Skip to main content
Log in

High-order finite elements reduced models for modal analysis of stiffened panels

  • Published:
International Journal of Mechanics and Materials in Design Aims and scope Submit manuscript

Abstract

A method is presented to build reduced (equivalent) models of stiffened panels made of thin-walled composite materials. The technique is developed to be used in the modal analysis of panels and wing boxes, allowing finite element modelling and analysis using a single-type, three-dimensional orthotropic p-element. The use of a single element guarantees speed and flexibility in the (re)modelling of the structure and reduces the modelling and analysis errors connected to finite element analysis in preliminary-design/multidisciplinary-optimization environments. The method is tested on two types of representative wing boxes. Different approaches for the equivalencing are tested and compared to each other. The results show that the equivalent models give results within few percent from those obtained running a full model, saving as much as one order of magnitude in the number of degrees of freedom employed.

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

Access this article

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

Instant access to the full article PDF.

Institutional subscriptions

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

Similar content being viewed by others

References

  • Babuska, I., Suri, M.: Locking effects in the finite element approximation of elasticity problems. Numerische Matematik 62, 439–463 (1992a)

    Article  MATH  MathSciNet  Google Scholar 

  • Babuska, I., Suri, M.: On locking and robustness in the finite element method. SIAM J. Numer. Anal. 29, 1261–1293 (1992b)

    Article  MATH  MathSciNet  Google Scholar 

  • Babuska, I., Szabo, B., Katz, I.: The p-version of the finite element method. SIAM J. Numer. Anal. 18(3), 515–545 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  • Bruhn, E.: Analysis and Design of Flight Vehicle Structures. Jacobs Publishing, Inc., USA (1973)

    Google Scholar 

  • Collier, C.: Stiffness, thermal expansion, and thermal bending formulation of stiffened, fiber-reinforced composite panels. In: AIAA (ed.) AIAA/ASME/ASCE/AHS/ACS 34th Structures, Dynamics, & Materials Conference, La Jolla, CA. Paper No. AIAA-93-1569 (1993)

  • Collier, C.: Thermoelastic formulation of stiffened, unsymmetric composite panels for finite element analysis of high speed aircraft. In: AIAA/ASME/ASCE/AHS/ACS 35th Structures, Dynamics, & Materials Conference, Hilton Head, SC. Paper AIAA 94-1579 (1994)

  • Düster, A.: High order finite elements for three dimensional, thin-walled nonlinear continua. PhD dissertation, Technische Universität München – Lehrstuhl für Bauinformatik (2001)

  • Gere, J., Timoshenko, S.: Mechanics of Materials. Van Nostrand Reinhold Co. Ltd (1987)

  • Hughes, T.J.R.: The Finite Element Method: Linear Static and Dynamic Finite Element Analysis. Prentice Hall, Englewood Cliffs, NJ (1987. Reprinted by Dover, NY, 2000)

  • Jones, R.: Mechanics of Composite Materials, Chapter 2–4. Taylor & Francis, Philadelphia, PA (1999)

    Google Scholar 

  • Lisandrin, P., van Tooren, M.: High-order finite elements reduced models for use in a flutter design tool. J. Aircraft 42(3), 748–754 (2005)

    Google Scholar 

  • Morino, L., Mastroddi, F., Bernardini, G., Piccirilli, M.: A hermite interpolation finite element for structural dynamics. In: AIDAA (ed.) XVI Congresso Nazionale AIDAA, Palermo, Italy. Associazione Italiana di Aeronautica e Astronautica (2001)

  • Stroud, J.: Elastic constants for bending and twisting of corrugation-stiffened panels. Technical report, NASA TR R-166, Langley, VA (1963)

  • Stroud, J.: Pasco: structural panel analysis and sizing code, capability and analytical foundations. Technical report, NASA TM 80181, Langley, VA (1981)

  • Stroud, J., Agranoff, N.: Minimum mass design of filamentary composite panels under combined loads: design procedure based on simplified buckling equations. Technical report, NASA TN D 8257, Langley, VA (1976)

  • Szabo, B., Sahrmann, G.: Hierarchic plate and shell models based on p-extension. Int. J. Numer. Methods Eng. 26, 1855–1881 (1988)

    Article  MATH  Google Scholar 

  • Timoshenko, S.P., Woinowsky-Krieger, S.: Theory of Plates and Shells, 2nd edn. McGraw-Hill Book Company, Inc. (1959)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Paolo Lisandrin.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lisandrin, P., van Tooren, M. High-order finite elements reduced models for modal analysis of stiffened panels. Int J Mech Mater Des 3, 111–127 (2006). https://doi.org/10.1007/s10999-006-9017-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10999-006-9017-8

Keywords

Navigation