Application Of SPH Method In Thermoelastic Deformation Of Functionally Graded Composites

Functionally Gradient Materials(FGMs),as a new generation of composites,inherits the advantage of designability from traditional composites,overcomes the disadvantages of thermal stress concentration and easy layering of traditional composites.Therefore,FGMs are called one of the most promising new materials in the 21st century,which can be processed into heat insulation coating and applied to space shuttle,nuclear reactor,advanced automobile,etc.Nowadays,the studies of FGMs’ thermoelasticity have become one of important issue in the field of solid mechanics.The paper starts form two aspects of research method and study contents.For research method,mesh methods are the main numerical methods in the studies of FGMs thermoelasticity.Whereas,for mesh-based method,mesh distortion or entanglement always appears in the problems of large deformation,structural damage,phase change,etc.whereupon,the study choose the meshfree method,SPH(Smoothed Particle Hydrodynamics)method,which are beneficial for researching large deformation,structural damage,phase change,etc.For study contents,firstly,the study of FGMs’ thermoelasticity can improve properties of thermotics and mechanics,upgrade aircraft engine,intensify abilities of thermal insulation and shock resistance,safeguard nuclear industry,etc.Secondly,until now most of studies concentrate on single-directional FGMs,but the fields of thermal and stress are usually loaded in two or three directions in its practical application.The paper have studied thermoelasticity of bi-directionally FGMs,which benefits the improvements and applications of FGMs.Whether the meshless SPH method can effectively solve the thermoelastic problem remains to be verified.The thermoelastic deformation behavior of bi-directionally FGMs needs to be studied.Firstly,in order to improve the computional accuracy of SPH method,the study replaces SPH method with SSPH(Symmetric Smoothed Particle Hydrodynamics)method,researches the effects of kernel function and smooth length,solve three kinds of Poisson-type equations in different discretization and discrete ways.Secondly,the study solves the heat conduction problems of FGMs,introduces two schemes to idealize material properties,and analyzes the influences of grade parameter.Thirdly,the study solves the thermoelastic problems of single-directional and bi-directional FGMs,analyzes the influences of component gradient,and compares with the results solved by MWLS(Meshless Weighted Least-Square Method)and COM SOL.The results of this paper are as follows.Firstly,cubic B-spline kernel function and the smooth length 1.1 Δ makes SSPH method take the least error norms,SSPH method can well handle Poisson-type equations in different discretizations and discrete ways and keep high accuracy.Secondly,the results solved by SSPH are close to the solutions of finite element method,the temperature fileds in specific time step are close to the results solved by ANASYS.Thirdly,in the thermoelastic study of FGMs,the study shows that results solved by SSPH are close to the solutions solved by MWLS and COMSOL with less particles.Accroding to former study,it is concluded that SSPH method can successfully solve the thermoelastic problems of FGMs,which are helpful for the problems of thermal shock and thermal fracture.