Topology optimization
Topology optimization is a computer-based calculation method by which a favorable basic shape (topology ) can be determined for components under mechanical stress. It is typically used in aviation and aerospace, automotive and transport equipment, but also in other branches of engineering.
The starting point of the method is a geometric body which is the area which is to be provided for the developing device to a maximum available. This body is referred to as a " space ." The calculation result is the information that parts of the design space to be occupied by material.
One can distinguish in continuous and discrete topology optimization. In the continuous topology optimization, the material distribution is sought in the space. In the discrete topology optimization of discrete elements to be searched as coverage of the design space. For example, an optimal truss are sought, which ultimately represents a topology of the entire object.
Continuous topology optimization
In practice, the topology optimization is used in the design process to obtain proposals for the first drafts of components. Here, the designer the maximum available space and the boundary conditions (loads and restraints ) must establish first. This data is converted into a finite element model (FE = finite elements).
A distinction is made for material and geometric topology optimization. In the geometric topology optimization, geometry of the component is described by the shape of the outer boundary, that is, the edges and surfaces. Besides, also the recesses are made in the boundary component and varied in shape. In the material topology optimization, the geometry of a component is described in the draft room. This is assigned a density each finite element in the design space. In simple optimization algorithms such as the Optimaltitätskriterien (eg Fully Stressed Design), the density is set as a simple power switch to either 0 or 100%. In Fully Stressed Design the elements remain, which are claimed close to the maximum allowable voltage, so that at the end of the optimization almost every element of the FE mesh is fully utilized in terms of strength. In the mathematical programming is an optimization algorithm that determines the partial derivatives of the objective function, the change of the parameters for the next iteration. Thus, in this case a constant density distribution for a differentiability must be present. In this case, in the so-called homogenization the change in density is described by a microscopic hollow elements in each of the finite and then transferred through a non-linear material law in a macroscopic change in the modulus. Thus, the stresses and deformations of the component can be calculated. As a result of such a topology optimization gives a rugged, porous design model that offers only a help to shape finding, due to the bone-like structure and the neglect of manufacturing constraints. One way to improve the result is the return of the FE model in a smoothed CAD surface model. This can be necessary, also take into account manufacturing constraints.