Eigenfunction solution for the plane stress problems of curved beams

The paper deals with the method of obtaining the plane stress solutions for problems associated with a long curved beam whose curved edges are free of tractions and upon whose straight edge stresses, displacements or mixed conditions are prescribed. It is shown that while closed solutions can be obtained for the mixed problems, the stress and displacement problems can be reduced to a system of linear algebraic equations in infinitely many unknowns. The decay properties of the stresses and the numerical convergence of the associated eigenfunction expansions have been illustrated for some self-equilibrating loads prescribed on the straight edge.