Complex strength-constrained topology structural optimization problem statement for rolling stock and special equipment of railway

B. M. Tovt

Abstract


Purpose. The main paper purpose is the development of the topology structural optimization scientific basis regarding to the complicated optimization problems of rolling stock and special railway equipment structures. Methodology. Mathematical programming and mathematical modeling are the creating tools for the topology structural optimization problem statement for the rolling stock and special railway equipment. Findings. The fundamental review and analysis of the topology structural optimization modern state is executed. The classical variation problem statement and FE-statement of the topology optimization problem are in the paper. The stress-constrained structure mass minimization problem statement is considered. The stress-constrained topology optimization problems have some difficulties, which are considered in the paper in detail. The strength condition by the fatigue strength safety factor criterion is transformed to the strength condition by the allowable stresses criterion. Originality. Scientific novelty is the development of the optimal design theory adapted to solving the rolling stock and special railway equipment structures problems. Practical value. Practical importance of the research is the adaptation of the existing topology structural optimization problem statements to the railway engineering industry problems.


Keywords


topology optimization; FEM; SIMP-method; stress constraints; fatigue strength; weight

References


Kostrytsia S.A., Tovt B.M. Chyselna realizatsiia metodiv matematychnoho prohramuvannia u zadachakh optymalnoho proektuvannia mekhanichnykh konstruktsiy [The numerical implementation of mathematical programming in problems of optimal design in mechanical structures]. Vіsnyk Dnіpropetrovskoho natsіonalnoho unіversytetu zalіznichnoho transportu іmenі akademіka V. Lazariana [Bulletin of Dnipropetrovsk National University named after Academician V. Lazaryan], 2009, issue 30, pp. 150-154.

Allaire G. Shape optimization by the homogenization method. New York, Springer Publ., 2002. 471 р.

Bendsoe M.P., Kikuchi N. Generating optimal topologies in structural design using a homogenization method. Computer Methods in Applied Mechanics and Engineering, 1988, no. 71, pp. 197-224.

Bendsoe M.P. Optimal shape design as a material distribution. Structure Optimization, 1989, no. 1, pp. 193-202.

Bendsoe M.P., Sigmund O. Topology Optimization: Theory, Methods and Application. Heidelberg, Springer Publ., 2003. 370 p.

Bruns T., Tortorelli D. Topology optimization of non-linear elastic structures and compliant mechanisms. Computer Methods in Applied Mechanics and Engineering, 2001, no. 190 (26-27), pp. 3443-3459.

Cheng G.D., Z. Jiang. Study on topology optimization with stress constraints. Engineering Optimization, 1992, no. 20 (2), pp. 129-148.

Christensen P.W., Klarbring A. An introduction to Structural Optimization. London, Springer Publ., 2009. 211 p.

Guilherme C.E.M., J.S.O. Fonseca Topology optimization of continuum structures with ε -relaxed stress constraints. ABCM Symposium Series in Solid Mechanics, 2007, no. 1, pp. 239-250.

Hajela P., Lee E. Genetic algorithms in truss topology optimization. International Journal Solids Structure, 1992, no. 32, pp. 3341-3357.

Holmberg E., Torstenfelt B., Klarbring A. Stress constrained topology optimization. Structural and Multidisciplinary Optimization, 2013, no. 48 (1), pp. 33-47.

Holmberg E., Torstenfelt Bo., Klarbring A. Fatigue constrained topology optimization. Structural and Multidisciplinary Optimization, 2013, preprint.

Le C., Norato J., Bruns T. Stress-based topology optimization for continua. Structural and Multidisciplinary Optimization, 2010, no. 41, pp. 605-620.

Lee E., James K. A., Martins J. R. R. A. Stress-constrained topology optimization with design-dependent loading. Structural and Multidisciplinary Optimization, 2012, no. 46 (5), pp. 647-661.

Lewinski T., Rozvany G.I.N. Exact analytical solutions for some popular benchmark problems in topology optimization II: three-side polygonal supports. Structural and Multidisciplinary Optimization, 2007, no. 33, pp. 337-350.

Michell A.G.M. The limits of economy of material in frame structures. Philosophical Magazine, 1904, no. 8, pp. 589-597.

Paris J., Navarrina F., Colominas I. Block aggregation of stress constraints in topology optimization of structures. Advances in Engineering Software, 2010, no. 41 (3), pp. 433-441.

Paris J., Navarrina F., Colominas I. Topology optimization of continuum structures with local and global stress constraints. Structural and Multidisciplinary Optimization, 2009, no. 39, pp. 419-437.

Pereira J., Francello E., Barcellos C. Topology optimization of continuum structures with material failure constraints. and Multidisciplinary Optimization, 2004, no. 26 (1), pp. 50-66.

Rozvany G.I.N. Aims, scope, methods, history and unified terminology of computer-aided topology optimization in structural mechanics. Structural and Multidisciplinary Optimization2001, no. 21, pp. 90-108.

Rozvany G.I.N. Difficulties in truss topology optimization with stress, local buckling and system stability constraints. Structural and Multidisciplinary Optimization, 1996, no. 11 (3), pp. 213-217.

Schmit L.A. Structural design by systematic synthesis. Proc. of the second ASCE Сonf. on electronic computation. Pittsburgh, 1960, pp. 105-122.

Spillers W.R., MacBain K.M. Structural Optimization. London, Springer Publ., 2009. 302 p.

Stolpe M., Svanberg K. On the trajectories of the epsilon-relaxation approach for stress-constrained truss topology optimization. Structural and Multidisciplinary Optimization, 2001, no. 21 (2), pp. 140-151.

Svanberg K. The method of moving asymptotes – a new method for structural optimization. International Journal for Numerical Methods in Engineering,1987, no. 24, pp. 359-373.

Xie Y.M., Steven G.P. Evolutionary structural optimization. London, Springer Publ., 1997. 540 p.


GOST Style Citations


1. Костриця, С. А. Чисельна реалізація методів математичного програмування у задачах оптимального проектування механічних конструкцій / С. А. Костриця, Б. М. Товт // Вісн. Дніпропетр. нац. ун-ту залізн. трансп. ім. акад. В. Лазаряна. – Д., 2009. – Вип. 30. – С. 150−154.

2. Allaire, G. Shape optimization by the homogenization method / G. Allaire. – New York : Springer, 2002. – 471 р.

3. Bendsoe, M. P. Generating optimal topologies in structural design using a homogenization method / M. P. Bendsoe, N. Kikuchi // Computer Methods in Applied Mechanics and Engineering. – 1988. − № 71. – P. 197−224.

4. Bendsoe, M. P. Optimal shape design as a material distribution / M. P. Bendsoe // Structure Optimization. – 1989. – № 1. – P. 193–202.

5. Bendsoe, M. P. Topology Optimization: Theory, Methods and Application / M. P. Bendsoe, O. Sigmund. – Heidelberg : Springer, 2003. – 370 p.

6. Bruns, T. Topology optimization of non-linear elastic structures and compliant mechanisms / T. Bruns, D. Tortorelli // Computer Methods in Applied Mechanics and Engineering. – 2001. – № 190 (26−27). – P. 3443–3459.

7. Cheng, G. D. Study on topology optimization with stress constraints / G. D. Cheng, Z. Jiang // Engineering Optimization. – 1992. – № 20 (2). – P. 129–148.

8. Christensen, P. W. An introduction to Structural Optimization / P. W. Christensen, A. Klarbring. – London : Springer, 2009. – 211 p.

9. Guilherme, C. E. M. Topology optimization of continuum structures with ε -relaxed stress constraints / C. E. M. Guilherme, J. S. O. Fonseca // ABCM Symp. Series in Solid Mechanics. – 2007. – № 1. – P. 239–250.

10. Hajela, P. Genetic algorithms in truss topology optimization / P. Hajela, E. Lee // Intern. J. Solids Structure. – 1992. – № 32. − P. 3341–3357.

11. Holmberg, E. Stress constrained topology optimization / E. Holmberg, Bo Torstenfelt, A. Klarbring // Structural and Multidisciplinary Optimization. – 2013. – № 48 (1). – P. 33–47.

12. Holmberg, E. Fatigue constrained topology optimization / E. Holmberg, B. Torstenfelt, A. Klarbring // Structural and Multidisciplinary Optimization. – 2013. – preprint.

13. Le, C. Stress-based topology optimization for continua / C. Le, J. Norato, T. Bruns, C. Ha // Structural and Multidisciplinary Optimization. – 2010. – № 41. – P. 605–620.

14. Lee, E. Stress-constrained topology optimization with design-dependent loading / E. Lee, K. A. James, J. R. R. A. Martins // Structural and Multidisciplinary Optimization. – 2012. − № 46 (5). – P. 647−661.

15. Lewinski, T. Exact analytical solutions for some popular benchmark problems in topology optimization II: three-side polygonal supports / T. Lewinski, G. I. N. Rozvany // Structural and Multidisciplinary Optimization. – 2007. − № 33. – P. 337−350.

16. Michell, A. G. M. The limits of economy of material in frame structures / A. G. M. Michell // Philosophical Magazine. – 1904. − № 8. – P. 589−597.

17. Paris, J. Block aggregation of stress constraints in topology optimization of structures / J. Paris, F. Navarrina, I. Colominas // Advances in Engineering Software. – 2010. – № 41 (3) – P. 433–441.

18. Paris, J. Topology optimization of continuum structures with local and global stress constraints / J. Paris, F. Navarrina, I. Colominas // Structural and Multidisciplinary Optimization. – 2009. – № 39. – P. 419–437.

19. Pereira, J. Topology optimization of continuum structures with material failure constraints / J. Pereira, E. Francello, C. Barcellos // Structural and Multidisciplinary Optimization. – 2004. – № 26 (1). – P. 50–66.

20. Rozvany, G. I. N. Aims, scope, methods, history and unified terminology of computer-aided topology optimization in structural mechanics / G. I. N. Rozvany // Structural and Multidisciplinary Optimization. – 2001. – № 21. – P. 90−108.

21. Rozvany, G. I. N. Difficulties in truss topology optimization with stress, local buckling and system stability constraints / G. I. N. Rozvany // Structural and Multidisciplinary Optimization. – 1996. − № 11 (3). – P. 213−217.

22. Schmit, L. A. Structural design by systematic synthesis / L. A. Schmit // Proc. of the second ASCE Conf. on Electronic Computation. – Pittsburgh : ASCE, 1960. – P. 105−122.

23. Spillers, W. R. Structural Optimization / W. R. Spillers, K. M. MacBain. – London : Springer, 2009. – 302 p.

24. Stolpe, M. On the trajectories of the epsilonrelaxation approach for stress-constrained truss topology optimization / M. Stolpe, K. Svanberg // Structural and Multidisciplinary Optimization. – 2001. – № 21 (2). – P. 140–151.

25. Svanberg, K. The method of moving asymptotes – a new method for structural optimization / K. Svanberg // Intern. J. for Numerical Methods in Engineering. – 1987. – № 24. – P. 359–373.

26. Xie, Y. M. Evolutionary structural optimization / Y. M. Xie, G. P. Steven. – London : Springer, 1997. – 540 p.



DOI: https://doi.org/10.15802/stp2013/17969

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

 

ISSN 2307–3489 (Print)
ІSSN 2307–6666 (Online)