3D Analytical Analysis Of Functionally Graded Plates With A Linear Crack Or Square Hole

Functionally graded material(FGM),a neoteric composite,whose properties have continuous gradient distribution on account of graded distribution of material components.In the 1980 s,the aerospace field presented daunting challenges to material science field,as a result,FGM came into being.Nowadays,FGM has been applied more and more widely in aerospace,architecture,medicine and other fields.Functionally graded plate-a typical structural form of FGM.In general,due to various unfavorable factors during material synthesis or practical application requirements,cracks,holes and other defects often appear in functionally graded plates.When subjected to load,stress concentration effect will appear in the vicinity of cracks or holes,which often contributes to strength reduction or even damage of functionally graded plates.Therefore,it is of great significance to study the functionally graded plates with cracks or holes.Based on the three-dimensional elasticity theory and the extended England–Spencer functionally graded plate theory,the equilibrium problem of functionally graded plates with cracks or square holes are investigated in present thesis.The following researches are carried out:(1)The three-dimensional stress field at the Griffith crack tip in a functionally graded plate is investigated.Based on the assumption that material parameters vary continuously along the thickness direction of the plate,the analytical solutions of three-dimensional stress field at crack tip of a functionally graded plate with a Griffith crack subjected to load at infinity and uniform internal pressure on the crack surface are given by utilizing the complex function method and the conformal mapping method.The numerical results shows that factors including material gradient factor,load type,size and action position and others have significant influence on the three-dimensional stress field of Griffith crack tip.(2)The three-dimensional stress field of a functionally graded plate with a square hole is investigated.Based on the assumption that material parameters vary continuously along the thickness direction of the plate,the analytical solutions of three-dimensional stress field of a functionally graded plate with a square hole subjected to load at infinity are given by using conformal mapping and Cauchy integral method.The numerical results show that factors including FGM type,material gradient factor,load type,size and action position and others have important influence on the three-dimensional stress field of the functionally graded plate with a square hole.The obtained above three-dimensional elasticity solutions absolutely satisfy all elasticity equations and exact boundary conditions of bottom and top surfaces,however,the boundary conditions are merely eased on the functionally graded plate's cylinder surface by means of Saint-Venant principle.Therefore,the analytical solutions obtained in the paper can be used as reference solutions to evaluate approximate plate theories and numerical methods applying in research of functionally graded plates.