**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**30236

##### Bi-Directional Evolutionary Topology Optimization Based on Critical Fatigue Constraint

**Authors:**
Khodamorad Nabaki,
Jianhu Shen,
Xiaodong Huang

**Abstract:**

This paper develops a method for considering the critical fatigue stress as a constraint in the Bi-directional Evolutionary Structural Optimization (BESO) method. Our aim is to reach an optimal design in which high cycle fatigue failure does not occur for a specific life time. The critical fatigue stress is calculated based on modified Goodman criteria and used as a stress constraint in our topology optimization problem. Since fatigue generally does not occur for compressive stresses, we use the p-norm approach of the stress measurement that considers the highest tensile principal stress in each point as stress measure to calculate the sensitivity numbers. The BESO method has been extended to minimize volume an object subjected to the critical fatigue stress constraint. The optimization results are compared with the results from the compliance minimization problem which shows clearly the merits of our newly developed approach.

**Keywords:**
topology optimization,
BESO method,
p-norm,
fatigue constraint

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1315731

**References:**

[1] Bendsøe, M. P. and N. Kikuchi, Generating optimal topologies in structural design using a homogenization method. Computer methods in applied mechanics and engineering, 1988. 71(2): pp. 197-224.

[2] Svanberg, K., The method of moving asymptotes—a new method for structural optimization. International journal for numerical methods in engineering, 1987. 24(2): pp. 359-373.

[3] Bruggi, M. and P. Duysinx, Topology optimization for minimum weight with compliance and stress constraints. Struct Multidisc Optim, 2012. 46(3): pp. 369-384.

[4] Holmberg, E., B. Torstenfelt, and A. Klarbring, Stress constrained topology optimization. Struct Multidisc Optim, 2013. 48(1): pp. 33-47.

[5] Jeong, S. H., D.-H. Choi, and G. H. Yoon, Separable stress interpolation scheme for stress-based topology optimization with multiple homogenous materials. Finite Elements in Analysis & Design, 2014. 82: pp. 16-31.

[6] Jeong, S. H., et al., Topology optimization considering static failure theories for ductile and brittle materials. Computers and Structures, 2012. 110-111: pp. 116-132.

[7] Le, C., et al., Stress- based topology optimization for continua. Struct Multidisc Optim, 2010. 41(4): pp. 605-620.

[8] París, J., et al., Stress constraints sensitivity analysis in structural topology optimization. Computer Methods in Applied Mechanics and Engineering, 2010. 199(33): pp. 2110-2122.

[9] Huang, X. and Y. M. Xie, Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite Elements in Analysis & Design, 2007. 43(14): pp. 1039-1049.

[10] Rozvany, G. I. N., A critical review of established methods of structural topology optimization. Structural and Multidisciplinary Optimization, 2009. 37(3): pp. 217-237.

[11] Holmberg, E., B. Torstenfelt, and A. Klarbring, Fatigue constrained topology optimization. Structural and Multidisciplinary Optimization, 2014. 50(2): pp. 207-219.

[12] Bendsøe, M. P., Topology Optimization: Theory, Methods, and Applications, ed. O. Sigmund. 2004, Berlin/Heidelberg: Berlin/Heidelberg : Springer Berlin Heidelberg.

[13] Cheng, G. and Z. Jiang, Study On Topology Optimization With Stress Constraints. Engineering Optimization, 1992. 20(2): pp. 129-148.

[14] Cheng, G. and X. Guo, ε-relaxed approach in structural topology optimization. Structural Optimization, 1997. 13(4): pp. 258-266.

[15] Rozvany, G. I. N., On design-dependent constraints and singular topologies. Struct Multidisc Optim, 2001. 21(2): pp. 164-172.

[16] Kirsch, U., On singular topologies in optimum structural design. Structural Optimization, 1990. 2(3): pp. 133-142.

[17] Cook, R. D., Concepts and applications of finite element analysis. 4th ed. ed, ed. R. D. Cook. 2001, New York: Wiley.

[18] Huang, X. and Y. Xie, Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. 2007.

[19] Huang, X. and Y. Xie, Evolutionary topology optimization of continuum structures with an additional displacement constraint. Struct Multidisc Optim, 2010. 40(1): pp. 409-416.

[20] Huang, X. and Y. Xie, Evolutionary topology optimization of geometrically and materially nonlinear structures under prescribed design load. Structural Engineering and Mechanics 2010. 34(5): pp. 581-595.

[21] Yi, J., et al., A topology optimization method for multiple load cases and constraints based on element independent nodal density. Structural Engineering and Mechanics, 2013. 6(45): pp. 759-777.

[22] Jensen, K. E., Solving stress and compliance constrained volume minimization using anisotropic mesh adaptation, the method of moving asymptotes and a global p-norm. Structural and Multidisciplinary Optimization, 2016. 54(4): pp. 831-841.