Application and Practice of Mathematical Optimization Method in Structural Mechanics Design

Mengze Liu

doi:10.54097/8a4r5x92

Authors

Mengze Liu

DOI:

https://doi.org/10.54097/8a4r5x92

Keywords:

Mathematical optimization; structural mechanics design; Genetic algorithm.

Abstract

This paper discusses the application of mathematical optimization method in structural mechanics design, and emphasizes its importance in improving the efficiency and accuracy of structural design such as buildings and bridges. Traditional design methods are limited by empirical formulas and trial-and-error methods, and they are unable to solve complex structural problems, while mathematical optimization methods can better find the global optimal solution. This paper introduces several optimization algorithms, including scatter-based, gradient-based and heuristic algorithms. Taking a truss structure as an example, it shows how to use genetic algorithm (GA) to optimize the design. The results show that the optimized truss structure has achieved significant weight reduction under the constraint conditions. At the same time, compared with the gradient-based method, the advantages of GA in global optimization are highlighted. Finally, the paper discusses the challenges and solutions encountered in practice, such as improving the algorithm, introducing parallel computing and synthesizing various optimization methods. These studies provide valuable reference for engineers and promote the development of this field.

Downloads

Download data is not yet available.

References

[1] Volchok, D. , Danishevskyy, V. , & Slobodianiuk, S. K. I. (2023). Fuzzy sets application in the problems of structural mechanics and optimal design. Acta Mechanica, 234(12), 6191-6204.

[2] Wu, D. , Wu, Y. , Chen, M. , Fan, R. , Yan, K. , & Xiao, W. (2024). Structural optimization and experimental study on the ti-alloy kagome structure formed by the superplastic forming/diffusion bonding process:. Journal of Sandwich Structures & Materials, 26(3), 303-316.

[3] Silva, A. L. F. D. , Salas, R. A. , & Silva, E. C. N. (2024). Topology optimization considering tsai–wu yield criterion for composite materials. Archive of Applied Mechanics, 94(9), 2719-2744.

[4] Ren, Y. , Qi, S. , & Pu, C. (2019). A direct topological reanalysis algorithm based on updating matrix triangular factorization. Engineering Computations, 36(8), 2651-2672.

[5] Julián L. Pita Ruiz, Amad, A. A. S. , Gabrielli, L. H. , & Antonio André Novotny. (2019). Optimization of the electromagnetic scattering problem based on the topological derivative method. Optics Express, 27(23), 33586.

[6] Wang, T. , Zhao, J. , Zhang, Q. , Liu, J. , Chen, H. , & Zhang, J. , et al. (2022). Extracting brillouin frequency shift accurately based on particle swarm optimization and a cross-correlation method. Applied optics, 61(2), 446-454.

[7] Sun, W. , Liu, H. , & Liu, Z. (2023). A regularized limited memory subspace minimization conjugate gradient method for unconstrained optimization. Numerical algorithms, 94(4), 1919-1948.

[8] Carmon, Y. , & Duchi, J. C. (2020). First-order methods for nonconvex quadratic minimization. SIAM Review, 62(2), 395-436.

[9] Petrov, P. V. , & Newman, G. A. (2019). Estimation of seismic source parameters in 3d elastic media using the reciprocity theorem. Geophysics, 84(6), 1-56.

[10] Meitei, N. Y. , Baishnab, K. L. , & Trivedi, G. (2020). 3d‐ic partitioning method based on genetic algorithm. IET Circuits, Devices & Systems, 14(7), 1104-1109.

[11] Xie, H. , & Chen, Z. G. (2019). Application of genetic simulated annealing algorithm in detection of corn straw cellulose. Chinese Journal of Analytical Chemistry, 47(12), 1987-1994.