Spherical Symmetry Elastoplastic Analysis In Functionally Graded Hollow Sphere

Based on the past research of FGMs, this paper studied the elastoplastic problemsof FGM hollow sphere in different boundary conditions through the analystical method,and this paper got the exact solutions of stress and displacement of FGM hollow sphere.Firstly, according to the symmetry of the compostion of material and stress inthe FGM hollow sphere, the reseach object was simplified, we got the hollow spherebasic equations under symmetry conditions, then the elastic modulus of functionallygradient material hollow sphere was assumed to change along the radius direction in theform of exponential function. this article combined the equilibrium differential equationof the FGM hollow sphere with the geometric equation and physical equation. The exactdisplacement and stress solution of the elastic FGM hollow sphere were deduced underthe strss boundary or mixed boundary through the displacement method.Then, this paper introduced the tresca yield condition expression on the base of theelastic displacement of the hollow sphere and the exact solutions of the stress formula,by which this paper deduced the formula of elastic-plastic FGM hollow sphere justunder the action of internal pressure.Finally, this paper demonstrated the validity of the research methods by using thematerial degradation as homogeneous materials, and this paper taked specificparameters into the analytical solutions of displacement and stress expressions tocalculate. This paper respectively obtained the displacement and stress distributionunder the five kinds of mechanical boundary conditions of only subjected to uniformlydistributed internal pressure, only subjected to external pressure uniform distribution,the uniform distribution inside and outside pressure, the uniform distribution of internalpressure and fixed outer boundary and uniform distribution. What’s more, this paperalso studied the influences of the size and material composition on FGM hollowspheres.This article has more extensive practical application value with the help of the sizeof the inner diameter and outer diameter in the study model can be changed arbitrarily,and this paper provided a precise theoretical basis for the future design of FGM hollowsphere. What’s more, the method in this paper can be used as a validation to other approximation method.