equation of a generic cell in the grid (adopting central difference scheme where needed). [4 pts] 9) Make a synthetic discussion…