Indexed on: 11 Dec '13Published on: 11 Dec '13Published in: Acta mechanica
A new element is proposed for describing a discontinuous medium, such as holes and cracks, inside the region of the element. The underlying idea is to construct numerically the base functions of the discontinuous region by capturing the results calculated by fine finite elements in small-scale and then to construct the element in macro-scale with the crack and hole based on the theories of the multi-scale finite element method and the extended finite element method. Some numerical analysis is performed. The results show that the proposed element can well describe the field of displacement, strain, and stress intensity of the discontinuous region inside the element and can significantly decrease the number of elements and nodes of the calculated porous structure. The precision of the proposed element is also acceptable.