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1 Politecnico di Milano – Master Degree in Biomedical Engineering Computational Biomechanics Laboratory Prof. D. Gastaldi A.A. 2021-22 – 15/02/2022 Surname.........................................................................................Name............................................................................................. Person Code............................................ MARK………………. The written examination will last 90 minutes. FINITE ELEMENT MODELING AND STRUCTURAL MECHANICS 1) Consider a 2D plane stress isoparametric 4-node elements with full integration: 1-a) Define the basics of the isoparametric element formulation and write the shape functions. 1-b) Describe the mandatory requirements of the shape functions. 1-c) Make comments about the role of the Jacobian matrix and its effects on FE-method. [6 pts] 2) Assuming a static linear problem of a solid component solved adopting the FEM numerical framework: 2-a) Describe the global stiffness matrix and its properties. 2-b) Describe the difference between the element stiffness matrix and the global stiffness matrix. [4 pts] 3) Make a synthetic description of the Newton-Raphson iterative scheme with comments about variants. [4 pts] 4) Make a discussion about the numerical integration procedure comparing the full vs reduced integration scheme with relevant effects on the FE results. [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…