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Personally, I solve problems by taking a look at all of the information given to me, and how this all applies together. From here, I can take all of this information and analyze in different ways, be it pictures or a brainstorm as to how it can be solved. One of the biggest things to do in solving any problem is to keep a level head about the situation and try and solve it as you analyze how each piece of the puzzle fits together. I have learned to solve problems this way starting with my 12th grade physics class, when we were told time and time again to use the "GUESS" Method, which stands for Givens, Unknowns, Equations, Solve, Solution. Using this method gives one a methodical way to go about solving the problem. After going through four years of engineering school, I have refined this method to apply to engineering problems, as you state your problem, then your givens, then perhaps a free body diagram, then start putting equations to it.
After taking MAE451 in fall 2010, I have learned that problems can be analyzed a completely different way that I have never seen before, which is in a House of Quality. This is a visual which connects Customer Requirements, or qualitative requirements to Engineering Specifications, or quantitative requirements. Here is an example House of Quality, which was used in our mini Project 3 (Click to enlarge):
This process of problem solving that I have learned in college not only applies to solving purely engineering problems, but it gives you the ability to think critically and apply these skills to common problems that could arise every day in life.
The way I solve problems is not the perfect way to go about solving problems, and it can always be improved. One way to improve upon this, is to survey others to see how they solve problems.
In order to begin to see how people solve problems, I asked three questions (click the link to see the answers!):
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