Optimization of material distribution for forged automotive components using hybrid optimization techniques
1Silesian University of Technology, Department of Computational Mechanics and Engineering, Konarskiego 18A, Gliwice, Poland.
The paper deals with the problem of optimal material distribution inside the provided design area. Optimization based on deterministic and stochastic algorithms is used to obtain the best result on the basis of the proposed objective function and constraints. The optimization of the shock absorber is used as an example of the described methods. One of the main difficulties addressed is the manufacturability of the optimized part intended for the forging process. Additionally, nonlinear buckling simulation with the use of the finite element method is used to solve the misuse case of shock absorber compression, where the shape of the optimized part has a key role in the total strength of the automotive damper. All of that, together with the required design precision, creates the nontrivial constrained optimization problem solved using the parametric, implicit geometry representation and a combination of stochastic and deterministic algorithms used with parallel design processing. Two methods of optimization are examined and compared in terms of the total amount of function calls, final design mass, and feasibility of the resultant design. Also, the amount of parameters used for the implicit geometry representation is greatly reduced compared to existing schemes presented in the literature. The problem addressed in this article is strongly inspired by the actual industrial example of the mass minimization process, but it is more focused on the actual manufacturability of the resultant component and admissible solving time. Commercially accessible software combined with authors’ procedures is used to resolve the material distribution task, which makes the proposed method universal and easily adapted to other fields of the optimization of mechanical elements.
Sebastjan, P., & Kuś, W. (2021). Optimization of material distribution for forged automotive components using hybrid optimization techniques. Computer Methods in Materials Science, 21(2), 63-74. https://doi.org/10.7494/cmms.2021.2.0746
Bendsøe, M. (1989). Optimal shape design as a material distribution problem. Structural Optimization, 1(4), 193–202.
Beyer, H.-G., & Schwefel, H.-P. (2002). Evolution strategies – A comprehensive introduction. Natural Computing, 1(1), 3–52.
Burczyński, T., & Orantek, P. (1999). Coupling of genetic and gradient algorithms. In Proceedings of Conference on Evolutionary Algorithms and Global Optimization (pp. 112–114).
Burczyński, T., Kuś, W., Beluch, W., Długosz, A., Poteralski, A., & Szczepanik, M. (2020). Inteligent Computing in Optimal Design. Springer International Publishing.
Ferrari, F., & Sigmund, O. (2020). Towards solving large-scale topology optimization problems with buckling constraints at the cost of linear analyses. Computer Methods in Applied Mechanics and Engineering, 363, 112911.
Guirguis, D., & Aly, M. (2016). A derivative-free level-set method for topology optimization. Finite Elements in Analysis and Design, 120, 41–56.
Hongwen, H., Lu, Y., & Peng, J. (2017). Combinatorial optimization algorithm of MIGA and NLPQL for a plug-in hybrid electric bus parameters optimization. Energy Procedia, 105, 2460–2465.
Hu, X., Chen, X., Zhao, Y., & Yao, W. (2014). Optimization design of satellite separation systems based on Multi-Island Genetic Algorithm. Advances in Space Research, 53, 870–876.
Li, H., Li, P., Gao, L., Li, Z., & Wu, T. (2015). A level set method for topological shape optimization of 3D structures with extrusion constraints. Computer Methods in Applied Mechanics and Engineering, 283, 615–635.
Ntintakis, I., Stavroulakis, G., & Plakia, N. (2020). Topology Optimization by the use of 3D Printing Technology in the Product Design Process. HighTech and Innovation Journal, 1(4), 161–171.
Schittkowski, K. (1986). NLPQLP: A Fortran Implementation of a Sequential Quadratic Programming Algorithm with Distributed and Non-Monotone Line Search. User’s Guide, Version 4.2.
Schittkowski, K., Zillober, C., & Zotemantel, R. (1994). Numerical comparison of nonlinear programming algorithms for structural optimization. Structural Optimization, 7, 1–19.
Stolpe, M., & Svanberg, K. (2001). An alternative interpolation scheme for minimum compliance topology optimization. Structural and Multidisciplinary Optimization, 22(2), 116–124.
Vatanabe, S.L., Lippi, T.N., Lima, C.R., de, Paulino, G.H., & Silva, E.C.N. (2016). Topology Optimization with Manufacturing Constraints: A Unified Projection-Based Approach. Advances in Engineering Software, 100, 97–112.
Wang, S., & Wang, M.Y. (2006). Radial basis functions and level set method for structural topology optimization. International Journal for Numerical Methods, 65(12), 2060–2090.
Whitley, D., Rana, S., & Hackendorn, R.B. (1999). The Island Model Genetic Algorithm: On Separability, Population Size and Convergence. Journal of Computing and Information Technology, 7(1), 33–47.
Zhou, M., Shyy, Y.K., & Thomas, H.L. (2001). Checkerboard and minimum member size control in topology optimization. Structural and Multidisciplinary Optimization, 21(2), 152–158.