In mathematics, an optimization problem consists on minimizing or maximizing a function taking into account some constraints.
I want to show you an example of how to apply mathematics in order to solve a problem in the real life: the design of super-lightweight components. That's possible by means of a topology optimization.
In a topology optimization, the function to be maximized is the stiffness of a component. The constraint to be satisfied is a limit on the mass.
Therefore, the result of the optimization is a component that not only is lighter but also is the stiffest possible for its weight.
That's the secret to design super-lightweight components. And they will be very strong!
Let me show you a practical example.
The first thing to do in a topology optimization is to determine the space to be optimized. That's called the design space.
Then, it's necessary to mesh the component and apply the boundary conditions (loads and constraints).
During the optimization process, it's decided which elements are really working and which are being a little bit lazy. The working elements are kept, while the lazy ones are removed. That's the way to keep the really important elements. That's Intelligent Use of Material!
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| Result of the topology optimization |
In this case, the optimization has been carried out with a weight reduction of 70%.
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| Final Design |
As you can see in the Finite Element Analysis of the optimized design, low-stressed areas (dark blue) are minimal, which means good use of material. This is the objective of a topology optimization, to use material only where it is necessary. There are no lazy elements. And there are no excessive working ones.
If you would like to learn more about topology optimization or want to find out how you can do it too, I invite you to visit my website:
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