Irregular Shaped Plates with Singularities

For irregular-shaped plates loaded by either a uniform transverse load or point loads with singularities resulting from either loading or corner conditions, a solution that exactly represents the singularity is obtained by polar eigenfunctions with equilibrium identically satisfied and conditions along part of the boundary approximated and the error minimized by numerical orthogonalization. Solutions to the reentrant corner plate built-in at the reentrant corner and with various boundary conditions along the outer edge are presented graphically and in tabular form. The maximum error in approximated boundary conditions is 1%. Comparison is made with finite difference solutions.