Suppose that your favorite finite element software boasted the following claims:
“Over a dozen equation solvers are available to approximate the solution of your problem, and each solver contains a rich set of parameters that you can define to tune the solver’s performance. To maximize the accuracy of your solution and the efficiency of the solution process, simply choose the solver that is intended for your problem type, and then tune it properly. Though it is often not possible to classify your problem type beforehand, usually the right solver can be identified within 3-5 attempts. Then, you can use an iterative tuning process to make the solution even more accurate and efficient.”
If the above statements were true, then each finite element solution would require a full-blown research project to find the right equation solver. The added time and cost of numerous solution iterations would offset many of the benefits of the finite element method within the design process. Continue reading
Quite often, design optimization problems involve semi-independent design variables. That is, some of the design variables may have to satisfy a certain relationship, but they vary independently. This would be true, for example, if you had three variables that were independent, but you wanted their sum to equal a certain value. In general, there are two ways to deal with these types of problems:
- You can impose a constraint on the design variable values using a formula-based response.
- You can redefine the design variables such that only designs that meet the imposed constraints can be created.
Thomas Edison demonstrated the first long-lasting, high-quality light bulb in 1879. His successful design resulted from a long and laborious trial-and-error search for the best filament material, a process we now call the Edisonian approach.
Edison’s determined and tireless pursuit of innovation is also evident in some of his famous quotes:
“When I have fully decided that a result is worth getting I go ahead of it and make trial after trial until it comes.”
“I have not failed. I’ve just found 10,000 ways that won’t work.”
While Edison had to create physical prototypes to test each new design, modern advances in computing power and computer-aided engineering (CAE) software now make it possible to create virtual prototypes based on mathematical models. As a result, design trials are easier, faster and cheaper than ever before. Continue reading