Abstract
Iso-grid structures provide high strength with reduced weights, which is an essential requirement for aerospace applications. Buckling of Ortho-grid structure is a phenomenon with complex interaction between skin, stiffeners and sub-stiffeners. Introduction of sub-stiffeners increases the load bearing capacity of the structures many folds as compared to the classical Iso-grid or Ortho-grid structure. In this work, a customized MATLAB® code is developed for computational analysis based on finite element (FE) analysis. In case of FE analysis, the degenerated shell element is used. In the first phase of the MATLAB® code development, an elasto-plastic analysis of a clamped quadratic-shell is performed and the results are verified with the published literature. In the next phase, the buckling analysis of thin-plate is performed and the results are again verified with the literature. After verification of developed code, FE analysis of the Ortho-grid-stiffened plates is successfully validated. The results attained from developed code are compared with analysis performed on ANSYS® software along with the published work. The results revalidate the fact that stiffeners increase buckling load by over fifty times, which stands the main motive for their use in aerospace industry.
Similar content being viewed by others
References
S.M. Huybrechts, S.E. Hahn, T.E. Meink, Grid stiffened structures: a survey of fabrication, analysis and design methods, in Proceedings of the 12th International Conference on Composite Materials (ICCM/12). Paris, France (1999)
J.P. Peterson, Buckling of Stiffened Cylinders in Axial Compression and Bending: A Review of Test Data (National Aeronautics and Space Administration, 1969)
J. Williams, R. Davis, Buckling experiments on stiffened cast-epoxy conical shells. Exp. Mech. 15(9), 329–338 (1975)
R. Meyer, Isogrid—a simple, efficient, stiffening concept, in 14th Structures, Structural Dynamics, and Materials Conference (AIAA, 1973), p. 365
J. Dyer, P. Slysh, Conical Isogrid Adapter Structural Test Results (General Dynamics Convair Aerospace Division, San Diego, 1974)
W.L. Heard Jr., M.S. Anderson, P. Slysh, An Engineering Procedure for Calculating Compressive Strength of Isogrid Cylindrical Shells with Buckled Skin (NASA Langley Research Center, 1976)
P. Slysh et al., Isogrid structural tests and stability analyses. J. Aircr. 13(10), 778–785 (1976)
L.W. Rehfield, R.B. Deo, Buckling of Continuous Filament Advanced Composite Isogrid Wide Columns in Axial Compression (Georgia Institute of Technology, 1978)
L. Parnas et al., Postbuckling and crippling of I-section composite stiffeners. J. Aerosp. Eng. 8(1), 32–42 (1995)
S. Huybrechts, T.E. Meink, Advanced grid stiffened structures for the next generation of launch vehicles, in Aerospace Conference, 1997. Proceedings, IEEE(IEEE, 1997)
H. Mahfuz, et al., Effect of Rib Geometry on the Buckling Behavior of Composite Isogrid Cylinders
D. Jensen, M. Redford, L. Francom, On the structural efficiency of three-dimensional isogrid designs, in 37th Structure, Structural Dynamics and Materials Conference (1996)
N. Jaunky, N.F. Knight, D.R. Ambur, Optimal design of grid-stiffened composite panels. J. Aircr. 35(3), 478–486 (1998)
M. Cho, W. Kim, Buckling analysis of grid-stiffened composite plates using hybrid element with drilling DOF, in 40th Structures, Structural Dynamics, and Materials Conference and Exhibit (1999)
T.D. Kim, Postbuckled behavior of composite isogrid stiffened shell structure. Adv. Compos. Mater 9(3), 253–263 (2000)
M. Yazdani et al., An experimental investigation into the buckling of GFRP stiffened shells under axial loading. Sci. Res. Essays 4(9), 914–920 (2009)
S.N. Nampy, E.C. Smith. Stiffness Analysis of Closed Cross-Section Composite Grid-Stiffened Cylinders, in Proceedings of the 51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Orlando, FL (2010)
A. Biskner, J. Higgins, Design and evaluation of a reinforced advanced-grid stiffened composite structure, in 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference (2005)
M.J. Weber, P. Middendorf, Semi-analytical skin buckling of curved orthotropic grid-stiffened shells. Compos. Struct. 108, 616–624 (2014)
C. Bisagni, R. Vescovini, C. Davila. Assessment of the damage tolerance of post-buckled hat-stiffened panels using single stringer specimens, in 51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference 18th AIAA/ASME/AHS Adaptive Structures Conference 12th (2010)
G. Ben, T. Suzuki, K. Sakata. Optimum structural design of CFRP isogrid cylindrical shells, in 15th European Conference on Composite Materials (2012)
G. Rahimi, M. Zandi, S. Rasouli, Analysis of the effect of stiffener profile on buckling strength in composite isogrid stiffened shell under axial loading. Aerosp. Sci. Technol. 24(1), 198–203 (2013)
Y. Bayat, H. EkhteraeiToussi, Exact solution of thermal buckling and post buckling of composite and SMA hybrid composite beam by layerwise theory. Aerosp. Sci. Technol. 67, 484–494 (2017)
D.J. Brimm, Unistructure—a new concept for light weight integrally stiffened skin structure. Aircr. Eng. Aerosp. Technol. 54(4), 2–8 (1982)
M.S. Anderson, Buckling of periodic lattice structures. AIAA J. 19(6), 782–788 (1981)
G. Totaro, F. De Nicola, Recent advance on design and manufacturing of composite anisogrid structures for space launchers. Acta Astronaut. 81(2), 570–577 (2012)
H. Kanou, S. Nabavi, J. Jam, Numerical modeling of stresses and buckling loads of isogrid lattice composite structure cylinders. Int. J. Eng. Sci. Technol. 5(1), 42–54 (2013)
Isogrid Design Handbook, McDonnell Douglas Astronautics Company (1973), p. G4295A
P. Slysh, Iso-Grid Weight Optimization (Society of Allied Weight Engineers, 1975) (Index category No. 22)
P. Slysh, Iiso-grid structural applications(Society of Allied Weight Engineers,1976) (Index category No. 22)
P. Slysh, Expert system for generation of flat patterns of isogrid shell structures with circular bosses, in Society of Allied Weight Engineers, Annual Conference, 44 th, Arlington, TX (1985)
M.H. Schneider et al., Buckling and vibration of externally pressurized conical shells withcontinuous and discontinuous rings. AIAA J. 29(9), 1515–1522 (1991)
R. Sabir et al., A survey of recent developments in optimization of iso-grid structure. J. Space Technol. 5(1), 103–115 (2016)
D. Darooka, D. Jensen, Advanced space structure concepts and their development, in 19th AIAA Applied Aerodynamics Conference (2001)
D. Baker, et al. Optimal design and damage tolerance verification of an isogrid structure for helicopter application, in 44th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference (2004)
O. Vanli, P. Michaleris, Distortion analysis of welded stiffeners. J. Ship Prod. 17(4), 226–240 (2001)
P. Wegner, J. Higgins, B. VanWest, Application of advanced grid-stiffened structures technology to the Minotaur payload fairing, in 43rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference (2002)
E. Byklum, J. Amdahl, Nonlinear buckling analysis and ultimate strength prediction of stiffened steel and aluminium panels, in The Second International Conference on Advances in Structural Engineering and Mechanics (2002)
J.-T. Yoo, Y.-S. Jang, Y.-M. Yi, Structural Design and Development of Isogrid Cylinder for Propellant Tank, in 56th International Astronautical Congress, IAC-05-C2 (2005)
I. Stanciulescu, L.N. Virgin, T.A. Laursen, Slender solar sail booms: finite element analysis. J. Spacecr. Rockets 44(3), 528–537 (2007)
P. Williams, et al., Complementary post-buckling analyses of truss-lattice shear panels, in 48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference (2007)
A. Barut, E. Madenci, Post-Buckling of Composite Panels with Isogrid Stiffeners, in 49th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 16th AIAA/ASME/AHS Adaptive Structures Conference, 10th AIAA Non-Deterministic Approaches Conference, 9th AIAA Gossamer Spacecraft Forum, 4th AIAA Multidisciplinary Design Optimization Specialists Conference (2008)
C. Collier, et al., Local Post Buckling: An Efficient Analysis Approach for Industry Use, in 50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference 17th AIAA/ASME/AHS Adaptive Structures Conference 11th AIAA No. (2009)
M. Paschero, M.W. Hyer, Axial buckling of an orthotropic circular cylinder: application to orthogrid concept. Int. J. Solids Struct. 46(10), 2151–2171 (2009)
R.P. Thornburgh, M.W. Hilburger, Longitudinal Weld Land Buckling in Compression-Loaded Orthogrid Cylinders (2010)
M. Paschero, M.W. Hyer, Improvement of axial buckling capacity of elliptical lattice cylinders. AIAA J. 49(2), 396–410 (2011)
G. Totaro, Local buckling modelling of isogrid and anisogrid lattice cylindrical shells with triangular cells. Compos. Struct. 94(2), 446–452 (2012)
M. Hilburger, et al., Design and analysis of subscale and full-scale buckling-critical cylinders for launch vehicle technology development, in 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference 20th AIAA/ASME/AHS Adaptive Structures Conference 14th AIAA (2012)
M. Hilburger, Developing the next generation shell buckling design factors and technologies, in 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference 20th AIAA/ASME/AHS Adaptive Structures Conference 14th AIAA (2012)
S. Nampy, E. Smith, Structural Behavior of Grid-stiffened Tubes Under Axial, Bending, and Torsion Loads, in 49th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 16th AIAA/ASME/AHS Adaptive Structures Conference, 10th AIAA Non-Deterministic Approaches Conference, 9th AIAA Gossamer Spacecraft Forum, 4th AIAA Multidisciplinary Design Optimization Specialists Conference (2008)
L. Rønning, A. Aalberg, P.K. Larsen, An experimental study of ultimate compressive strength of transversely stiffened aluminium panels. Thin Walled Struct. 48(6), 357–372 (2010)
G. Brando, G. De Matteis, Experimental and numerical analysis of a multi-stiffened pure aluminium shear panel. Thin Walled Struct. 49(10), 1277–1287 (2011)
D. Quinn et al., Non-prismatic sub-stiffening for stiffened panel plates—stability behaviour and performance gains. Thin Walled Struct. 48(6), 401–413 (2010)
R. Paulo, F. Teixeira-Dias, R. Valente, Numerical simulation of aluminium stiffened panels subjected to axial compression: Sensitivity analyses to initial geometrical imperfections and material properties. Thin Walled Struct. 62, 65–74 (2013)
G. Totaro, F. De Nicola, P. Caramuta, Local buckling modelling of anisogrid lattice structures with hexagonal cells: an experimental verification. Compos. Struct. 106, 734–741 (2013)
M.A. Crisfield, J.J. Remmers, C.V. Verhoosel, Nonlinear Finite Element Analysis of Solids and Structures (Wiley, New York, 2012)
E. Reissner, The effect of transverse shear deformation on the bending of elastic plates (1945)
R. Mindlin, Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates. J. Appl. Mech. 18, 31 (1951)
O. Zienkiewicz, R. Taylor, J. Too, Reduced integration technique in general analysis of plates and shells. Int. J. Numer. Meth. Eng. 3(2), 275–290 (1971)
E. Pugh, E. Hinton, O. Zienkiewicz, A study of quadrilateral plate bending elements with ‘reduced’integration. Int. J. Numer. Meth. Eng. 12(7), 1059–1079 (1978)
H. Parisch, A critical survey of the 9-node degenerated shell element with special emphasis on thin shell application and reduced integration. Comput. Methods Appl. Mech. Eng. 20(3), 323–350 (1979)
T. Belytschko, J.S.-J. Ong, W.K. Liu, A consistent control of spurious singular modes in the 9-node Lagrange element for the Laplace and Mindlin plate equations. Comput. Methods Appl. Mech. Eng. 44(3), 269–295 (1984)
T. Belytschko, C.S. Tsay, A stabilization procedure for the quadrilateral plate element with one-point quadrature. Int. J. Numer. Meth. Eng. 19(3), 405–419 (1983)
E. Hinton, B. Suarez Arroyo, Finite Elements Software for Plates and Shells (1984)
H.-C. Huang, Static and Dynamic Analyses of Plates and Shells: Theory, Software and Applications (Springer, Berlin, 2012)
M. Ozakca, A. Murphy, S. Van Der Veen. Buckling and post-buckling of sub-stiffened or locally tailored aluminium panels, in 25th International Congress of the Aeronautical Sciences (2006)
A.R. Pouladkhan, E. Jalil, S. Majid, Numerical Study of Buckling of Thin Plates (World Academy of Science, Engineering and Technology, 2011), p. 152–157
J.G. Williams, et al., Recent developments in the design, testing and impact-damage tolerance of stiffened composite panels, in Fibrous Composites in Structural Design (Springer, Berlin, 1980), p. 259–291
A.E. Lovejoy, M.W. Hilburger, SBKF Modeling and Analysis Plan: Buckling Analysis of Compression-Loaded Orthogrid and Isogrid Cylinders (2013)
J. Lavin, E. Gutierrez-Miravete, Buckling of Isogrid Plates (Rensselaer Polytechnic Institute, Hartford, CT, 2010)
K. Sakata, G. Ben, Fabrication method and compressive properties of CFRP isogrid cylindrical shells. Adv. Compos. Mater 21(5–6), 445–457 (2012)
S.B. Mulani, D. Locatelli, R.K. Kapania, Grid-stiffened panel optimization using curvilinear stiffeners, in AIAA paper (2011–1895) (2011)
M.W. Hilburger, et al., Design and analysis of subscale and full-scale buckling-critical cylinders for launch vehicle technology development. NASA REPORT (2012)
X. Qu, R.T. Haftka, Reliability-based design optimization of stiffened panels, in Fourth International Symposium on Uncertainty Modeling and Analysis, 2003. ISUMA 2003 (IEEE, 2003)
D. Wang, M.M. Abdalla, W. Zhang, Buckling optimization design of curved stiffeners for grid-stiffened composite structures. Compos. Struct. 159, 656–666 (2017)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Sabir, R., Khan, A.A., Hasham, H.J. et al. Buckling Load Prediction in Ortho-Grid Plates for Aerospace Structures. J Fail. Anal. and Preven. 18, 647–658 (2018). https://doi.org/10.1007/s11668-018-0453-1
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11668-018-0453-1