Biomedical Engineering - Computational Biomechanics Laboratory

Full exam

1 Politecnico di Milano – Master Degree in Biomedical Engineering Computational Biomechanics Laborator y Prof. D. Gastaldi A.A. 20 2 1 - 2 2 – 15 / 0 2 / 20 2 2 Surname...................................................................... ........ ... .. ......Name................................................................................. .. .......... Person Code ............................................ MARK …………… …. T he written examination will last 9 0 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 compon ent 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 d escription 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 FINI TE 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 2 D 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 1 st 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 (a dopting central difference scheme where needed ) . [ 4 pts] 9) Make a synthetic discussion about a comparison between segregated and coupled methods in CFD . [ 3 pts]