ABSTRACT
Within the space industry there is a need for low mass structures in order to reduce costs of materials but also costs of fuel required to get these structures into space. In addition, novel manufacturing methods, like additive manufacturing, allow for the creation of more complex geometries which in turn require a more complex design process. Optimising such structures in terms of mass, while at the same time fulfilling all requirements regarding functionality and allowable values such as stresses, strains and displacements, poses a huge challenge. Gradient-based optimisation strategies, but also evolutionary algorithms are characterised by the curse of dimensionality which leads to a large number of required model evaluations or to the situation where no global optimum can be identified.
For this reason, a novel approach is proposed where the optimisation problem is tackled by a heuristic adaption procedure on element level. During the FE-analysis, the structural requirements like allowable stresses or strains are checked and -if necessary- the thickness and/or material orientation of the element is updated. Access to the element routines in the FE-analysis is therefore a requirement for this strategy for which reason a number of state-of-the-art element routines have been developed and adopted as user element routines to be linked with the commercial FEM software ABAQUS. The optimisation process is performed in an iterative manner, meaning that the external loading is applied in several load portions until the full force magnitudes are active. The main advantage of this approach is the applicability to large and complex FE-models, with the possibility of the structure having multiple local optimums. In addition, the strategy can be used for models involving different kinds of elements, like shell elements including layered composite, sandwich or isotropic (metallic) shell sections, and also fastener elements.
This approach by itself could lead to local concentrations of mass caused by high stresses concentrations. These stresses might be artificial, depending on the constitutive law used, and can occur near sharp corners, boundary conditions or load introduction areas. To reduce these peak masses a smoothing algorithm is developed which smoothes the stress concentrations by averaging over multiple elements. The domain over which smoothing occurs for a specific element depends on a certain maximum distance from the element centroid and the similarity of neighbouring elements with regards to how their stresses change with increasing load. Using this approach, artificial peak stresses can be smoothed out without the risk of oversmoothing and underestimation of stresses. Additionally, stiffness driven stresses can be smoothed or shifted as well with this algorithm.
In order to handle the large amount of data involved in the optimisation process, SQLite-databases are used, which act as a means of exchanging information between the algorithms and the FE-software. With these databases the full optimisation procedure remains traceable and, for example, the convergence behaviour of the process can be investigated. Also, it allows for the model itself and all of its properties and results to be visualised and filtered in an efficient manner. Finally, the layup stored in the database can easily be used for an automated model build, resulting in a complete and robust design/optimisation workflow.
In this work, the theoretical backgrounds, the logic of the workflow and practical issues of the applications are discussed. An industrial example illustrates distinct features of all the process and shows the advantages of the approach for industrial applications.