Special finite elements including stress concentration effects of a hole

Special finite elements are developed for efficient evaluation of stress concentration around a hole in complex structures. The complex variable formulation is used to derive a special set of stress functions which embody the stress concentration effects of a hole. The stress functions in combination with an independent displacement field assumed along the element boundary are used to construct the special elements with the hybrid displacement finite element method. Several numerical examples are presented to show that the used of special finite elements to model critical regions around a hole, together with conventional finite elements to model other regions away from the hole, is not only very convenient but also highly accurate.