The Characteristic Analysis Of Singularity For Notches In Functionally Materials

In engineering structures, we will often meet the question with v-notch. There are some stress concentration around the tip of v-notch. It will have a significant impact on the mechanical properties of engineering materials structure. So, it has important theoretical significance and application value for the research of the stress singularity around the tip of the v-notch. At the same time, due to the capability of the conversion between mechanical, electric and magnetic energy, magneto-electro-elastic (MEE) materials can be applied to design sensors, actuators and other smart products. So it has widely attention in recent years.In this paper, based on linear elastic theory, introduce the function asymptotic expansion on their tip generalized displacement field asymptotic expansion, make the balance equation to the characteristics of differential equation about the singular index of incision. It is a set of nonlinear characteristics of differential equations. By introducing a new set of functions, and adopt the method of variable substitution, conversion the nonlinear differential equations into linear differential equations. At last, at once introduced interpolation matrix method to calculate the singularity index of the incision.For functionally graded plate, adopt the free-free and clip-clip boundary conditions to calculate. For the function gradient thin plate, adopted at both ends of the simply supported boundary conditions to calculate. Use interpolation matrix method, easy to draw the singularity index and Angle of characteristic function. Rapid and effective avoid to solving the differential equation. With this method of magneto-electro-elastic material and composite materials incision were studied, to calculate the stress singularity index of incision. The results show that this method is a very effective means of accurately to analysis of stress singularity index of incision.