Boundary Value Problems Of Partial Differential Equations In Fracture Mechanics Of Orthotropic Composite Material

Composite materials have been more and more abroad applied into industry domain because of superiority of material performance. The fracture mechanics analysis is important to the optimized design of material. In composite materials the dynamic fracture behavior is very complex, which leads to more difficulty in mathematic study. So by use of apt mathematic methods, solving the stress and displacement fields of crack in composite materials, forcasting and judging the happening and development process are important to settling actual fracture problems in engineering. But in current studies there are seldom studied on analytic solutions of stress and displacement fields at crack tip in composite material and most concentrate in numerical value solving.For this problem, in this paper the stress and displacement fields of I mode, II mode, I + II mode crack at crack tip in orthotropic composite materials are studied. By use of elastic mechanics knowledge and fracture mechanics theory the composite material fracture problems are transformed into a class of edge value problem of partial differential equation, and by operator transformation, the partial differential equation is been transformed into abroad sense repetitive concoction equation. By subtly constructing new stress function and using composite material fracture complex function method and uncertain coefficient method a class of partial differential equation edge value problem is solved effectively. Get1) The theoretic formulae of I mode crack stress and displacement fields at crack tip in orthotropic composite material;2) The theoretic formulae of II mode crack stress and displacement fields at crack tip in orthotropic composite material; 3) The theoretic formulae of I + II mixed mode crack stress and displacement fields at crack tip in orthotropic composite material.The theoretic formulae of stress and displacement near crack tip in orthotropic composite material obtained in this paper show: when r approaches zero,σx,σy,τxy approach infinite, and there are stress concentration phenomenon and singularity of . These results provide theoretical basis in settling actual fracture problems in engineering.