EngineeringCOMPUTER

AIDED ENGINEERING EMEC 100 CAE is… ? A. Modeling fish motion B. Videogame graphics C. Designing/Analyzing a wind turbine D. Surgery 2 Common Acronyms • CAD – Computer Aided Drafting – Computer Aided/Assisted Design • CAE – Computer Aided Engineering • CFD – Computational Fluid Dynamics – DNS – Direct Numerical Simulation – LES – Large Eddy Simulation – RANS – Reynolds Averaged Navier Stokes • FD – Finite Difference • FEA – Finite Element Analysis • FSI – Fluid Structure Interaction 3 Acronyms • CAD – Computer Aided Drafting – Computer Aided/Assisted Design • CFD – Computational Fluid Dynamics • FEA – Finite Element Analysis 4 THE Workflow 3 2 1. Build Model 2. Mesh 3. Apply Loads and Boundary Conditions 4. Computational Analysis 7. Visualization 2 kN 5. Error Estimation Error? 6. Remesh/Refine/Improve Adaptivity Loop Error < e Error > e User supplies meshing parameters Analysis Code supplies meshing parameters from: Steve Owen. An Introduction to Mesh Generation Algorithms. 14th IMR Short Course. San Diego, Sep 11-14, 2005. 5 Building a geometry • Take idea or drawing and create a 2/3- dimensional version of it on the computer – Part – Assembly 6 Build a geometry • Anything else? 7 Image processing • Reverse engineering 8 Image processing [Zhang 2007] 9 Image processing SPIV through wedge at 255° phase angle. 10 Sketchingto-CAD 11 from: Levent Burak Kara. Thesis (2013). Sketchingto-CAD 12 from: Levent Burak Kara. Thesis (2013). Analysis • FEA – Commonly used for structural, thermal, electromagnetic • CFD – Broadly used to describe RANS Finite Volume Method (FVM), but applies also to: • Finite element formulation of Navier Stokes • Free Vortex Method (also FVM) • Panel Methods 13 FEA 14 FEA 15 FEA 16 28.91 Hz 65.60 Hz 80.51 Hz 151.91 Hz FEA 17 from: Matt Peterson CFD Navier-Stokes equations (1822) Big whorls have little whorls that feed on their velocity, And little whorls have lesser whorls and so on to viscosity. - Lewis Fry Richardson (1922) 18 CFD 2.5 m 1.25 ft 19 CFD 55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 Torque [N-m] Time [s] Blade A Blade B Blade C 1600 1800 2000 0.6 0.65 0.7 0.75 0.8 0.85 0.9 Thrust [N] Blade A Blade B Blade C 20 CFD 21 CFD • DNS 22 8,690,991,616 cells 12,000 cores 2 weeks Analysis • Are there more interesting problems? 23 FSI 24 FSI 25 MD/SPH • Molecual Dynamics (MD) • Smoothed Particle Hydrodynamics (SPH) – Mesh-free methods that model atoms/molecules (or “mass” of continuum) to capture dynamic motion 26 from: Nobutada Ohno, Nagoya University. Optimization • Find “optimal” result – Root finding – Gradient searches – Genetic algorithms – Surface annealing – Ant colony 27 Dynamics 28 Controls • https://www.youtube.com/watch?v=HH sNhBULPfI 29 RoboManip • https://www.youtube.com/watch?v=8V LjDjXzTiU 30 AI 31 Shape Grammars 32 From: M.J. Pugliese, Cpaturing a rebel: modeling the Harley-Davidson brand through a motorcycle shape grammar. Research in Engineering Design, 13 (2002) Shape grammars 33 Acoustics 34 Fish Navigation Eulerian mesh node Sensory Ovoid Sensory Point x Eulerian mesh z y PCA analysis for parsing scenarios Sensory system linkage to CFD output Existing conditions Fish ladder 35 Whales 36 Entertainment • https://www.youtube.com/watch?v=mg YztcjOvRQ 37 Homework • Take a picture of something interesting • Describe how you would analyze it • Submit to D2L 38 8. Economics 1 Problem Set 3 MSU EC 410 Prof. Ahlin due 11/10/15 1a. Use the H-augmented Solow model to determine the a) instantaneous impact on GDP per capita, b) instantaneous impact on consumption per capita, c) long-run impact on GDP per capita, d) long-run impact on consumption per capita, e) impact on long-run GDP per capita growth rate, and f) impact on long-run GDP growth rate of a permanent and instantaneous increase in the fraction of national resources devoted to investment in human capital, q. Assume the country begins at its steady state values of k* and h* before this event occurs. Justify your answer by use of graph and/or equation. 1b. How does each answer compare to the answer the original Solow model would give when s increases, both qualitatively (whether the amount goes up or down) and quantitatively (the amount by which it goes up or down)? 2. Consider the Solow model with total factor productivity At constantly growing at rate g>0. a. Determine the a) instantaneous impact on GDP per capita, b) instantaneous impact on consumption per capita, c) long-run impact on GDP per capita (i.e. compare the level of GDP per capita with and without the parameter change, in the long-run), d) long-run impact on consumption per capita (i.e. compare the level of consumption per capita with and without the parameter change, in the long-run), and e) impact on long-run GDP per capita growth rate of a one-time and instantaneous increase (jump) in productivity At, through a significant and non-repeatable invention. Assume the country begins at its “steady state value” of k* before this event occurs. Justify your answer by use of graph and/or equation. [Hint: this should not be considered a change in g, since productivity resumes growth at rate g after the one-time jump; it should be modeled as a onetime jump in At.] b. Graph the path of yt and ct against time (or better yet, ln(yt) and ln(ct), which will be linear) for the event analyzed in part a. c. Repeat parts a&b for a permanent, instantaneous increase in the growth rate of productivity, g. 3. Growth Simulations. See PS3GrowthSimulationQuestion.xlsx posted on D2L. Fill in 200 years of data using the H-D model, the Solow model, and the H-Solow model using the functions and parameters given in the “GrowthCalculations” worksheet. The savings rate in all cases increases to 30% at year 25. Specifically: 3.1. For the H-D model, A=0.25, n=0.01, d=0.04, and s=0.2. Capital per person starts at $4000. Fill out k, y, ln(y), c, ln(c), actual investment, break-even investment, ?k, and gy for 200 years. 3.2. For the Solow model, f(k) = k 1/3 , A=50, n=0.005, d=0.02, and s=0.2. Capital per person starts at $8000. Fill out k, y, c, actual investment, break-even investment, ?k, and gy for 200 years. 3.3. For the H-Solow model, f(k,h) = k 1/3h 1/3 , A=5, n=0.01, d=0.04, and s=0.2. Physical capital per person starts at $4000, human capital per person starts at 2000. Fill out k, h, y, c, ?k, ?h, and gy for 200 years. Note that in all cases, the savings rate s switches at 0.3 at the 25th year. Make sure to incorporate this in your answers. [Hint: it will only affect the consumption formula and the actual investment column formula for the H-D and Solow models, and it will only affect the consumption formula and the ?k column formula for the HSolow model.] [Hint: Of course, you need only specify each column’s formula once, then copy and paste down the column for all the years. The formulas are pretty straightforward, and can be found by looking back at the key equations for each model. It is simplest for actual investment not to recalculate income, but simply use the fact that actual investment equals a fixed fraction of income, sy in the case of physical capital and qy in the case of human capital.] 2 a. Give the income and consumption levels in year 200 for each of the three models. In which model is the increase in s most effective? In which model is it least effective? Justify your answer. b. Look at the graphs for the three models (which are in the other worksheets and should be filled out automatically from the data you generate in the GrowthCalculations worksheet). Look at both H-D graphs, but focus on the one using logs. Discuss one significant way in which all three models’ graphs are similar. How do the Solow and H-Solow graphs differ? 4. Imagine that a bank will only lend if it can earn a rate of return of 6% on a loan. Further, imagine it incurs administrative costs of $40 per loan it makes, regardless of the size of the loan. Throughout the problem, assume for simplicity that the loans are all repaid with certainty, i.e. there is no risk. a. If the bank makes five loans – of $100, $200, $500, $1000, and $10,000 – what are the respective interest rates it must charge to break even on each loan? b. Imagine the bank makes the same loans but must charge all borrowers the same interest rate. What interest rate will it charge to break even overall? Which borrowers pay less, which pay more in this case than in part a.? This practice of making losses on some loans and profits on others is called “cross-subsidization”. c. How might competition between banks eliminate any one bank’s ability to cross-subsidize smaller borrowers? Specifically, ci) could a rival lender lure away any of the customers of a bank carrying out the policy of part b., and cii) how would this affect the ability to cross-subsidize of a bank carrying out the policy of part b.? d. It may not be accurate to assume that every loan incurs the same administrative cost, irrespective of size. Larger loans may require more work. Redo part a. under the assumption that the administrative cost of a loan is $40 per loan plus 1% of the size of the loan. (Thus a loan of $5000 would cost the bank $40 + 1%*$5000 = $90, while a loan of $500 would cost the bank $40 + 1%*$500 = $45. The cost structure is still linear, but with a positive intercept and slope.)