Abstract
This paper presents a new method exactly to solve the bending of elastic thin plates with arbitrary shape. First the analytic solution of differential equation of elastic thin plate is derived in polar coordinate, then the analytic solution is substituted into the boundary conditions of elastic thin plate with arbitrary shape. The boundary equations are expanded along the boundary by the use of Fourier series, all unknown coefficients can be decided. The results are exact.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
ZhangFufan,Elastic Thin Plates, Second Ed., Science Press, Beijing (1984). (in Chinese)
ChienWeizang,Variational Method and Finite Element, Science Press, Beijing (1980). (in Chinese)
ZhangFufan, Asymmetric bending of rectangular cantilever plates,Acta Mechanica Solida Sinica,5, 2 (1980), 170–182. (in Chinese)
XieXiusong and WangLei, Kantorovich solution for the problem of bending of a ladder plate,Appl. Math. and Mech. (English Ed.).5, 3 (1984), 1365–1374.
S. Timoshenko, et al.,Theory of Plates and Shells, McGraw-Hill (1959).
Author information
Authors and Affiliations
Additional information
Communicated by Pan Lizhou
Project supported by the Science Foundation of Nanjing University of Technology
Rights and permissions
About this article
Cite this article
Ding, Z. An exact method of bending of elastic thin plates with arbitrary shape. Appl Math Mech 17, 1189–1192 (1996). https://doi.org/10.1007/BF02498707
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02498707