# Topology optimization

The topology optimization as a part of the structural optimization helps engineers to design products or single parts to meet the contrived requirements in an optimal way. This can be maximum stiffness with low volume or maximum stability with low mass. Thereby great possible savings can be achived in terms of less application of energy in production, less material usage and less workload in development. These benefits facilitate a kind of construction and production which meets the principle of sustainabilty.
For best use of these possible savings, the topology optimization is applied in the early concept phase of the product development process. Here a great freedom in design exists, which later on has a great influence on the upcoming costs. At the same time the costs for modifications are pretty low.
The effort for a topology optimization is fairly humble. At first the operator defines the available design space for the considered part. Then the location and amount of strain as well as regions in which the part’s shape should not be altered – i. e. drilling holes – are specified. After that an optimization run can be started and the optimization software does the rest.
Depending on the used method and the pursued target, the optimization software gains the required data for processing from a Finite-Element-Analysis (FEA). Among other things, this can be displacements or the part’s stress.
With the help of the FEA data, the structure of the part is altered by variation of the Young’s Modulus of the finite elements. In the process a low Young’s Modulus represents a hole and a high Young’s Modulus describes a solid element. With this new distribution a FEA is performed in the next iteration, at which an element with a low Young’s Modulus shows a fairly flexible behaviour and does not – like a hole – contribute to the stiffness of the structure. At some methods the Young’s Modulus is indirectly determined through another parameter. All variables which are customized by the optimization algorithm are called design variables.
How the Young’s Modulus is modified depends on the used method. The existing techniques can be roughly subclassified in mathematical and empirical methods. For the mathematical optimization the design variables are varied based on a mathematically derived principle leading to optimality. On the other hand, empirical methods change the design variables based on a rule which assumes optimality and generally generate a good result in a short amount of time. Z88Arion® uses methods from both groups.