Numerical Simulation Method Of Plane Discontinuous Elastic Structure Based On Global Displacement Mode

With the development of computer software and hardware,numerical simulation technology has become an important instrument of scientific engineering research.The most representative methods for discontinuous structure at present mainly include extended finite element method and element free galerkin method.The extended finite element method introduces enriched functions with discontinuous character on the basis of finite element method,and describes the discontinuous interface by level set method,thus it makes the grid independent of the discontinuous interface,and avoids the difficulty of high density grid on the crack tip and remeshing problems when dealing with crack structure;Element free galerkin method generates the trial space by data fitting method,avoids the difficulty cause by grid reliance,otherwise it also has some insufficiency such as the complex form of fitting function and the problem of forced boundary condition.This paper proposes a numerical simulation method based on entire displacement mode for plain elastic discontinuous structure.In the method,the trial function space can be divided into two parts,one part for the continuous displacement field in the area and the other part for the discontinuous displacement field on the boundary.The discontinuous part can also be divided as strong discontinuous problem like crack and weak discontinuous problem like hole and inclusion.For the continuous part,the trial function can be easily taken as power series,and for the discontinuous part,boundary modified term is introduced to describe its discontinuous character,this paper provides the specific form of the trial space and the boundary modified function of discontinuous such as linear crack,curvilinear crack,central crack and hole.This paper simultaneously proposes a method for the exertion of displacement boundary condition based on the level set method,includes the displacement boundary condition in the approximate displacement field expression by introducing displacement boundary level set function,gives the expression of approximate displacement field,stiffness and load matrix on the condition of single displacement boundary constraint,single freedom constraint and multi displacement boundary constraint;On the basis of the theory,we compile the program of the rectangle plate with different discontinuous interface on static load with MATLAB,and contrasting the calculation result with FEM or XFEM method in abaqus.Calculation case and analysis result indicate that:for general plain elastic static problem,this paper's method can avoid the ill-condition problem of stiffness matrix effectively,reduce the order of the stiffness matrix,decrease the cost of linear equations solution while keeping enough accuracy;Meanwhile,it can avoid the difficulty of shape function fitting and displacement boundary processing in meshless method;Furthermore,it is very convenient to introduce the boundary modified terms into trial matrix,thus this paper's method is more advantageous on complex inner boundary like multi cracks and multi holes;Boundary modified function can be taken as different forms for different boundary condition,so that this paper's method has great expanding space on application.