Numerical Methods
MatLab Projects
"Mathematics is an elegant and precise subject: however when numerical answers are required one sometimes needs to rely on approximate methods to obtain useable answers. There are many problems which simply do not have analytical solutions, or those whose exact solution is beyond our current state of knowledge. There are also many problems which are too long (or tedious) to solve by hand. When such problems arise we can exploit numerical analysis to reduce the problem to one involving a finite number of unknowns and use a computer to solve the resulting equations."
From An Introduction to Programming and Numerical Methods in MATLAB by S.R. Otto and J.P. Denier.
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November 2013
This project was basically an earthquake-resistant analysis, for which I evaluated the dynamic response of a structure that was subjected to seismic excitation resulting from the movement of the tectonic plates of the lithosphere. For this, a simplified one-dimensional model was developed based on beam theory.
The equation of motion for a mechanical system was solved using the function to solve linear systems of MatLab, in order to be able to evaluate the response of the model and to determine the deflection of the building.
Specifically, I calculated the building deformation, the critical excitation frequency, the response of the three building slabs as a function of time, and the response of each slab versus time for a given damping. Finally, based on my own criteria, I estimated the reduction percentage of the vibration amplitude as vibration increases.
This project served to reinforce the knowledge of vibrations as well as to improve my MatLab skills.
This was the first of two projects for the Computational Mechanics course at my university. The main objective of this course was to learn how to handle MatLab software in order to solve problems related to the application of numerical methods, as well as to improve the software management skills.
From the equation that governs the diffusion of a pollutant that was spilled in the middle of a corridor and taking into consideration the border conditions and dimensions of the domain, the Finite Difference Method was used to determine the time that the worker had to leave the corridor before the average concentration reached a specific value. Additionally, the distribution of contaminant was plotted for the final time instant.