The elastic equilibrium of isotropic plates and cylinders

Abstract

Abstract 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-ordinate Z, or in power series in Z, the coefficients of the series being certain functions of the x and y co-ordinates which are sufficient to satisfy boundary conditions over two bounding cylindrical surfaces normal to the planes Z = ±h. The form of the theory is greatly simplified by making use of complex combinations of stress components, and by using the complex variable z = 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.