Abstract
A hybrid method is presented for the analysis of layers, plates, and multilayered systems consisting of isotropic and linear elastic materials. The problem is formulated for the general case of a multilayered system using a total potential energy formulation and employing the layerwise laminate theory of Reddy. The developed boundary integral equation model is two-dimensional, displacement based and assumes piecewise continuous distribution of the displacement components through the system's thickness. A one-dimensional finite element model is used for the analysis of the multilayered system through its thickness, and integral Fourier transforms are used to obtain the exact solution for the in-plane problem. Explicit expressions are obtained for the fundamental solution of a typical infinite layer (element), which can be applied in a two-dimensional boundary integral equation model to analyze layered structures. This model describes the three-dimensional displacement field at arbitrary points either in the domain of the layered medium or on its boundary. The proposed method provides a simple, efficient, and versatile model for a three-dimensional analysis of thick plates or multilayered systems.
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References
Brebbia, C. A., Telles, J. C. F. and Wrobel, L. C., Boundary Element Techniques, Springer-Verlag, Berlin, 1984.
Beskos, D. E. (ed.), Boundary Element Analysis of Plates and Shells, Springer-Verlag, Berlin, 1991.
Dougall, J., ‘An Analytical Theory of the Equilibrium of an Isotropic Elastic Plate’, Trans. Roy. Soc. Edinburgh 41, 1904, 129–228.
Burmister, D. M., ‘The General Theory of Stresses and Displacements in Layered Systems I, II, III’, J. Appl. Phys. 16, 1945, 89–94, 126–127, 296–302.
Bufler, H., ‘Theory of Elasticity of a Multilayered Medium’, J. Elasticity 1, 1971, 125–143.
Benitez, F. G. and Rosakis, A. J., ‘Three-Dimensional Elastostatics of a Layer and a Layered Medium’, J. Elasticity 18, 1987, 3–50.
Reddy, J. N., ‘A Generalization of Two-Dimensional Theories of Laminated Composite Plates’, Communications in Applied Numerical Methods 3, 1987, 173–180.
Reddy, J. N., Energy and Variational Methods in Applied Mechanics, Wiley, New York, 1984.
Sneddon, I. N., Application of Integral Transforms in the Theory of Elasticity, Springer-Verlag, New York, 1975.
Sneddon, I. N., Fourier Transforms, McGraw-Hill, New York, 1951.
Reddy, J. N., An Introduction to the Finite Element Method, 2nd edn, McGraw-Hill, New York, 1993.
Kokkinos, F. T. and Reddy, J. N., ‘A Layerwise Boundary Integral Equation Model for Layers and Layered Media’, J. Elasticity 38, 1995, 221–259.
Watson, G. N., A Treatise on the Theory of Bessel Functions, 2nd edn, Cambridge University Press, London, 1945.
Wheelon, A. D., Tables of Summable Series and Integrals Involving Bessel Functions, Holden-Day, San Francisco, 1968.
Abramowitz, M. and Segun, I. A., Handbook of Mathematical Functions, Dover Publications, New York, 1968.
Cruse, T. A., The Transient Problem in Classical Elastodynamics Solved by Integral Equations, Ph.D. Dissertation, University of Washington, 1967.
Kellogg, O. D., Foundations of Potential Theory, Springer-Verlag, Berlin, 1929.
Hartmann, F., ‘Computing the C Matrix in Non-Smooth Boundary Points’, in New Developments in Boundary Element Methods, C. A. Brebbia (ed.), CML Publications, Southampton, 1980, 367–379.
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Visiting Assistant Professor
Oscar S. Wyatt, Jr. Chair
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Kokkinos, F.T., Reddy, J.N. Layerwise fundamental solutions and three-dimensional model for layered media. Appl Compos Mater 3, 277–300 (1996). https://doi.org/10.1007/BF00134971
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DOI: https://doi.org/10.1007/BF00134971