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A computational model for analysing interactive buckling and delamination growth in composite structures

  • Special Issue On Computational Structural Mechanics
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Abstract

In this paper, a unified method is presented: (i) to model delaminated stiffened laminated composite shells; (ii) for synthesising accurate multiple post-buckling solution paths under compressive loading; and (iii) for predicting delamination growth. A multi-domain modelling technique is used for modelling the delaminated stiffened shell structures. Error-free geometrically nonlinear element formulations — a 2-noded curved stiffener element (BEAM2) and a 3-noded shell element (SHELL3) — are used for the finite element analysis. An accurate and simple automated solution strategy based on Newton type iterations is used for predicting the general geometrically nonlinear and postbuckling behaviour of structures. A simple method derived from the 3-dimensionalJ-integral is used for computing the pointwise energy release rate at the delamination front in the plate/shell models. Finally, the influence of post-buckling structural behaviour and the delamination growth on each other has been demonstrated.

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References

  • Atluri S N (ed.) 1986 Energetic approaches and path independent integrals in fracture mechanics.Computational methods in mechanics of fracture (Amsterdam: North-Holland)

  • Babu C R, Prathap G 1988 A linear thick curved beam element.Int. J. Numer. Methods Eng. 23: 1313–1328

    Article  MathSciNet  Google Scholar 

  • Barlow J 1976 Optimal stress locations in finite element models.Int. J. Numer. Methods Eng. 10: 243–251

    Article  MATH  Google Scholar 

  • Bergan P G 1980 Solution algorithms for nonlinear structural problems.Comput. Struct. 12: 497–509

    Article  MATH  MathSciNet  Google Scholar 

  • Bergan P G, Mollestad E 1984 Static and dynamic solution strategies in nonlinear analysis. em Numerical methods for nonlinear problems (ed.) C Taylor, (Swansea: Pineridge) pp. 3–17

    Google Scholar 

  • Bergan P G, Horrigmoe B, Krakeland B, Soreide T H 1978 Solution techniques as applied to a nonlinear finite element problem.Int. J. Numer. Methods. Eng. 12: 1677–1696

    Article  MATH  Google Scholar 

  • Bottega W J, Maewal A 1983 Delamination buckling and growth in laminates.J. Appl. Mech. 50: 184–189

    MATH  Google Scholar 

  • Brendel B, Ramm R 1980 Linear and nonlinear stability analysis of cylindrical shells.Comput. Struct. 12: 549–558

    Article  MATH  Google Scholar 

  • Chai H, Babcock C D, Knauss W G 1981 One-dimensional modeling of failure in laminated plates by delamination buckling.Int. J. Solids Struct. 17: 1069–1083

    Article  MATH  Google Scholar 

  • Chan S L 1988 Geometric and material nonlinear analysis of beam-columns and frames using the minimum residual displacement method.Int. J. Numer. Methods Eng. 26: 2657–2669

    Article  MATH  Google Scholar 

  • Crisfield M A 1981 A fast incremental/iterative solution procedure that handles “snap-through”.Comput. Struct. 13: 55–62

    Article  MATH  Google Scholar 

  • Evans A G, Hutchinson J W 1984 On the mechanics of delamination and spalling in compressed film.Int. J. Solids Struct. 20: 455–466

    Article  Google Scholar 

  • Flanagan G 1988 Two-dimensional delamination growth in composite laminates under compression loading.Eighth Conf. on Composite Materials — Testing and Design (ed.) J D Whitcomb, ASTM STP 972 (Philadelphia: Am. Soc. Testing Mater.) pp. 180–190

    Google Scholar 

  • Gierlinski J T, Smith T R G 1985 A variable load iteration procedure for thin-walled structures.Comput. Struct. 21: 1085–1094

    Article  MATH  Google Scholar 

  • Gilletta D 1988 Theories non lineaires des stratifies composites en compression avee delaminage. Rapport technique ONERA

  • Huang B-Z, Atluri S N 1995 A simple method to follow post-buckling paths in finite element analysis.Comput. Struct. 57: 477–489

    Article  MATH  Google Scholar 

  • Huang B-Z, Shenoy V B, Atluri S N 1994 A quasi-conforming triangular laminated composite shell element based on a refined first order theory.Comput. Mech. 13: 295–314

    Article  MATH  Google Scholar 

  • Huang B-Z, Naganarayana B P, Atluri S N 1995 NONCAT—ANONlinear Computational Analysis Tool for analysis of delaminated composite structures.Computational Modeling of Aircraft Structures, CMAS Symposium’95, Somerset, NJ

  • Kachanov L M 1976 Separation failure of composite materials.Polymer Mech. 5: 918–922

    Google Scholar 

  • Koiter W T 1945On the stability of elastic equilibrium (Amsterdam: Polytechnic Institute Delft, H J Paris) (Also NASA TT F-10.833, 1967; and AFFDL-TR-70-25, 1970)

    Google Scholar 

  • Naganarayana B P 1995 Incremental iterative strategies for automated post-buckling analysis.Comput. Struct. (in press)

  • Naganarayana B P, Atluri S N 1995a Equivalent domain integral for delamination growth estimation.ICES ′95, Hawaii

  • Naganarayana B P, Atluri S N 1995b Energy release rate evaluation for delamination growth prediction in a multi-plate model of a laminate composite.Comput. Mech. 15: 443–459

    Article  MATH  Google Scholar 

  • Naganarayana B P, Atluri S N 1995c Strength reduction and delamination growth in thin and thick composite plates under compressive loading.Comput. Mech. 16: 170–189

    Article  MATH  Google Scholar 

  • Naganarayana B P, Huang B-Z 1995 Multi-domain modeling of delaminated stiffened composite structures.Symp. on Advanced Engineering Sciences, New Orleans

  • Naganarayana B P, Prathap G P 1996 Locking in a geometrically nonlinear beam element.AIAA J. (accepted)

  • Naganarayana B P, Huang B-Z, Atluri S N 1995 Multi-domain modeling and analysis of delaminated stiffened composite structures.AIAA J. (in press)

  • Nikishkov G P, Atluri S N 1987a Calculation of fracture mechanics parameters for an arbitrary 3-dimensional crack by equivalent domain integral method.Int. J. Numer. Methods Eng. 24: 1801–1822

    Article  MATH  Google Scholar 

  • Nikishkov G P, Atluri S N 1987b An equivalent domain integral method for computing crack tip parameters in non-elastic thermo-mechanical fracture.Eng. Fracture Mech. 26: 851–867

    Article  Google Scholar 

  • Nishioka T, Atluri S N 1981 Analytical solutions for embedded cracks and finite element alternating method for elliptical surface cracks subjected to arbitrary loadings.Eng. Fracture Mech. 17: 247–268

    Article  Google Scholar 

  • Parks D M 1974 A stiffness derivative finite element technique for determination of elastic crack tip stress intensity factors.Int. J. Fracture Mech. 10: 487–502

    Article  Google Scholar 

  • Powell G, Simons J 1981 Improved iteration strategy for nonlinear structures.Int. J. Numer. Methods. Eng. 17: 1455–1467

    Article  MATH  Google Scholar 

  • Prathap G 1993The finite element method in structural mechanics (Dordrecht: Kluwer Academic Publications)

    MATH  Google Scholar 

  • Prathap G, Naganarayana B P 1991 FEPACS, A finite element package for analysis of composite structures. PD ST 9139, National Aerospace Laboratories, Bangalore

  • Prathap G, Naganarayana B P, Somashekar B R 1994 FEPACS (Version 2.0); Finite element package for analysis of composite structures — Theoretical manual. PD ST 9405, National Aerospace Laboratories, Bangalore

  • Ramm E 1981 Strategies for tracing the nonlinear response near limit points.Nonlinear finite element analysis in structural mechanics (eds) W Wunderlichet al (Berlin: Springer-Verlag) pp. 63–89

    Google Scholar 

  • Rice J R 1968 A path independent integral and approximate analysis of strain concentration by notches and cracks.J. Appl. Mech. ASME 35: 379–386

    Google Scholar 

  • Riks E 1979 An incremental approach to the solution of snapping and buckling problems.Int. J. Solids Struct. 15: 529–551

    Article  MATH  MathSciNet  Google Scholar 

  • Riks E 1984 Some computational aspects of the stability analysis of nonlinear structures.Comput. Methods Appl. Mech. Eng. 47: 219–259

    Article  MATH  Google Scholar 

  • Rybicki E F, Kanninen M F 1977 A finite element calculation of stress intensity factors by a modified crack closure integral.Eng. Fracture Mech. 9: 931–938

    Article  Google Scholar 

  • Tsao D, Duan D, Ji W 1991 Delamination fracture analysis of composite laminates caused by local buckling and postbuckling.SAE Trans. 100 (sect. 1; pt 2;911986): 2034–2043

    Google Scholar 

  • Wagner W, Wriggers 1988 A simple method for the calculation of post-critical branches.Eng. Comput. 5: 103–109

    Google Scholar 

  • Wempner G A 1979 Discrete approximations related to nonlinear theories of solids.Int. J. Solids Struct. 7: 1581–1599

    Article  Google Scholar 

  • Whitcomb J D 1989 3-dimensional analysis of a post-buckled embedded delamination.J. Compos. Mater. 23: 862–889

    Article  Google Scholar 

  • Whitcomb J D, Shivakumar K N 1989 Strain energy release rate analysis of plates with post-buckled delaminations.J. Compos. Mater. 23: 714–734

    Article  Google Scholar 

  • Yin W L 1984 The energy release rate in the growth of a 1-dimensional delamination.J. Appl. Mech. 51: 939–941

    Article  Google Scholar 

  • Yin W L 1985 Axisymmetric buckling and growth of a circular delamination in a compressed laminate.Int. J. Solids and Struct. 21: 503–514

    Article  MATH  Google Scholar 

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Naganarayana, B.P., Atluri, S.N. A computational model for analysing interactive buckling and delamination growth in composite structures. Sadhana 21, 547–575 (1996). https://doi.org/10.1007/BF02744103

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