Open AccessThe elastic equilibrium of isotropic plates and cylinders
Author(s) -
Albert Edward Green,
Albert Edward Green
Publication year - 1949
Publication title -
proceedings of the royal society of london. series a, mathematical and physical sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.814
H-Index - 135
eISSN - 2053-9169
pISSN - 0080-4630
DOI - 10.1098/rspa.1949.0008
Subject(s) - isotropy , bounding overwatch , fourier series , series (stratigraphy) , power series , mathematical analysis , mathematics , shear (geology) , boundary value problem , bending of plates , stress (linguistics) , bending , geometry , physics , materials science , optics , composite material , computer science , paleontology , artificial intelligence , biology , linguistics , philosophy , thermodynamics
A general solution of the elastic equations is obtained for problems of stress distributions in plates or cylinders when the bounding faces of the plates Z = ±h , or the flat ends of the cylinders, are free from applied normal and shear stresses. The solution is expressed either in the form of Fourier series in the co-ordinateZ , or in power series inZ , the coefficients of the series being certain functions of thex andy co-ordinates which are sufficient to satisfy boundary conditions over two bounding cylindrical surfaces normal to the planesZ = ±h . The form of the theory is greatly simplified by making use of complex combinations of stress components, and by using the complex variablez =x +iy . A first approximation to the part of the theory which deals with the bending of the plate yields a theory similar in character to that given recently by Reissner.