The Study And Application Of Finite Block Method On Functionally Graded Materials

Functionally Graded Materials(FGMs)are composite materials whose properties are directionally dependent.FGMs are widely used in thermal barrier coatings of the airplane,bone tissue implants in bioengineering as well as electrodes in solid oxide fuel cells.In general,it is hard to find fundamental solutions of the mechanical problems because of their complex structure.Traditional methods like Finite Element Method(FEM)are difficult to generate mesh on FGMs and obtain satisfactory accuracy when they solve this kind of problems.Based on meshless method,Finite Block Method(F-BM)does not require fundamental solutions when it constructs the algebraic equations and it has more flexible collocation points and higher accuracy.FBM is proposed here to address inverse moving boundary problems,two-dimensional heat transfer problems and conforming contacts problems.An inverse moving boundary problem on iron-making furnace is considered here.We need to determine the inner boundary location(corroded point)of the furnace which is simulated through multilayer FGMs walls.Then the location of corroded point can be got by a virtual rectangle domain.In addition,the use of modified Chebyshev points will improve the convergence of FBM.Then FBM is applied to solve two-dimensional heat transfer problems on a FGMs disk.FBM in polar coordinate systems is proposed here due to the relevance between mechanical properties and the radius of the disk.Meanwhile,the heat transfer equations and boundary conditions in matrix form are presented here.Finally,the model of flat punch on an elastic foundation under compressive load is studied and FBM with boundary type is proposed here.In the process of analyzing the conforming contacts problems,we can find that the method can reduce the number of unknowns and it can improve the computational efficiency at the same time.In five numerical examples,comparison with Finite Element Method(FEM)and Radial Basis Functions(RBF)are presented to demonstrate the stability,efficiency and accuracy of the proposed method.