Skip to main content
SpringerLink
Log in

On the Semi-analytical Modelling of the Free-Edge Stress Field in Cross-Ply Laminated Shells Under Mechanical Loads

  • Chapter
  • First Online:
Progress in Structural Mechanics

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 199))

  • 144 Accesses

Abstract

This contribution provides a semi-analytical model for the assessment of the three-dimensional stress field in thick, cylindrically curved cross-ply laminated shells subjected to different kinds of mechanical loadings under consideration of the free-edge effect. The model superimposes a closed-form analytical solution with a layerwise approach and the governing equations as well as the boundary conditions are derived by means of the minimum total potential energy principle utilizing the general Euler-Lagrange equations. Numerical results for thick cross-ply laminated shells undergoing uniform edge loadings and sinusoidal outer pressure are presented and the accuracy is verified by comparisons with full-scale, three-dimensional finite element computations. Those reveal an excellent agreement between the highly efficient semi-analytical model and the finite element approach for the free-edge stress fields in cross-ply laminated shells.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. . Kant T, Swaminathan K (2000) Estimation of transverse/interlaminar stresses in laminated composites – a selective review and survey of current developments. Composite Structures 49(1):65–75

    Article  Google Scholar 

  2. Mittelstedt C, Becker W (2007) Free-edge effects in composite laminates. Applied Mechanics Reviews 60(5):217–245

    Article  ADS  Google Scholar 

  3. Mittelstedt C, Becker W, Kappel A, Kharghani N (2022) Free-edge effects in composite laminates—a review of recent developments 2005–2020. Applied Mechanics Reviews 74(1):010,801

    Google Scholar 

  4. Srinivas S (1974) Analysis of laminated, composite, circular cylindrical shells with general boundary conditions. Nasa tr r-412, Langley Research Center, Hampton, Va. 23665

    Google Scholar 

  5. Ren JG (1987) Exact solutions for laminated cylindrical shells in cylindrical bending. Composites Science and Technology 29(3):169–187

    Article  Google Scholar 

  6. Lekhnitskii SG (1963) Theory of elasticity of an anisotropic elastic body. Holden-Day series in mathematical physics, Holden-Day, San Francisco, CA

    Google Scholar 

  7. Lekhnitskii SG (1968) Anisotropic plates. Gordon and Breach, London, UK

    Google Scholar 

  8. Ko WL, Jackson RH (1989) Multilayer theory for delamination analysis of a composite curved bar subjected to end forces and end moments. Technical memorandum no. 4139, NASA Research Center, Edwards, CA, USA

    Google Scholar 

  9. Varadan TK, Bhaskar K (1991) Bending of laminated orthotropic cylindrical shells—an elasticity approach. Composite Structures 17(2):141–156

    Article  Google Scholar 

  10. Miri AK, Nosier A (2011) Interlaminar stresses in antisymmetric angle-ply cylindrical shell panels. Composite Structures 93(2):419–429

    Article  Google Scholar 

  11. Miri AK, Nosier A (2011) Out-of-plane stresses in composite shell panels: layerwise and elasticity solutions. Acta Mechanica 220(1-4):15–32

    Article  MATH  Google Scholar 

  12. Nosier A, Miri AK (2010) Boundary-layer hygrothermal stresses in laminated, composite, circular, cylindrical shell panels. Archive of Applied Mechanics 80(4):413–440

    Article  ADS  MATH  Google Scholar 

  13. Tahani M, Andakhshideh A, Maleki S (2016) Interlaminar stresses in thick cylindrical shell with arbitrary laminations and boundary conditions under transverse loads. Composites Part B: Engineering 98:151–165

    Article  Google Scholar 

  14. Schnabel JE, Yousfi M, Mittelstedt C (2017) Free-edge stress fields in cylindrically curved symmetric and unsymmetric cross-ply laminates under bending load. Composite Structures 180:862–875

    Article  Google Scholar 

  15. Kappel A, Mittelstedt C (2020) Free-edge stress fields in cylindrically curved cross-ply laminated shells. Composites Part B: Engineering 183:107,693

    Google Scholar 

  16. Kappel A, Mittelstedt C (2021) Interlaminar stress fields in circular cylindrical cross-ply laminated shells subjected to transverse loadings. International Journal of Solids and Structures 228:111,096

    Google Scholar 

  17. Ahmadi I (2019) Free edge stress prediction in thick laminated cylindrical shell panel subjected to bending moment. Applied Mathematical Modelling 65:507–525

    Article  MathSciNet  MATH  Google Scholar 

  18. Ahmadi I (2020) A three-dimensional formulation for levy-type transversely loaded cross-ply shell panels. International Journal of Mechanical Sciences 167:105,224

    Google Scholar 

  19. Kappel A, Dillen S, Mittelstedt C (2021) Hygrothermomechanical analysis of the free-edge stress fields in cylindrical cross-ply laminated shells. Mechanics of Advanced Materials and Structures 30(4):1–18

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Institute for Lightweight Engineering and Structural Mechanics, Darmstadt University of Technology, Darmstadt, Germany

    Andreas Kappel & Christian Mittelstedt

Authors
  1. Andreas Kappel
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Christian Mittelstedt
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Andreas Kappel .

Editor information

Editors and Affiliations

  1. Institute of Mechanics, Otto-von-Guericke University Magdeburg, Magdeburg, Sachsen-Anhalt, Germany

    Holm Altenbach

  2. Composite Materials, Fraunhofer Institute for Mechanics of Materials, Freiburg im Breisgau, Baden-Württemberg, Germany

    Jörg Hohe

  3. Fachbereich Maschinenbau, Technical University of Darmstadt, Darmstadt, Hessen, Germany

    Christian Mittelstedt

Rights and permissions

Reprints and permissions

Copyright information

© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Kappel, A., Mittelstedt, C. (2024). On the Semi-analytical Modelling of the Free-Edge Stress Field in Cross-Ply Laminated Shells Under Mechanical Loads. In: Altenbach, H., Hohe, J., Mittelstedt, C. (eds) Progress in Structural Mechanics. Advanced Structured Materials, vol 199. Springer, Cham. https://doi.org/10.1007/978-3-031-45554-4_6

Download citation

Publish with us

Policies and ethics

Search

Navigation