TECHNICAL PAPERS
Jul 1, 1984

Plates on Elastic Foundation by Bie Method

Publication: Journal of Engineering Mechanics
Volume 110, Issue 7

Abstract

In this investigation the boundary integral equation (BIE) method with numerical evaluation of the boundary integral equations is applied to the analysis of simply supported plates of any shape, resting on an elastic foundation. The numerical results are compared with those available from analytical solutions. Moreover, the efficiency of the BIE method is demonstrated and examined.

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References

1.
Abramowitz, M., and Stegun, I., eds., Handbook of Mathematical Functions, Dover Publications, New York, N.Y., 1972, pp. 379–385.
2.
Banaugh, R. P., and Goldsmith, W., “Diffraction of Steady Elastic Waves by Surfaces of Arbitrary Shape,” Journal of Applied Mechanics, Vol. 30, 1963, pp. 589–597.
3.
Banerjee, P. K., and Butterfield, R., Boundary Element Methods in Engineering Science, McGraw‐Hill Book Co., London, 1981.
4.
Banerjee, P. K., Butterfield, R., and Tomlin, G. R., “Boundary Element Methods for Two Dimensional Problems of Transient Ground‐Water Flow,” International Journal for Numerical Methods in Geomechanics, Vol. 5, pp. 15–31.
5.
Bezine, G., “Boundary Integral Equations for Plate Flexure with Arbitrary Boundary Conditions,” Mechanics Research Communications, Vol. 5, No. 4, 1978, pp. 197–206.
6.
Brebbia, C. A., and Dominguez, J., “Boundary Element Methods for Potential Problems,” Applied Mathematical Modelling, Vol. 1, 1977, pp. 372–378.
7.
Brebbia, C. A., ed., Recent Advances in Boundary Element Method, Pentech Press, London, 1978.
8.
Brebbia, C. A., and Nagaguma, R., “Boundary Elements in Stress Analysis,” Journal of the Engineering Mechanics Division, ASCE, No. EM1, 1979, pp. 55–69.
9.
Burgoyne, F. D., “Approximations to Kelvin Functions,” Mathematics of Computation, Vol. 17, 1963, pp. 295–298.
10.
Christiansen, S., and Hansen, E., “A Direct Integral Equation Method for Computing the Hoop Stress at Holes in Plane, Isotropic Sheets,” Journal of Elasticity, Vol. 5, No. 1, 1975, pp. 1–14.
11.
Courant, R., and Hilbert, D., “Methods of Mathematical Physics,” Interscience, New York, 1953.
12.
Cruse, T., and Rizzo, F., “A Direct Formulation and Numerical Solution of the General Transient Elastodynamic Problem I,” Journal of Mathematical Analysis and Applications, Vol. 22, 1968, pp. 244–259.
13.
Cruse, T., “A Direct Formulation and Numerical Solution of the General Transient Elastodynamic Problem II,” Journal of Mathematical Analysis and Applications, Vol. 22, 1968, pp. 341–355.
14.
Cruse, T., and Rizzo, F., eds., “Boundary‐Integral Equation Method: Computational Applications in Applied Mechanics,” AMD‐Vol. 11, American Society of Mechanical Engineers, New York, N.Y., 1975.
15.
Dubois, M., and Lachat, C., “The Integral Formulation of Boundary Value Problems,” International Conference on Variational Methods in Engineering, Southampton University, 1972, pp. 9/89‐9/109.
16.
Fletcher, H. J., and Thorne, C. J., “Thin Rectangular Plates on Elastic Foundation,” Journal of Applied Mechanics, Vol. 19, 1952, pp. 361–368.
17.
Fredholm, I., “Öfversigt af Kongl. Svenska Vetenskaps‐Akademiens Förhandligar,” Vol. 57, 1900, pp. 39–46.
18.
Fredholm, I., “Solution d'un Probleme Fondamental de la Theorie de l'Elasticité,” Arkiv för Matematik, Astronomi och Fysik, Vol. 2, No. 28, 1906, pp. 1–8.
19.
Green, G., An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism, Nottingham, 1928.
20.
Jaswon, E., “The Integral Equation Approach to Thin Plate Problems,” thesis presented to the Technion Israel Institute of Technology, in 1973, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
21.
Jaswon, M. A., “Integral Equation Methods in Potential Theory I,” Proceedings, Royal Society of London, Ser. A, Vol. 275, 1963, pp. 23–32.
22.
Jaswon, M. A., Maiti, M., and Symm, G. T., “Numerical Biharmonic Analysis and Some Applications,” International Journal of Solids and Structures, Vol. 3, 1967, pp. 309–332.
23.
Jaswon, M. A., and Maiti, M., “An Integral Equation Formulation of Plate Bending Problems,” Journal of Engineering Mathematics, Vol. 2, No. 1, 1968, pp. 83–93.
24.
Jaswon, M. A., and Ponter, A. R., “An Integral Equation Solution of the Torsion Problem,” Proceedings, Royal Society of London, Ser. A, Vol. 273, No. 1353, 1963, pp. 237–246.
25.
Katsikadelis, J. T., “The Analysis of Plates on Elastic Foundation by the Boundary Integral Equation Method,” thesis presented to the Polytechnic Institute of New York, in 1982, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
26.
Katsikadelis, J. T., Massalas, C. V., and Tzivanidis, G. J., “An Integral Equation Solution of the Plane Problem of the Theory of Elasticity,” Mechanics Research Communications, Vol. 4, No. 3, 1977, pp. 199–208.
27.
Katsikadelis, J. T., and Armenàkas, A. E., “Numerical Evaluation of Double Integrals with a Logarithmic or a Cauchy‐type Singularity,” Journal of Applied Mechanics, ASCE, Vol. 105, 1983, pp. 682–684.
28.
Kellogg, O. C., Foundations of Potential Theory, Springer Verlag, Berlin, 1967.
29.
Luke, Y. L., Mathematical Functions and Their Approximations, Academic Press, New York, N.Y., 1975.
30.
Maiti, M., and Chakrabarty, S., “Integral Equation Solutions for Simply Supported Polygonal Plates,” Journal of Engineering Sciences, Vol. 12, 1974, pp. 793–806.
31.
Mendelson, A., “Elastic‐Plastic Torsion Problems for Strain‐Hardening Materials,” NASA, TN D‐4391, 1968.
32.
Mendelson, A., “Solution of Elastoplastic Torsion Problem by Boundary Integral Method,” NASA, TN D‐7872, 1975.
33.
Mendelson, A., “Boundary Integral Methods in Elasticity and Plasticity,” NASA, TN D‐7418, 1973.
34.
Rim, K., and Henry, S., “Improvement of an Integral Equation Method through Modification of Source Density Representation,” NASA, CR‐1273, 1969.
35.
Rim, K., and Henry, S., “An Integral Equation Method in Plane Elasticity,” NASA, CR‐779, 1967.
36.
Rizzo, F., “An Integral Equation Approach to Boundary Value Problems of Classical Elastostatics,” Quarterly of Applied Mathematics, Vol. 25, No. 1, 1967, pp. 83–95.
37.
Rizzo, F., and Shippy, D., “A Method for Stress Determination in Plane Anisotropic Elastic Bodies,” Journal of Composite Materials, Vol. 4, 1970, pp. 36–61.
38.
Rzasnicki, W., “Plane Elastoplastic Analysis of V‐Notched Plate Under Bending by Boundary Integral Equation Method,” thesis presented to the University of Toledo, in 1975, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
39.
Rzasnicki, W., Mendelson, A., and Albers, L., “Application of Boundary Integral Method to Elastic Analysis of V‐Notched Beams,” NASA, TN D‐7424, 1973.
40.
Schleicher, F., “Kreisplatten auf Elastischer Unterlage,” Spring Verlag, Berlin, 1926.
41.
Segedin, C., and Brickel, D., “An Integral Equation Method for a Corner Plate,” Journal of the Structural Division, ASCE, Vol. 94, No. ST1, 1968, pp. 41–52.
42.
Stern, M., “A General Boundary Integral Formulation for the Numerical Solution of Plate Bending Problems,” International Journal of Solids Structures, Vol. 15, 1979, pp. 769–782.
43.
Stern, M., “Boundary Integral Equations for Bending of Thin Plates,” Progress in Boundary Element Methods‐2, Pentech Press, London, 1983.
44.
Stroud, A. H., Approximate Calculation of Multiple Integrals, Prentice‐Hall, Englewood Cliffs, N.J., 1971.
45.
Symm, G. T., “Integral Equation Methods in Elasticity and Potential Theory,” MA‐51, National Physics Laboratory, 1964.
46.
Symm, G. T., “An Integral Equation Method in Conformal Mapping,” Numerische Mathematik, Vol. 9, 1966, pp. 250–258.
47.
Timoshenko, S., and Woinowsky‐Krieger, S., Theory of Plates and Shells, McGraw‐Hill, New York, N.Y., 1959.
48.
Vogel, S., and Rizzo, F., “An Integral Equation Boundary Value Problems,” Journal of Elasticity, Vol. 3, No. 3, 1970, pp. 203–206.

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Go to Journal of Engineering Mechanics
Journal of Engineering Mechanics
Volume 110Issue 7July 1984
Pages: 1086 - 1105

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Published online: Jul 1, 1984
Published in print: Jul 1984

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J. T. Katsikadelis
Lect., Inst. of Struct. Analysis, National Technical Univ. of Athens, Greece
A. E. Armenàkas, M. ASCE
Prof. of Aerospace Engrg., Polytechnic Inst. of New York; also Prof. and Dir. of the Inst. of Struct. Analysis, National Technical Univ. of Athens, Greece

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