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 20 - 2 1 – Dat e 1 0 / 0 2 / 20 2 1 Surname...................................................................... ........ ... .. ......Name................................................................................. .. .......... Person Code ............................................ MARK …………… …. T he written examination will last 120 minutes. FINITE ELEMENT MODELING AND STRUCTURAL MECHANICS Consider the FEM structure in the Figure composed by 2D plane str ess isoparametric 4 - node elements with full integration . 1) Define the basics of the isoparametric element formulation and d etermine the shape functions. [ 4 pts] 2) D etermine the Jacobian matrix for all the elements . [ 4 pts] 3) Determine the nodal force vector equivalent to reaction forces and t o external loads: distributed traction ( q ) and concentrated force s F =qL . [ 6 pts] 4) Make a graphical representation of the nodal forces acting on the structure . [ 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]