Full exam for Computational Biomechanics Laboratory in the Biomedical Engineering degree programme at Politecnico di Milano. The document covers: 1 Politecnico di Milano – Master Degree in Biomedical Engineering Computational Biomechanics Laboratory Prof. D. Gastaldi A.A. 2020-21 – Date 20/01/2021
Full exam for Computational Biomechanics Laboratory in the Biomedical Engineering degree programme at Politecnico di Milano. The document covers: 1 Politecnico di Milano – Master Degree in Biomedical Engineering Computational Biomechanics Laboratory Prof. D. Gastaldi A.A. 2020-21 – Date 20/01/2021
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1 Politecnico di Milano – Master Degree in Biomedical Engineering Computational Biomechanics Laboratory Prof. D. Gastaldi A.A. 2020-21 – Date 20/01/2021 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 the external loads: distributed traction (q1, q2) and concentrated force F=q1L. [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 concept in order to obtain the equation of energy conservation. [2 pts] 6) Consider a generic property Φ transported in steady state condition by means of convection and diffusion in two-dimensions without body forces with the direction of flow as indicated in the figure. Adopting the finite volume approach, consider the central difference scheme for the diffusive term and the 1st order upwind scheme for the advective term. 6a) Write the contribution of each face of cell P to the advective term. [4 pts] 6b) Assuming !"!#=0 in the whole…
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