The Research And Application Of Coupling Of Meshless And Finite Element Method In Engineering Problems

This paper studies a coupling of meshless and finite element method, which in thefield of structural mechanics has some conclusions, but still need further study. The paperexpands the coupling of meshless and finite element method, and applies the expandedmethod in crack propagation problems and temperature field. The paper makes thefollowing aspects of works:Firstly, the paper discusses the advantages and disadvantages of meshless method andfinite element method (FEM). Moreover, the paper compared meshless method with finiteelement method.Secondly, elasticity and fracture mechanics theory knowledge are discussed.Elasticity theory knowledge mainly discusses basic concepts of elasticity, basic equationsand problems of plane stress and strain. Fracture mechanics theory knowledge mainlydiscusses the development process of fracture mechanics and major methods of solvingfracture mechanics problems. The paper discusses the formulas of solving stress intensityfactor in the crack propagation process, and J integral definition and choices of basisfunctions in crack propagation problems.Then, basis functions and test functions are expanded in the radial point interpolation,forming an extended radial point interpolation meshless method. Then ERPIM and FEMare coupled, forming a coupling of extended radial point interpolation meshless methodand finite element method. The paper applies it to crack propagation problems in fracturemechanics and establishes corresponding mathematical models. The method is proved it isfeasible and effective by solving numerical examples.Finally, calculation principle of ERPIM-FEM is discussed. The paper obtainscalculation principle of ERPIM-FEM by controlled equations of temperature field andvariation principles. The method is applied to solving typical stable heat conductionproblems, and the validity and efficiency of the method are demonstrated.