Annular sector plates under in-plane loading: General symbolic solution and its application to the collinear compression case

The single Fourier series technique—made both simpler and more powerful through symbolic computation (so as to bypass the need for repetitive equation solving, thus resulting in a truly closed-form analytical solution)—and Fejér's summability are applied to the plane-stress problem of an annular circular sector plate under completely arbitrary normal and/or shear loading along the two curved edges. The approach is then used for a systematic parametric study of annular sector plates of arbitrary geometry under collinear radial compression (encompassing both point and patch loadings). This leads to the identification of key tensile and compressive stresses (in non-dimensionalized form) within the plate and enables the definition of what constitutes a ‘long’ plate to be made. Such characteristics are compared with their counterparts for rectangular plates.