Method Filtering Singular Part Of Fracture Problems

Analytical continuation integrated with separating singularity of complexpotential is one of the common analytic methods for solving the fracture problems.However, this method and other existing classical analytic methods are not easy tountangle the singularity of transform function. The problems of elliptic hole plate, theplane problems and anti-plane problems of parabolic crack being taken as the researchobject, and improvement being made on the method separating principle singularity ofcomplex potential, a set of methods capable of overcoming the difficulties caused bythe singular transformation function and simplifying the analysis process areestablished. The main content and innovation are as follows:A formula directly calculating crack tip stress intensity factor for the fractureproblem under residual stresses is derived by using complex potential.An approach filtering the singular part of complex functions is developed in thisthesis, and it is then employed to analyze infinite plate problem with an oval hole,plane problme and auti-plane problem with a parabolic crack. The plane with aparabolic crack is mapped into the outside of a unit circle by conformaltransformation. After the singularities of the transformation function being handledand the formula being proposed directly calculating the crack tip stress intensityfactor by means of complex potential, closed form for the crack tip stress intensityfactor of the homogeneous parabolic crack problem is obtained. The result can bedegenerated into the classical solution for line crack when the parabolic crackapproaches to line crack.The plane problem and anti-plane problem with a parabolic crack under residualstress, the anti-plane problem with a parabolic crack in quasicrystal material underresidual stress are also investigated in this study. The last problem can be turned intoa problem coupling the phonon field with the phason field. Posterior to obtaining theclosed form of the stress intensity factors at the tip of parabolic crack, relevantnumerical cuvertures are plotted, and then variation law of the crack tip stressintensity factors depending on various physical parameters are discussed in detail.The method filtering the singular part of complex function and the formuladirectly calculating stress intensity factors at the tip of crack directly by usingcomplex potential propsed in this paper, simplify the process of solving the crack problems, and can be used to analyze complex boundary value problems with complexboundary shapes. The method dealing with the singularity of the transform functionsenlarges the bound of applying complex variable function method to obtain closedform solutions of the boundary problems.