A Study on Robust Design Optimization of Layered Plates Bonding Process Considering Uncertainties

불확정성을 고려한 적층판 결합공정의 강건최적설계

  • 이우혁 (한국항공대학교 항공우주 및 기계공학부) ;
  • 박정진 (한국항공대학교 항공우주 및 기계공학부) ;
  • 최주호 (한국항공대학교 항공우주 및 기계공학부) ;
  • 이수용 (한국항공대학교 항공우주 및 기계공학부)
  • Published : 2007.01.01


Design optimization of layered plates bonding process is conducted by considering uncertainties in a manufacturing process, in order to reduce the crack failure arising due to the residual stress at the surface of the adherent which is caused by different thermal expansion coefficients. Robust optimization is peformed to minimize the mean as well as its variance of the residual stress, while constraining the distortion as well as the instantaneous maximum stress under the allowable reliability limits. In this optimization, the dimension reduction (DR) method is employed to quantify the reliability such as mean and variance of the layered plate bonding. It is expected that the DR method benefits the optimization from the perspectives of efficiency, accuracy, and simplicity. The obtained robust optimal solution is verified by the Monte Carlo simulation.


Dimension Reduction Method;Reliability Analysis;Robust Optimization; Monte Carlo Simulation;Layered Plates Bonding


  1. Basaran, C. and Zhao, Y., 2001, 'Mesh Sensitivity and FEA for Multi-Layered Electronic Packaging,' Trans. ASME, J. Electron. Packag. Vol. 123 (3), pp. 218-224
  2. Suhir, E., 1989, 'Interfacial Stresses in Bimetal Thermostats,' ASME J. Appl. Mech., Vol. 56, pp. 595-600
  3. Suhir, E. and Weld, J.D., 1998, 'Application of a `Surrogate' Layer for Lower Bending Stress in a Vulnerable Material of a Tri-Material Body,' Microelectronics Reliability, Vol. 38, pp. 1949-1954
  4. Rahman, S. and Xu, H., 2004, 'A Univariate Dimension-Reduction Method for Multi-Dimensional Integration in Stochastic Mechanics,' Probabilistic Engineering Mechanics, Vol. 19, pp. 393-408
  5. Park, G. J., Lee, T. H., Lee, K. H. and Hwang, K. H., 2004, 'A review of Robust Design Methodologies,' Trans. of the KSME (A), Vol. 28, No. 9, pp. 1368-1383
  6. Jiang, Z. Q., Huang, Y. and Chandra, A., 1997, 'Thermal Stresses in Layered Electronic Assemblies,' J. Electron. Pack., Vol. 119, pp. 127-133
  7. Glaser, J. C., 1989, 'Thermal Stresses in Compliantly-Joined Materials,' ASME Winter Annual Meeting, Paper No. 89-WA/EEP-14, San Francisco, CA, December
  8. Shih, C. F. and Asaro, R. J., 1988, 'Elasto-Plastic Analysis of Cracks on Bi-Material Interfaces: Part I - Small Scale Yielding,' ASME, J. Appl. Mech., Vol. 55, pp. 299-316
  9. Shih, C. F. and Asaro, R. J., 1989, 'Elasto-Plastic Analysis of Cracks on Bi-Material Interfaces: Part II - Structure of a Small-Scale Yielding Fields,' ASME, J. Appl. Mech., Vol. 56, pp. 763-779
  10. Plotner, M., Donat, B. and Benke, A., 1991, 'Deformation Properties of Indium-Based Solders at 294 and 77 K,' Cryogenics, Vol. 31(3) , pp. 159-162
  11. ANSYS Release 9.0 Documentation, SAS IP, Inc., 2004
  12. Youn, B. D., Choi, K. K. and Du, L., 2005, 'Performance Moment Integration (PMI) Method for Quality Assessment in Reliability-Based Robust Design Optimization,' Mechanics Based Design of Structures and Machines, Vol. 33, pp. 185-213
  13. Lin, C. Y., Huang, W. H., Jeng, M. C. and Doong, J. L., 1997, 'Study of an Assembly Tolerance Allocation Model Based on Monte Carlo Simulation,' Journal of Materials Processing Technology, Vol. 70, pp. 9-16
  14. McAllister, C. D. and Simpson, T. W., 2003, 'Multidiscip Linary Robust Design Optimization of an Internal Combustion Engine,' Vol. 125, No. 2, pp. 124-130
  15. Jung, D. H. and Lee, B. C., 2002, 'Development of a Simple and Efficient Method for Robust Optimization,' International Journal for Numerical Methods in Engineering, Vol. 53, pp. 2201-2215
  16. Liu, P. L. and Kiureghian, A. D., 1991. 'Optimization Algorithms for Structural Reliability Analysis,' Computers & Structures, Vol. 52, No. 1, pp. 103-111
  17. Lee, Y. B., Lee, H. J., Kim, M., S., and Choi, D., H., 2005, 'Sequential Approximate Optimization Based on a Pure Quadratic Response Surface Method with Noise Filtering,' Trans. of the KSME (A), Vol. 29, No. 6, pp. 842-851
  18. Suhir, E., 2001, 'Predicted Thermal Stresses in a Bimaterial Assembly Adhesively Bonded at the Ends,' Journal of Applied Physics, Vol. 89(1), pp. 120-129
  19. Chen, D., Cheng, S. and Gerhardt, T. D., 1982, 'Thermal Stresses in Laminated Beams,' J. Thermal Stresses, Vol. 5, pp.67-84
  20. Varghese, P., Braswell, R.N., Wang, B. and Zhang, C., 1996, 'Statistical Tolerance Analysis Using FRPDF and Numerical Convolution,' Computer-Aided Design, Vol. 28, No. 9, pp. 723-732
  21. Wu, Y.-T. and Wirsching, P. H., 1987, 'New Algorithm for Structural Reliability Estimation,' Journal of Engineering Mechanics, ASCE, Vol. 113, No. 9, pp. 1319-1336

Cited by

  1. Reliability Analysis Using Dimension Reduction Method with Variable Sampling Points vol.33, pp.9, 2009,