Skip to main content

Optimization of finite element model of laser forming in circular path using genetic algorithms and ANFIS


Determining suitable mesh density for complicated finite element analysis, e.g., laser forming process, has always been the main concern of analytical engineers because of its high computation time and costs. Few works addressed the application of optimization methods for finite element analysis of linear path laser scan; however, no study has yet considered optimum finite element analysis of circular path laser forming. The main objective of this article is to develop a method for determining optimum mesh density to estimate the deflection caused by laser beam circular path scan considering analysis time and forming accuracy. Optimum ranges of mesh densities are investigated first and then a deflection estimating process based on adaptive-network-based fuzzy inference system has been introduced. The proposed model was finally optimized using genetic algorithm considering accuracy and time. The numerical analysis results were finally confirmed by the conducted experimental results.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16


  • Alberti N, Fratini L et al (1994) Numerical simulation of the laser bending process by a coupled thermal mechanical analysis. In: Proceedings of the Laser assisted net shape engineering, LANE’94, Me Germany

  • Balanethiram VS, Daehn GS (1994) Hyperplasticity: increased forming limit at high workpiece velocity. Scripta Materiala 30:515–520

  • Chen D-J, Xiang Y-B et al (2002) Application of fuzzy neural network to laser bending process of sheet metal. Mater Sci Technol 18(6):677–680

    MathSciNet  Article  Google Scholar 

  • Cheng P, Lin S (2000) Using neural networks to predict bending angle of sheet metal formed by laser. Int J Mach Tools Manuf 40(8):1185–1197

    MathSciNet  Article  Google Scholar 

  • Cheng JG, Yao YL (2004) Process synthesis of laser forming by genetic algorithm. Int J Mach Tools Manuf 44(15):1619–1628

    Article  Google Scholar 

  • Fan Y, Yang Z et al (2007) Investigation of effect of phase transformations on mechanical behavior of AISI 1010 steel in laser forming. Trans ASME J Manuf Sci Eng 129:110–116

    Article  Google Scholar 

  • Hennige T (2000) Development of irradiation strategies for 3D-laser forming. J Mater Process Technol 103:102–108

    Article  Google Scholar 

  • Holland JH (1975) Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence. U Michigan Press

  • Holzer H, Arnet M et al (1994) Physical and numerical modelling of the Buckling mechanism. In: Proceedings of the laser assisted net shape engineering, LANE’94, Bamberg, Germany

  • Hsiao Y-C, Shimizu H et al (1997) Finite element modelling of laser forming. In: Proceedings of the international Congress on applications of lasers and electro-optics, (ICALEO97), San Diego, USA

  • Jang JS (1993) ANFIS: adaptive-network-based fuzzy inference system. IEEE Trans Syst Man Cybern 23(3):665–685

    Article  Google Scholar 

  • Jung HC (2006) A study on laser forming processes with finite element analysis. University of Canterbury, Christchurch

  • Labeas GN (2008) Development of a local three-dimensional numerical simulation model for the laser forming process of aluminium components. J Mater Process Technol 207:248–257

    Article  Google Scholar 

  • Liu FR, Chan KC et al (2008) Numerical modeling of the thermo-mechanical behavior of particle reinforced metal matrix composites in laser forming by using a multi-particle cell model. Compos Sci Technol 68:1943–1953

    Article  Google Scholar 

  • Liu J, Sun S, Guan Y (2009) Numerical investigation on the laser bending of stainless steel foil with pre-stresses. J Mater Process Technol 209:1580–1587

  • Maji K, Pratihar DK, Nath AK (2013) Analysis and synthesis of laser forming process using neural networks and neuro-fuzzy inference system. Soft Comput 17:849–865

  • Nadeem Q, Na SJ (2011) Deformation behavior of laser bending of circular sheet metal. Chin Opt Lett 09(09):4

  • Safdara S, Lia L et al (2007) Finite element simulation of laser tube bending: effect of scanning schemes on bending angle, distortions and stress distribution. Opt Laser Technol 39:1101–1110

    Article  Google Scholar 

  • Shekhar Chakraborty S, Racherla V et al (2012) Parametric study on bending and thickening in laser forming of a bowl shaped surface. Opt Lasers Eng 50(11):1548–1558

    Article  Google Scholar 

  • Shi Y, Yao Z et al (2006) Research on the mechanisms of laser forming for the metal plate. Int J Mach Tools Manuf 46:1689–1697

    Article  Google Scholar 

  • Shimizu H (1997) A heating process algorithm for metal forming by a moving heat source, Massachusetts Institute of Technology

  • Takagi T, Sugeno M (1983) Derivation of fuzzy control rules from human operator’s control actions. In: IFAC symposium on fuzzy information, knowledge representation and decision analysis, pp 55–60

  • Vollertsen F, Geiger M et al (1993) FDM- and FEM-simulation of laser forming: a comparative study. In: Advanced technology of plasticity, Proceedings of the fourth international conference on technology of plasticity

  • Yanjin G, Sheng S et al (2003) Finite element modeling of laser bending of pre-loaded sheet metals. J Mater Process Technol 142(2):400–407

    Article  Google Scholar 

  • Yu G, Masubuchi K et al (2001) FEM simulation of laser forming of metal plates. J Manuf Sci Eng 123:405–410

    Article  Google Scholar 

  • Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353

    MathSciNet  Article  MATH  Google Scholar 

  • Zhang L, Reutzel EW et al (2004) Finite element modeling discretization requirements for the laser forming process. Int J Mech Sci 46:623–637

    Article  MATH  Google Scholar 

  • Zhang P, Yu J et al (2009) Deformation behaviors of laser forming of ring sheet metals. Tsinghua Sci Technol 14(Supplement 1):132–136

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Rasoul Tarkesh Esfahani.

Additional information

Communicated by V. Loia.

Appendix: Results of experiments for determining acceptable ranges

Appendix: Results of experiments for determining acceptable ranges

See Tables 9, 10 and 11.

Table 9 The effect of number of elements in thickness
Table 10 The effect of the number of elements in length
Table 11 The effect of band width (width of element) on deflection

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Tarkesh Esfahani, R., Golabi, S. & Zojaji, Z. Optimization of finite element model of laser forming in circular path using genetic algorithms and ANFIS. Soft Comput 20, 2031–2045 (2016).

Download citation

  • Published:

  • Issue Date:

  • DOI:


  • Laser forming
  • Circular path
  • Finite element modeling
  • Genetic algorithm