Skip to main content

Advertisement

SpringerLink
Log in

Optimization of anisotropic composite panels with T-shaped stiffeners including transverse shear effects and out-of-plane loading

  • Research Paper
  • Published:
Structural and Multidisciplinary Optimization Aims and scope Submit manuscript

Abstract

A two-step method to optimize anisotropic composite panels with T-shaped stiffeners, including a new formulation of the transverse shear properties and an approximation of the ply contiguity (blocking) constraints as functions of the lamination parameters is provided. At the first step, a representative element of the stiffened panel (superstiffener) is optimized using mathematical programming and lamination parameters subjected to combined loading (in-plane and out-of-plane) under strength (laminate or ply failure), buckling and practical design constraints. Ply blocking constraints are imposed at this step to improve convergence towards practical laminates. At the second step, the actual superstiffener’s laminates are obtained by using a genetic algorithm. Results, for the case considered, show that the inclusion of transverse shear effects has an associated 2.5% mass penalty and that neglecting its effects might invoke earlier buckling failure. In addition, the influence of designing for failure strength at laminate or ply level is assessed.

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

  • Almroth BO, Brogan FA (1976) The STAGS computer code. NASA CR-2950, NASA. Langley Research Centre, Hampton, VA

    Google Scholar 

  • Anonymous (2004) MSC/NASTRAN reference manual, chapter 13, section 2.3. MSC Software, Santa Ana, CA

  • Ashton JE, Waddoups ME (1969) Analysis of anisotropic plates. J Compos Mater 3:148–165

    Article  Google Scholar 

  • Autio M (2000) Determining the real lay-up of a laminate corresponding to optimal lamination parameters by genetic search. Struct Multidisc Optim 20:301–310

    Article  Google Scholar 

  • Berthlot JM (1998) Composite materials. Springer, New York

    Google Scholar 

  • Bushnell D (1987a) Theoretical basis of the PANDA computer program for preliminary design of stiffened panels under combined in-plane loads. Comput Struct 27:541–563

    Article  MATH  Google Scholar 

  • Bushnell D (1987b) PANDA2-Program for minimum weight design of stiffened, composite, locally buckled panels. Comput Struct 25:469–605

    Article  MATH  Google Scholar 

  • Bushnell D, Bushnell WD (1994) Minimum weight design of a stiffened panel via PANDA2 and evaluation of the optimized panel via STAGS. Comput Struct 50:569–602

    Article  Google Scholar 

  • Butler R, Williams FW (1990) Optimum design features of VICONOPT, an exact buckling program for prismatic assemblies of anisotropic plates. Cardiff University, Cardiff, Wales, AIAA-1990-1068-226

    Google Scholar 

  • Chamis CC (1969) Buckling of anisotropic composite plates. J Struct Div 95:2119–2139

    Google Scholar 

  • Coley DA (1999) An introduction to genetic algorithms for scientist and engineers. World Scientific, Singapore

    Google Scholar 

  • Datoo MH (1991) Mechanics of fibrous composites. Elsevier Science, England, pp 31–32

    Google Scholar 

  • Diaconu CG, Sekine H (2004) Layup optimization for buckling of laminated composite shells with restricted layer angles. AIAA J 42:2153–2163

    Article  Google Scholar 

  • Fukunaga H, Vanderplaats GN (1991) Stiffness optimization of orthotropic laminated composites using lamination parameters. AIAA J 29:641–646

    Article  Google Scholar 

  • Fukunaga H, Sekine H, Sato M, Iino A (1995) Buckling design of symmetrically laminated plates using lamination parameters. Comput Struct 57:643–649

    Article  MATH  Google Scholar 

  • Giles GL, Anderson MS (1972) Effects of eccentricities and lateral pressure on the design of stiffened compression panels. Langley Research Centre, Hampton, VA, NASA TN-D-6784

    Google Scholar 

  • Goldberg DE (1989) Genetic algorithms in search, optimization and machine learning. Addison-Wesley Longman, Reading, MA

    MATH  Google Scholar 

  • Grenestedt JL (1991) Layup optimization against buckling of shear panels. Struct Optim 3:115–120

    Article  Google Scholar 

  • Gürdal Z, Haftka RT, Hajela P (1999) Design optimization of laminated composite materials. Wiley, New York

    Google Scholar 

  • Haftka RT, Walsh JL (1992) Stacking sequence optimization for buckling of laminated plates by integer programming. AIAA J 30:814–819

    Article  Google Scholar 

  • Herencia JE, Weaver PM, Friswell MI (2007) Optimization of long anisotropic laminated fiber composite panels with T-shaped stiffeners. AIAA J 45:2497–2509

    Article  Google Scholar 

  • Johnson EH (2005) MSC/NASTRAN design sensitivity and optimization, user’s guide. MSC Software, Santa Ana, CA

    Google Scholar 

  • Jones RM (1999) Mechanics of composite materials, 2nd edn. Taylor and Francis, Philadelphia, PA

    Google Scholar 

  • Kogiso N, Watson LT, Gürdal Z, Haftka RT, Nagendra S (1994) Minimum thickness design of composite laminates subject to buckling and strength constraints by genetic algorithms. Proceedings of the AIAA/ASME/ASCE/AHS/ASC 35th Structures, Structural Dynamics and Materials Conference, Hilton Head, NC, 18–20 April, pp 2257–2275

  • Laitinen M, Lahtinen H, Sjölind S (1995) Transverse shear correction factors for laminates in cylindrical bending. Commun Numer Methods Eng 11:41–47

    Article  MATH  Google Scholar 

  • Lee JM (2003) MSC/NASTRAN linear static analysis, user’s guide, chapter 13, linear buckling. MSC Software, Santa Ana, CA

    Google Scholar 

  • Le Riche R, Haftka RT (1993) Optimization of laminate stacking sequence for buckling load maximization by genetic algorithm. AIAA J 31:951–956

    Article  MATH  Google Scholar 

  • Liu W, Butler R, Mileham AR, Green AJ (2006) Bi-level optimization and postbuckling of highly strained composite stiffened panels. AIAA J 44:2562–2570

    Article  Google Scholar 

  • Liu B, Haftka RT (2004) Single level composite wing optimization based on flexural lamination parameters. Struct Multidiscipl Optim 26:111–120

    Article  Google Scholar 

  • MATLAB (2006) Software package V.7.1. The MathWorks

  • MD NASTRAN (2006) Software package 2006r1. MSC Software, Santa Ana, CA

    Google Scholar 

  • Miki M, Sugiyama Y (1991) Optimum design of laminated composite plates using lamination parameters. Proceedings of the AIAA/ASME/ASCE/AHS/ASC 32nd Structures, Structural Dynamics and Materials Conference, Baltimore MD, Part 1, pp 275–283

  • Nagendra S, Haftka RT, Gürdal Z (1992) Stacking sequence optimization of simple supported laminates with stability and strain constraints. AIAA J 30:2132–2137

    Article  Google Scholar 

  • Nagendra S, Haftka RT, Gürdal Z (1993) Design of a blade stiffened composite panel by a genetic algorithm. Proceedings of the AIAA/ASME/ASCE/AHS/ASC 34th Structures, Structural Dynamics and Materials Conference, San Diego, CA, 19–21 April, Part 4, pp 2418–2436

  • Nagendra S, Jestin D, Gürdal Z, Haftka RT, Watson LT (1996) Improved genetic algorithm for the design of stiffened composite panels. Comput Struct 58:543–555

    Article  MATH  Google Scholar 

  • Nemeth MP (1986) Importance of anisotropy on buckling of compression-loaded symmetric composite plates. AIAA J 24:1831–1835

    Article  Google Scholar 

  • Niu CYM (1992) Composite airframe structures—practical design information and data. Hong Kong Conmilit Press, Hong Kong

    Google Scholar 

  • Reissner E (1945) The effect of transverse shear deformation on the bending of elastic plates. J Appl Mech 67:A69–A77

    MathSciNet  Google Scholar 

  • Rolfes R, Rohwer K (1997) Improved transverse shear stress in composite finite elements based on first order shear deformation theory. Int J Numer Methods Eng 40:51–60

    Article  Google Scholar 

  • Schmit LA, Farshi B (1973) Optimum laminate design for strength and stiffness. Int J Numer Methods Eng 7:519–536

    Article  Google Scholar 

  • Schmit LA, Farshi B (1977) Optimum design of laminated fiber composite plates. Int J Numer Methods Eng 11:623–640

    Article  MATH  Google Scholar 

  • Stroud WJ, Agranoff N (1976) Minimum mass design of filamentary composite panels under combined loads: design procedure based on simplified equations. Langley Research Centre, Hampton, VA, NASA TN D-8257

  • Stroud WJ, Anderson MS (1981) PASCO-Structural panel analysis and sizing code, capability and analytical foundations. Langley Research Centre, Hampton, VA, NASA-TM-80181

    Google Scholar 

  • Timoshenko SP, Gere JM (1961) Theory of elastic stability. McGraw-Hill, New York

    Google Scholar 

  • Todoroki A, Haftka RT (1998) Lamination parameters for efficient genetic optimization of the stacking sequences of composite panels. AIAA Paper 98-4817, Proceedings of the 7th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, St. Louis, MO, 2–4 September, pp 870–879

  • Tsai SW, Hahn HT (1980) Introduction to composite materials. Technomic, Stamford, CT

    Google Scholar 

  • Tsai SW, Pagano NJ (1968) Composite materials workshop. Technomic, Stamford, CT, pp 233–253

    Google Scholar 

  • Vanderplaats GN (1973) A FORTRAN program for constrained function minimization: user’s manual. NASA Ames, CA, NASA-TM-X-62282

  • Vanderplaats GN (2001) Numerical optimization techniques for engineering design, 3rd edn. Vanderplaats Research & Development, Colorado Springs, CO

  • Vinson JR, Sierakowski RL (1986) The behavior of structures composed of composite materials. Martinus Nijhoff, Dordrecht, The Netherlands

    MATH  Google Scholar 

  • Whitney JM (1969) The effect of transverse shear deformation on the bending of laminated plates. J Comput Math 3:534–547

    Google Scholar 

  • Whitney JM (1973) Shear correction factors for orthotropic laminates under static loading. J Appl Mech 40:302–304

    Google Scholar 

  • Wittrick WH, Williams FW (1974) Buckling and vibration of anisotropic or isotropic plate assemblies under combined loadings. Int J Mech Sci 16:209–239

    Article  Google Scholar 

  • Yamazaki K (1996) Two-level optimization technique of composite laminate panels by genetic algorithms. AIAA Paper 96-1539-CP, Presented at the AIAA/ASME/ASCE/AHS 37th Structures, Structural Dynamics and Materials Conference, pp 1882–1887

Download references

Author information

Authors and Affiliations

  1. Department of Aerospace Engineering, University of Bristol, Bristol, BS8 1TR, UK

    J. Enrique Herencia, Paul M. Weaver & Michael I. Friswell

Authors
  1. J. Enrique Herencia
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Paul M. Weaver
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Michael I. Friswell
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Paul M. Weaver.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Herencia, J.E., Weaver, P.M. & Friswell, M.I. Optimization of anisotropic composite panels with T-shaped stiffeners including transverse shear effects and out-of-plane loading. Struct Multidisc Optim 37, 165–184 (2008). https://doi.org/10.1007/s00158-008-0227-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00158-008-0227-6

Keywords

Search

Navigation