Abstract
This paper deals with the development and use of scaled-down models in order to predict the structural behavior of large prototypes. The concept is fully described and examples are presented which demonstrate its applicability to beam-plates, plates and cylindrical shells of laminated construction. The concept is based on the use of field equations, which govern the response behavior of both the small model as well as the large prototype. The conditions under which the experimental data of a small model can be used to predict the behavior of a large prototype are called scaling laws or similarity conditions and the term that best describes the process is structural similitude. Moreover, since the term scaling is used to describe the effect of size on strength characteristics of materials, a discussion is included which should clarify the difference between “scaling law” and “size effect”. Finally, a historical review of all published work in the broad area of structural similitude is presented for completeness.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Ashton, J. E. and Whitney, J. M. (1970), Theory of Laminated Plates, Technomic Publ., Stamford, CT.
Bazant, Z. P. and Rajapakse, Y.D.S. (editors) (1999), Fracture Scaling, Kluwer Academic Publishers, Dordrecht.
Camponeschi, G. (1994), “The Effects of Specimen Scale on the Compression Strength of Composite Materials,” NASA CP 3271, pp. 81–99.
Charlton, T. M. (1954), Model Analysis of Structures, John Wiley & Sons, New York.
Chouchaoui, C.S. and Ochoa, O.O. (1999a), “Similitude Study for a Laminated Cylindrical Tube Under Tensile, Torsion, Bending, Internal and External Pressure, Part I: Governing Equations,” Composite Structures, Vol. 44, pp. 221–229.
Chouchaoui, C.S., Parks, P. and Ochoa, O.O. (1999b), “Similitude Study for a Laminated Cylindrical Tube Under Tensile, Torsion, Bending, Internal and External Pressure. Part II: Scale Models,” Composite Structures, Vol. 44, pp. 231–236.
Daniel, I.M. and Hsiao, H.M. (1999), “Is There a Thickness Effect on Compressive Strength of Unnotched Composite Laminates?” in Fracture Scaling, Z.P. Bazant and Y.D.S. Rajapakse (editors), Klumer Academic Publishers, pp. 143–158.
Ezra, A.A. (1962), “Similitude Requirements for Scale Model Determination of Shell Buckling under Impulsive Pressure,” NASA TN D-1510, pp. 661–670.
Goodier, J.N. and Thomson, W.T. (1944), “Applicability of Similarity Principles to Structural Models,” NACA Tech. Note 993.
Goodier, J. N. (1950), “Dimensional Analysis,” Handbook of Experimental Stress Analysis (Edited by M. Hetenyi), pp. 1035–1045, John Wiley & Sons, NY.
Greszczuk, L.B. (1999), “Private Communication,” September 23, 1999.
Grimes, G.C. (1994), “Experimental Observations of Scale Effects on Bonded and Bolted Joints in Composite Structures,” NASA CP 3271, pp. 57–80.
Gukhman, A.A. (1965), Introduction to the Theory of Similarity, Academic Press, New York.
Hsu, C.S., Griffin, J.H. and Bielak, J. (1989), “How Gravity and Joint Scaling Affect Dynamic Response,” AIAA Journal, Vol. 27, No. 9, pp. 1280–87.
Jackson, K.E. (compiler) (1994), “Workshop on Scaling Effects in Composite Materials and Structures,” NASA Conference Publication 3271, July 1994.
Jackson, K.E. and Kellas, S. (1994), “Sub-Ply Level Scaling Approach Investigated for Graphite-Epoxy Composite Beam-Columns,” NASA CP 3271, pp. 19–36.
Jackson, K. E. (1990), “Scaling Effects in the Static and Dynamic Response of Graphite-Epoxy Beam-Columns,” NASA TM 102697.
Johnson, D.P., Morton, J., Kellas, S. and Jackson, K.E. (1994), “Scaling Effects in the Tensile and Flexure Response of Laminated Composite Coupons,” NASA CP 3271, pp. 265–282.
Jones, R.M. and Morgan, H.S. (1975), “Buckling and Vibration of Cross-Ply Laminated Circular Cylindrical Shells,” AIAA Journal, Vol. 13, No. 5, pp. 664–671.
Kline, S.J. (1965), Similitude and Approximation Theory. McGraw-Hill, NY.
Langhaar, H.L. (1951), Dimensionless Analysis and Theory of Models, John Wiley & Sons, New York.
Letchworth, R., McGowan, P. E. and Gronet, J. J. (1988), “Space Station: A Focus for the Development of Structural Dynamics Scale Model for Large Flexible Space Structures,” presented at AIAA/ASME/ASCE/AHS 29th SDM Conference (not included in Proceedings), Williamsburg, VA, April 18–20, 1988.
Macagno, E.O. (1971), “Historico-Critical Review of Dimensional Analysis,” J. Franklin Inst., Vol. 292, No. 6, pp. 39l–402.
McDougal, R.L. (1987), Private Communications, Structural Division, the Lockheed-Georgia Company, Marietta, GA.
McGowan, P.E., Edighoffer, H.E. and Wallace, J.W. (1990), “Development of an Experimental Space Station Model for Structural Dynamics Researches,” NASA Technical Memorandum 102601.
Morgen, G. W. (1964), Scaling Techniques for orthotropic Cylindrical Aerospace Structures,” Proceedings of AIAA 5th Structures and Materials Conference, Pal springs, pp. 333–343.
Morton, J. (1988), “Scaling of Impact Loaded Carbon Fiber Composites,” AIAA Journal, Vol. 26, No. 8, pp. 989–994.
Murphy, G. (1950), Similitude in Engineering, Ronald Press, New York.
O’Brien, T. K. (1994), “Damage and Strength of Composite Materials: Trends, Predictions and Challenges,” NASA CP 3271, pp. 145–160.
Pankhust, R. C. (1964), Dimensional Analysis and Scale Factors, Chapman & Hall, London, Reinhold, New York.
Qian, Y., Swanson, S. R., Nuismer, R. J. and Bucinell, R.B. (1990), “An Experimental Study of Scaling Rules for Impact Damage in Fiber Composites,” J. Composite Materials, Vol. 24, No. 5, pp. 559–570.
Rayleigh, Lord (1915), “The Principle of Similitude,” Nature, 95, 66–68.
Rezaeepazhand, J. and Simitses, G. J. (1997), “Structural Similitude for Vibration Response of Laminated Cylindrical Shells with Double Curvature,” Composites, Part B, Vol. 28B, pp. 195–200.
Rezaeepazhand, J., Simitses, G.J. and Starnes, J. H. Jr. (1996), “Scale Models for Laminated Cylindrical Shells Subjected to Axial Compression,” Composite Structures, Vol. 34, No. 4, pp. 371–379.
Rezaeepazhand, J., Simitses, G.J. and Starnes, J.H., Jr. (1995a), “Design of Scaled Down Models for Stability of Laminated Plates,” AIAA Journal, Vol. 33, No. 3, pp. 515–519.
Rezaeepazhand, J., Simitses, G.J. and Starnes, J.H., Jr. (1995b), “Use of Scaled Down Models for Predicting Vibration Response of Laminated Plates,” Composite Structures, Vo. 30, pp. 419–426.
Shih, C., Chen, J. C. and Garba, J. (1987), “Verification of Large Beam-Type Space Structures,” NASA Report No. 87-22712.
Sierakowski, R.L. (1994), “Private Communication,” Ohio State University, Columbus, OH.
Simitses, G.J. (1999), “Structural Similitude for Flat Laminated Surfaces,” Composite Structures, accepted for publication.
Simitses, G.J. and Rezaeepazhand, J. (1995), “Structural Similitude and Scaling Laws for Buckling of Cross-Ply Laminated Plates,” J. Thermoplastic Composite Materials, Vol. 8, pp. 240–251.
Simitses, G.J. and Rezaeepazhand, J. (1993), “Structural Similitude for Laminated Structures,” J. Composites Engineering, Vol. 3, Nos. 7–8, pp.; 751–765.
Simitses, G.J., Rezaeepezhand, J. and Sierakowski, R.L. (1997), “Scaled Models for Laminated Cylindrical Shells Subjected to External Pressure,” Mechanics of Comp. Materials & Structures, Vol. 4, pp. 267–280.
Singer, J., Arbocz, I. and Weller, T. (1997), Buckling Experiments, John Wiley and Sons, Chickester, England.
Soedel, W. (1971), “Similitude Approximations for Vibrating Thin Shells,” J. Acoustical Society of America, Vol. 49, No. 5, pp. 1535–41.
Szucs, E. (1980), Similitude and Modelling, Elsevier, NY.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Kluwer Academic Publishers
About this chapter
Cite this chapter
Simitses, G.J., Starnes, J., Rezaeepazhand, J. (2001). Structural Similitude and Scaling Laws for Plates and Shells: A Review. In: Durban, D., Givoli, D., Simmonds, J.G. (eds) Advances in the Mechanics of Plates and Shells. Solid Mechanics and its Applications, vol 88. Springer, Dordrecht. https://doi.org/10.1007/0-306-46954-5_19
Download citation
DOI: https://doi.org/10.1007/0-306-46954-5_19
Publisher Name: Springer, Dordrecht
Print ISBN: 978-0-7923-6785-7
Online ISBN: 978-0-306-46954-1
eBook Packages: Springer Book Archive