Visualization for Finite Element Method Education | Matlab | Visualization (Graphics)

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  Worcester Polytechnic Institute Interdisciplinary Qualifying Project Visualization for Finite Element Method Education Authors: Donald BourqueStephen Kelly Date:  December 4, 2013 Advisor:  Prof. Nima Rahbar  Abstract In this project, common practices for visualizing scientific data were studied. Inaddition, the science of cognition and data display was reviewed. The resultsof this investigation was applied to augment a Civil Engineering introductorycourse on Finite Element Method at WPI. Software enhancements allowed threedimensional visualization for simulation of engineering structures. The researchon cognition and data graphics was used to improve understanding of these vi-sual aids. The plotting function, developed in MATLAB and Julia environmentsduring the course of this project, can help all students visualize the results of their numerical codes.i  Contents 1 Introduction 12 Literature Review 1 2.1 The Theory of the Finite Element Method . . . . . . . . . . . . . 12.2 Visual Cognition . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.3 Data Representation . . . . . . . . . . . . . . . . . . . . . . . . . 22.4 Data Interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . 42.5 Scientific Visualization . . . . . . . . . . . . . . . . . . . . . . . . 4 3 Programming Languages in Scientific Computing 4 3.1 MATLAB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43.2 GNU Octave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53.3 Scilab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63.4 R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63.5 Python . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73.6 Julia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83.7 Review Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 9 4 Results and Discussion 10 4.1 MATLAB Plotting Modifications . . . . . . . . . . . . . . . . . . 104.2 Julia Implementation . . . . . . . . . . . . . . . . . . . . . . . . . 124.3 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164.3.1 IPython Multi-User Support . . . . . . . . . . . . . . . . 164.3.2 IJulia for Coursework . . . . . . . . . . . . . . . . . . . . 17 5 Conclusion 17 ii  List of Figures 1 The MATLAB graphical user interface. . . . . . . . . . . . . . . 52 The Octave graphical user interface. . . . . . . . . . . . . . . . . 63 The Scilab graphical user interface. . . . . . . . . . . . . . . . . . 74 A demo of the IPython notebook. . . . . . . . . . . . . . . . . . . 85 Visual performance benchmarks. . . . . . . . . . . . . . . . . . . 106 Initial Truss Visualization . . . . . . . . . . . . . . . . . . . . . . 117 Initial Deformed Truss Visualization . . . . . . . . . . . . . . . . 128 3D Simple Truss Visualization . . . . . . . . . . . . . . . . . . . . 139 3D Simple Truss Example . . . . . . . . . . . . . . . . . . . . . . 1410 3D Simple Truss FEA Data . . . . . . . . . . . . . . . . . . . . . 1511 Output of the Truss FEM code in IJulia. . . . . . . . . . . . . . . 16 List of Tables 1 Representational Frameworks for Shape Information . . . . . . . 22 Performance benchmarks. . . . . . . . . . . . . . . . . . . . . . . 9iii
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