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Boundary Value Problems of Partial Differential Equations in Fracture Mechanics of Orthotropic Composite Material

Author: XieXiuFeng
Tutor: LiJunLin
School: Taiyuan University of Science and Technology
Course: Applied Mathematics
Keywords: Composites Orthotropic Crack Stress field Displacement field
CLC: O346.1
Type: Master's thesis
Year: 2008
Downloads: 77
Quote: 1
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Abstract


Composites have remarkable advantages due to its material properties , and thus in the industrial sector has been more widely used . Fracture mechanics analysis of the materials optimized design is essential , dynamic fracture behavior in the composite is very complicated , so that more difficult mathematical research and application of appropriate mathematical methods , solution the composite crack stress field and displacement field , and thus predict and judge the occurrence and development process of composite material failure and so is very important to solve the problem of engineering fracture theoretical value and practical significance , but the current research work , the analytical solution of composite crack tip stress and displacement field theory is still relatively small, mostly concentrated in the numerical solution to solve this problem , this paper orthotropic composite plate type I , II type , I II hybrid crack tip stress field and displacement field . elasticity knowledge and theory of fracture mechanics , composite fracture into a class of partial differential equations of the boundary value problem operator transform the partial differential equations into generalized biharmonic equation . cleverly constructed a new function of the stress , the use of a the composite fracture complex variable function method and the method of undetermined coefficients , effectively solving a class of boundary value partial differential equations problem : 1 ) orthotropic composite type I crack tip stress field and displacement field theoretical formula ; 2) the Orthotropic Composite II crack tip stress field and the displacement field theoretical formula ; 3) Orthotropic Composite material I II hybrid crack tip stress field and displacement field theoretical formulas obtained in this study orthotropic composite plate crack tip near stress field theoretical formulas show that : when r tends to 0 , σx, σy, τxy tends to infinity these theoretical results provide a theoretical basis to solve practical engineering fracture problem , the presence of stress concentration , and r ? 12 singularity at the crack tip .

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CLC: > Mathematical sciences and chemical > Mechanics > Solid Mechanics > Strength theory > Fracture theory
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