A Topology Optimization Method Based on Non-Uniform Rational Basis Spline Hyper-Surfaces for Heat Conduction Problems

This work deals with heat conduction problems formulation in the framework of a CAD-compatible topology optimization method based on a pseudo-density field as a topology descriptor. In particular, the proposed strategy relies, on the one hand, on the use of CAD-compatible Non-Uniform Rational Basis Spline (NURBS) hyper-surfaces to represent the pseudo-density field and, on the other hand, on the well-known Solid Isotropic Material with Penalization (SIMP) approach. The resulting method is then referred to as NURBS-based SIMP method. In this background, heat conduction problems have been reformulated by taking advantage of the properties of the NURBS entities. The influence of the integer parameters, involved in the definition of the NURBS hyper-surface, on the optimized topology is investigated. Furthermore, symmetry constraints, as well as a manufacturing requirement related to the minimum allowable size, are also integrated into the problem formulation without introducing explicit constraint functions, thanks to the NURBS blending functions properties. Finally, since the topological variable is represented by means of a NURBS entity, the geometrical representation of the boundary of the topology is available at each iteration of the optimization process and its reconstruction becomes a straightforward task. The effectiveness of the NURBS-based SIMP method is shown on 2D and 3D benchmark problems taken from the literature.

Fractal Plots of Topology Optimization Efficiency in Solving of the Problem for Strength Dependence on the Grid

In this research is solved the problem for determining of dependencies describing the strength redundancy of a part obtained by means of topology optimization using the SIMP method under a variety of grid’s finite elements. For this purpose, in the research was performed a digital experiment, during which almost fifty variants of part’s computer models were obtained, and their mechanical properties were studied. Based on the obtained data were constructed plots for the strength efficiency of topological optimization, which reflect fractal properties of part’s strength parameters changing. Upon reaching the research goal were solved the problems of software selection and applying a programs combination, which allowed automate the creation of models based on the topology optimization results. The main tool for topology optimization was the Autodesk Fusion 360 product, providing a free access to cloud computing, and Autodesk ReCap Photo was used when models converting. On the results of the experiment were formulated recommendations for obtaining the part’s optimized topology without critical defects of shape, using the SIMP method. With great probability, these recommendations are important when using other methods for topological optimization, such as ESO, BESO, or Level-Set. The received recommendations were tested in solution the problem of increasing the structures’ strength efficiency on the example of the rocker-Bogie wheel suspension using in modern Curiosity-type Mars rovers. The topology optimization results are openwork parts that can withstand heavy loads at low weight. This was confirmed by strength analysis, which had showed an increase in specific strength up to 13.5 times, relative to the prototype used in the Curiosity-type Mars rover’s suspension.