Topological optimization processes

Michal Holdy Michal Holdy,Juraj Beniak Juraj Beniak

doi:10.30574/gjeta.2022.10.1.0023

Abstract

The method of topological optimization is based on a mathematical algorithm, which is based on the distribution and intensity of detail stress on the investigated component. It was developed using the Rhino-Grasshopper theory. This is a complicated FEM analysis with the help of the Nastran solver in the Siemens NX software environment. The topology detail is controlled by the degree of iteration of the algorithm, changing the size and distribution of the elements in relation to the incoming force stresses of the FEM simulation. The goal of topological optimization is a clearly defined shape of the component for a given design solution.

Highlights

Topological optimization processes are used in mechanical, and in other industries in order to reduce the amount of material used and the deformation energy of construction details, while maintaining mechanical strength
Solid Isotropic Material with Penalization (SIMP) technique The SIMP method was defined by Bendsoe - Kikuchi (1988) and Rozvany - Zhou (1992)
Mathematical model, boundary conditions, dimensions, forces are shown in the figure

Summary

Introduction

Topological optimization processes are used in mechanical, and in other industries in order to reduce the amount of material used and the deformation energy of construction details, while maintaining mechanical strength. Boundary conditions can be understood as, for example, the incoming loading forces of the system, the physical and mechanical properties of the material used, the safety coefficients etc The result of such optimization is a targeted shape, as the most optimal for a given construction detail. At each stage of the optimization iteration, the algorithm performs a so-called sensitivity analysis It is a process in which the impact of different material densities on the function of the purpose of the system is evaluated, in order to maximize the stiffness. During the sensitivity analysis process, elements that are loaded with low material density coefficients eventually lose their structural importance and are subsequently eliminated in subsequent iteration stages. This is an undesirable state, forming discontinuous, illogical volumes of the overall topological optimization This checkerboard effect is minimized by averaging the sensitivities of the elements during iterative cycles. The 3D CAD model is compiled by binary matrices of database structural grids with subsequent transformation into a * .stl format model

Results and discussion

Conclusion

Compliance with ethical standards Acknowledgments