Full exam for Computational Biomechanics Laboratory in the Biomedical Engineering degree programme at Politecnico di Milano. The document covers: Politecnico di Milano - Corso di Laurea magistrale in Ingegneria Biomedica Computational Biomechanics Laboratory Date 17/1/18 1) Consider the element in the figure. (14 pts) 1a) Find the shape functions for the element with respect to the system of coordinates at node 1. (6 pts)
Full exam for Computational Biomechanics Laboratory in the Biomedical Engineering degree programme at Politecnico di Milano. The document covers: Politecnico di Milano - Corso di Laurea magistrale in Ingegneria Biomedica Computational Biomechanics Laboratory Date 17/1/18 1) Consider the element in the figure. (14 pts) 1a) Find the shape functions for the element with respect to the system of coordinates at node 1. (6 pts)
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Politecnico di Milano - Corso di Laurea magistrale in Ingegneria Biomedica Computational Biomechanics Laboratory Date 17/1/18 1) Consider the element in the figure. (14 pts) 1a) Find the shape functions for the element with respect to the system of coordinates at node 1. (6 pts) 1b) Calculate the deformed configuration of the element for the displacement field (2pts) 𝐮= ⎣⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎡u'v'u)v)u*v*u+v+u,v,u-v-⎦⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎤ = ⎣⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎡000.25𝐿000.25𝐿000.5𝐿0.5𝐿00⎦⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎤ 1c) Calculate the deformation field (small strain field) associated with the previous displacement field as a function of (x,y) (6 pts) 2) Which are the differences between an iso-parametric and a sub-parametric finite element formulation. Give an example. (2pts) 3) What is the difference between the conservative and non-conservative form of the Navier-Stoke equations? For numerical applications, when either formulation is used? (2 pts) 4) Consider a two-dimensional stationary flow without body forces with the direction of flow as indicated in the figure. (10 pts) In this case, the momentum equation reduces to: ∇∙(𝜌𝒗𝒗)−∇∙(𝜇∇𝒗)=0 4a) Determine the contribution of each face of cell P to the x-component of the convective term when using the finite volume method with first order upwind. Consider known the velocity field from the previous time step at each cell. (8 pts) 4b) Which are the contributions if the mesh is distorted as shown in the figure (2 pts) 5) When analyzing the convergence of the mesh in a CFD or in a stress analysis what type of variables are recommended to monitor and why? (2 pts) Politecnico di Milano Computational Biomechanics Laboratoy Solution of Final Exam (Call: 17/1/2018) Problem 1 The shape function for the ith node of a quadratic triangular element in terms of x andy coordinate…
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