Begging The Solution Of Some Theorical Problems In Fracture Mechanics With Complex Functions

In this thesis, we research for single cracks andperiodic cracks. The cracks are familiar and important modelI , model II and mixed model of I - II . In this thesis, weeduce the expression of stress field , displacement fieldand stress intensity factors with two complex functions .The thesis includes introduction ,text ,conclusion and showing thanks. In the first part,we describe the background, present condition of this work and discuss its use value and theories meaning in national economy.In the second part, theories analysis, calculation method and formula deduces are given.The conclusion is that we can adopt Westergaard stress function for any cracks and that we find out the logical mathematics contact of the two functions and we can unify them.We adopt Westergaard stress function for cracks I and cracks II ;but Muskhelishvili stress function for mixed cracks of I - II . So we have such an illusion that we -can only adopt Muskhelishvi1i stress function for cracks I - II . The purpose to compose this thesis is to look after the relation of the two stress functions and unify them.The researching methods adopted are Muskhelishvi1i and Westergaard stress functions.The main content is to find out the stress field and the displacement field of I - II mixed model.Then we degenerate the mixed crack to a single crack and compare the solution of mixed cracks with that of single cracks. The hard core of this thesis is the eduction of Westergaard stress function for I - II mixed model cracks.