Abstract
This paper deals with the problem of the design of a laminated plate possessing the required set of stiffnesses under the condition of using the minimum number of layers and minimum number of materials. It is shown that the minimum number of layers is not more than four and the minimum number of materials is not more than two. We consider the case when three types of stiffness (bending, in-plane and out-of-plane) are prescribed and the case when two types of stiffness (physical bending and in-plane) are prescribed. It is proved that for both cases the sets of the possible values of physical stiffnesses are the same but the sets of designs can be different. A design algorithm is developed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Banichuk, N.V.: Introduction to Optimization of Structures. Springer, Berlin Heidelberg New York (1990)
Bendsøe, M.P.: Optimization of Structural Topology, Shape and Material. Springer, Berlin Heidelberg New York (1995)
Gurdal, Z., Haftka, R.T., Hajela, P.: Design and Optimization of Laminated Composite Materials. Wiley, New York (1999)
Obraztsov, I.F., Vasil’ev, V.V., Bunakov, V.A.: Optimal Design of Shells of Revolution from Composite Materials. Mashinostroenie, Moscow, Russia (1977) [in Russian]
Reddy, J.N.: Mechanics of Laminated Composite Plates. CRC New York (1997)
Lewinski, T., Telega, J.J.: Elastic plates and shells of minimal compliance. In: Gutkowski, G., Mroz, Z. (eds.) Second World Cong. Struct. Multidisciplinary Optimization. V.2. IFTR. Warsaw, Poland, pp. 841–846
Kalamkarov, A.L., Kolpakov, A.G.: Analysis, Design and Optimization of Composite Structures. Wiley, New York (1997)
Kolpakov, A.A., Kolpakov, A.G.: Solution of the laminated plates design problem. New problems and algorithms. Comput. Struct. 83(12–13), 964–975 (2005)
Schapery, R.A.: Composite materials. V.2. In: Sendeckyj, G.P. (ed.) Mechanics of Composite Materials. Academic, New York (1974)
Christensen, R.M.: Mechanics of Composite Materials. Krieger, Malabar, FL (1991)
Feller, W.: An Introduction to Probability Theory and its Applications, 3rd edn. Wiley, New York (1970)
Caillerie, D.: Thin elastic and periodic plates. Math. Methods Appl. Sci. 6, 159–191 (1984)
Andrianov, I.V., Awrejcewicz, J., Manevich, L.I. (eds.): Asymptotical Mechanics of Thin-Walled Structures. Springer, Berlin Heidelberg New York (2004)
Panasenko, G.P.: Multi-scale Modeling for Structures and Composite. Springer, Berlin Heidelberg New York (2005)
Kolpakov, A.G.: Stressed Composite Structures: Homogenized Models for Thin-walled Nonhomogeneous Structures with Initial Stresses. Springer, Berlin Heidelberg New York (2005)
Kaplunov, J.: Universal dynamic theory of shells. In: Kienzler, R., Altenbach, H., Ott, I. (eds.) Theories of Plates and Shells, pp. 77–84. Springer, Berlin Heidelberg New York (2004)
Tikhonov, A.N., Arsenin, V.Y.: Solution of Ill-posed Problems. Halsted, New York (1977)
Rudin, W.: Principles of Mathematical Analysis. McGraw-Hill, New York (1964)
Liao, S.: Beyond Perturbation. Introduction to Homotopy Analysis Method. CRC, Boca Raton, FL (2004)
Kuchling, H.: Physics. Leipzig, VEB Fachbuchverlag, Leipzig (1980)
Timoshenko, S., Voinowsky-Krieger, S.: Theory of Plates and Shells. McGraw-Hill, NY (1959)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kolpakov, A.A. Design of a Laminated Plate Possessing the Required Stiffnesses Using the Minimum Number of Materials and Layers. J Elasticity 86, 245–261 (2007). https://doi.org/10.1007/s10659-006-9092-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10659-006-9092-y
Key words
- design
- laminated plate
- minimum number of layers
- minimum number of materials
- physical stiffnesses
- neutral plane