Cylinders and Circular Plates
The bounded harmonic potentials of equations (24.27) in combination with solutions A, B and E provide a complete solution to the problem of a solid circular cylinder loaded by axisymmetric polynomial tractions on its curved surfaces. The corresponding problem for the hollow cylinder can be solved by including also the singular potentials of equation (24.42). The method can be extended to non-axisymmetric problems using the results of §24.7. If strong boundary conditions are imposed on the curved surfaces and weak conditions on the ends, the solutions are most appropriate to problems of ‘long’ cylinders in which L >> a, where L is the length of the cylinder and a is its outer radius. At the other extreme, where L << a, the same harmonic functions can be used to obtain three-dimensional solutions for in-plane loading and bending of circular plates, by imposing strong boundary conditions on the plane surfaces and weak conditions on the curved surfaces. As in Chapter 5, some indication of the order of polynomial required can be obtained from elementary Mechanics of Materials arguments.
KeywordsCircular Plate Hollow Cylinder Axisymmetric Problem Solid Cylinder Complete Stress
Unable to display preview. Download preview PDF.