Skip to main content
SpringerLink
Log in

Sensitivity analysis of composite laminated plates with bonding imperfection in Hamilton system

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

Sensitivity analysis of composite laminated plates with bonding imperfection is carried out based on the radial point interpolation method (RPIM) in a Hamilton system. A set of hybrid governing equations of response and sensitivity quantities is reduced using the spring-layer model and the modified Hellinger-Reissner (H-R) variational principle. The analytical method (AM), the semi-analytical method (SAM), and the finite difference method (FDM) are used for sensitivity analysis based on the reduced set of hybrid governing equations. A major advantage of the hybrid governing equations is that the convolution algorithm is avoided in sensitivity analysis. In addition, sensitivity analysis using this set of hybrid governing equations can obtain response values and sensitivity coefficients simultaneously, and accounts for bonding imperfection of composite laminated plates.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Arora, J. S. and Haug, E. J. Methods of design sensitivity analysis in structural optimization. AIAA Journal 17(9), 970–974 (1979)

    Article  MathSciNet  Google Scholar 

  2. Choi, K. K., Santos, J. L. T., and Fredericks, M. C. Implementation of design sensitivity analysis with existing finite element codes. ASME Journal of Mechenisms, Transmission and Autionation in Design 109(3), 385–391 (1987)

    Article  Google Scholar 

  3. Haftka, R. T. Sensitivity calculations for iteratively solved problems. International Journal for Numerical Methods in Engineering 21(8), 1535–1546 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  4. Haftka, R. T. and Barthelemy, B. On the accuracy of shape sensitivity. Structural Optimization 3(1), 1–6 (1991)

    Article  Google Scholar 

  5. Choi, K. K. and Chang, K. H. A study of design velocity field computation for shape optimal design. Finite Elements in Analysis Design 15(4), 317–341 (1994)

    Article  MATH  Google Scholar 

  6. Gu, Y. X., Zhao, H. B., Chen, B. S., and Kang, Z. Sensitivity analysis and design optimization of thermal-stress coupled structures (in Chinese). Acta Mechanica Sinica 33(5), 685–691 (2001)

    Google Scholar 

  7. Guo, X., Gu, Y. X., and Zhao, K. Adjoint shape sensitivity analysis based on generalized variational principle (in Chinese). Acta Mechanica Sinica 36(3), 288–295 (2004)

    Google Scholar 

  8. Barthelemy, B. and Haftka, R. T. Accuracy analysis of semi-analytical method for shape sensitivity calculation. Mechanics Based Design of Structures and Machines 18(3), 407–432 (1990)

    Article  Google Scholar 

  9. Olhoff, N., Rasmussen, J., and Lund, E. Exact numerical differentiation for error elimination in finite element based semi-analytical shape sensitivity analysis. Mechanics Based Design of Structures and Machines 21(1), 1–66 (1993)

    Article  MathSciNet  Google Scholar 

  10. Qian, L. X., Cheng, G. D., Sui, Y. K., and Zhong, W. X. Structural optimization theory and methods of some progress (in Chinese). Natural Science Process 5(1), 64–69 (1995)

    Google Scholar 

  11. Cheng, Z. Q., Kennedy, D., and Williams, F. W. Effect of interfacial imperfection on buckling and bending behavior of composite laminates. AIAA Journal 34(12), 2590–2595 (1996)

    Article  MATH  Google Scholar 

  12. Cheng, Z. Q., Jemah, A. K., and Williams, F. W. Theory for multi-layered anisotropic plates with weakened interfaces. Journal of Applied Mechanics 63(4), 1019–1026 (1996)

    Article  MATH  Google Scholar 

  13. Cheng, Z. Q., He, L. H., and Kitipornchai, S. Influence of imperfect interfaces on bending and vibration of laminated composite shell. International Journal of Solids and Structures 37(15), 2127–2150 (2000)

    Article  MATH  Google Scholar 

  14. Chen, W. Q., Cai, J. B., and Ye, G. R. Exact solution of cross-ply laminates with bonding interfacial imperfections. AIAA Journal 41(11), 2244–2250 (2003)

    Article  Google Scholar 

  15. Chen, W. Q. and Lee, K. Y. Exact solution of angle-ply piezoelectric laminates in cylindrical bending with interfacial imperfections. Composite Structures 65(3–4), 239–337 (2004)

    Google Scholar 

  16. Chen, W. Q., Cai, J. B., Ye, G. R., and Wang, Y. F. Exact three-dimensional solutions of laminated orthotropic piezoelectric rectangular plates featuring interlaminar bonding imperfections modeled by a general spring layer. International Journal of Solids and Structures 41(18–19), 5247–5263 (2004)

    Article  MATH  Google Scholar 

  17. Zhou, Y. Y., Chen, W. Q., and Lu, C. F. Semi-analytical solution for orthotropic piezoelectric laminates in cylindrical bending with interfacial imperfections. Composite Structures 92(4), 1009–1018 (2010)

    Article  Google Scholar 

  18. Fan, J. R. Exact Theory of Laminated Thick Plates and Shells (in Chinese), Science Press, Beijing, 111–385 (1996)

    Google Scholar 

  19. Zhong, W. X. A New Systematic Methodology for Theory of Elasticity, Dalian University of Technology Press, Dalian, 182–187 (1995)

    Google Scholar 

  20. Zhong, W. X. Symplectic System of Applied Mechanics, Science Press, Beijing, 22–44 (2003)

    Google Scholar 

  21. Qing, G., Qiu, J., and Ta, N. Modified H-R mixed variational principle for piezoelectric material and exact solution of piezoelectric laminates (in Chinese). Engineering Mechanics 22(5), 43–47 (2005)

    Google Scholar 

  22. Chen, X. F., Xu, J. F., and Qing, G. H. B-spline wavelet finite element method for analyzing natural frequencies of laminated plates (in Chinese). Journal of Dynamics and Control 7(1), 50–54 (2009)

    Google Scholar 

  23. Qing, G. H., Qiu, J., and Liu, Y. H. Free vibration analysis of stiffened laminated plates. International Journal of Solids and Structures 43(6), 1357–1371 (2006)

    Article  MATH  Google Scholar 

  24. Liu, G. R. and Gu, Y. T. An Introduction to Meshfree Methods and Their Programming, Springer, Berlin (2005)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Aeronautical Engineering, Civil Aviation University of China, Tianjin, 300300, P. R. China

    Ding-he Li  (李顶河), Jian-xin Xu  (徐建新) & Guang-hui Qing  (卿光辉)

Authors
  1. Ding-he Li  (李顶河)
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jian-xin Xu  (徐建新)
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Guang-hui Qing  (卿光辉)
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jian-xin Xu  (徐建新).

Additional information

Project supported by the National Natural Science Foundation of China (No. 60979001) and the Major Project of Civil Aviation University of China (No.CAUC2009ZD0101)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Li, Dh., Xu, Jx. & Qing, Gh. Sensitivity analysis of composite laminated plates with bonding imperfection in Hamilton system. Appl. Math. Mech.-Engl. Ed. 31, 1549–1560 (2010). https://doi.org/10.1007/s10483-010-1383-9

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-010-1383-9

Key words

Chinese Library Classification

2000 Mathematics Subject Classification

Search

Navigation