Topology optimization

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The topology optimization is a computer-based calculation method by which a favorable basic form (topology) can be determined for components under mechanical stress. It is typically used in aerospace engineering, in automobile and vehicle construction, but also in other branches of mechanical engineering.

The starting point of the process is a geometric body that represents the space that should be made available to the maximum for the component to be developed. This body is referred to as the "installation space". The calculation result consists of the information which parts of the installation space are to be covered with material.

For the calculation process, it is necessary to repeatedly determine the load distribution in the installation space. To this end, programs for topology optimization usually use the finite element method (FEM) today . While some implementations contain their own modules for the FEM calculation, others require the integration of an external FEM program.

Continuous and discrete topology optimization

One can differentiate between continuous and discrete topology optimization. With continuous topology optimization, the material distribution in the installation space is sought. In discrete topology optimization, discrete elements are sought to cover the installation space. For example, an optimal framework can be sought, which ultimately represents a topology of the overall object.

Continuous topology optimization

Lower right and upper right forces act alternately upwards and downwards and the left edge is supported.
The results of the topology optimization of a clamp with the help of TopOpt-2D software.

In practice, topology optimization is used in the design process to get suggestions for initial component designs. The designer must first define the maximum available installation space and the boundary conditions (loads and restraints). These data are converted into an FE model (FE = Finite Elements).

A basic distinction is made between material and geometric topology optimization. In geometric topology optimization, the geometry of the component is described by the shape of the outer boundary, i.e. the edges and surfaces. Recesses are also made within the component edge and their shape is varied. In the material topology optimization, the geometry of a component is described in the design space. Here, each finite element in the design space is assigned a density. With simple optimization algorithms such as the optimality criteria (e.g. fully stressed design), the density is set to either 0 or 100% like a simple on / off switch. With fully stressed design, the elements that are stressed close to the maximum permissible stress are retained, so that at the end of the optimization, almost every element of the FE mesh is fully utilized in terms of strength. Mathematical programming is an optimization algorithm that uses the partial derivatives of the objective function to determine the change in the individual parameters for the next iteration. Accordingly, there must be a constant density distribution for differentiability. In the so-called homogenization method, the change in density through a microscopic hollow body in each of the finite elements is described and then converted into a change in the modulus of elasticity via a non-linear, macroscopic material law. This allows the stresses and deformations of the component to be calculated. The result of such a topology optimization is a jagged, porous design model, which, due to the bone-like structure and the neglect of manufacturing restrictions, only offers an aid to finding the shape. One way to improve the result is to return the FE model to a smooth CAD surface model. Manufacturing restrictions can also be taken into account.

Discrete topology optimization

One of the first topology optimizations was done by Anthony George Maldon Michell . But even today topology optimizations are carried out using frameworks. The reason for this lies in the low computing time; although the closeness to reality is much more distant than with continuous topology optimization.

See also

Web links

Individual evidence

  1. ↑ Bendsøe MP, Sigmund, O .: Topology Optimization - Theory, Methods and Applications. ISBN 978-3-540-42992-0 .
  2. ↑ Michell AGM (1904) The limits of economy of material in frame structures. Philosophical Magazine 8 (47): 589-597 doi : 10.1080 / 14786440409463229 .
  3. ↑ Bendsøe MP, Ben-Tal A., Zowe J. (1994): Optimization methods for truss geometry and topology design. Structural and Multidisciplinary Optimization 7: 141-159, doi : 10.1007 / BF01742459 .