International Journal of Safety

The Korean Society of Safety (한국안전학회)
권호 표지

Application of the Boundary Element Method to Finite Deflection of Elastic Bending Plates

  • Kim, Chi Kyung (Department of Safety Engineering, University of Incheon)
  • Published : 2003.06.01
Download PDF
⟨ Previous Next ⟩

Abstract

The present study deals with an approximate integral equation approach to finite deflection of elastic plates with arbitrary plane form. An integral formulation leads to a system of boundary integral equations involving values of deflection, slope, bending moment and transverse shear force along the edge. The basic principles of the development of boundary element technique are reviewed. A computer program for solving for stresses and deflections in a isotropic, homogeneous, linear and elastic bending plate is developed. The fundamental solution of deflection and moment is employed in this program. The deflections and moments are assumed constant within the quadrilateral element. Numerical solutions for sample problems, obtained by the direct boundary element method, are presented and results are compared with known solutions.

Keywords

References

  1. Alterio, J. and Sikarskie, L., 'A Boundary Integral Method Applied to Plates of Arbitrary Plan Forms,' Computers and Structures, Vol. 9, pp. 163-168, 1978 https://doi.org/10.1016/0045-7949(78)90134-7
  2. Ameen, M., 'Boundary Element Analysis,' Alpha Sci-ence International Ltd, pp. 115-133, 2001.
  3. Banerjee, P. and Butterfield, R., 'Boundary Element Methods in Engineering Science,' McGraw-Hill, pp. 289-296, 1981
  4. Bezine, G., 'A Boundary Integral Equation Method for Plate Flexure with Conditions Inside the Domain,' International Journal for Numerical Methods in Engi-neering, Vol. 17, pp. 1647-1657, 1981 https://doi.org/10.1002/nme.1620171106
  5. Brebbia, C. A., 'Progress in Boundary Element Meth-ods Volume 1,' Pentech Press Ltd, pp. 143-163, 1981
  6. Brebbia, C. A., Telles, J. C. and Wrobel, L. C., 'Boundary Element Techniques,' Springer-Verlag, pp. 324-336, 1984
  7. Jaswon, M. A. and Maiti. M. S. K., 'An Integral Equa-tion Formulation of Plate Bending Problems,' Journal Engineering Mathematics, Vol. 2, pp. 83-93, 1968 https://doi.org/10.1007/BF01534962
  8. Kamiya, N. and Sawaki, Y., 'An Integral Equation Approach to Finite Deflection of Elastic Plates,' International Journal for Nonlinear Mechanics, Vol. 17, pp.187-194, 1982 https://doi.org/10.1016/0020-7462(82)90018-X
  9. Maiti, M. and Chakraborty, S. K., 'Integral Equation Solutions for Simply Supproted Polygonal Plates,' International Journal for Engineering Sciences, Vol. 12, pp. 793-806, 1974 https://doi.org/10.1016/0020-7225(74)90017-2
  10. Mukherjee, S., 'Boundary Element Methods in Creep and Fracture,' Applied Science Publishers Ltd, pp. 122-149, 1982
  11. Paris, F. and Leon, S.D., 'Simply Supproted Plates by the Boundary Integral Equation Methods,' Interna-tional Journal for Numerical Methods in Engineering, Vol. 23, pp. 173-191, 1986
  12. Stern, M., 'A General Boundary Integral Formulation for the Numerical Solution of Plate Bending Prob-lems,' International Journal for Solids and Structures, Vol. 15, pp. 769-782, 1979
  13. Ween, F. V., 'Application of the Boundary Integral Equation Method to Reissner's Plate Model,' Interna-tional Journal for Numerical Methods in Engineering, Vol. 18, pp. 1-10, 1982