| There are usually generalized phases in solid materials,such as particles,inclusions,holes,cracks and other inhomogeneities.These generalized phases in solid materials greatly influence the mechanical properties of materials.Therefore,the accurate and efficient understanding of the state of the embedded generalized phases in solid materials is of great significance to the research and prediction as well as design of materials.However,the traditional numerical methods for the large-scale numerical simulation of multiphase solids are often faced with the problems of large discrete scale and low computational efficiency.For the purpose of improving computational efficiency and accuracy,numerical algorithms for large-scale generalized multiphase solids problems have been studied.Based on the boundary element method(BEM)and the Eshelby equivalent inclusion theory,the eigenstrain boundary integral equation(BIE)with iterative procedures is proposed,and a series of high-order smooth boundary elements is constructed,which can effectively solve large-scale multiphase solid problems.The main contributions of the present work in this dissertation are as follows:1)The establishment of the computation model of eigenstrain BIE with calculation programs for multiphase solids.By introducing the concepts of the equivalent inclusion of Eshelby with eigenstrains into BIE,a novel computational model of the eigenstrain formulation of boundary integral equations with corresponding iterative solution procedures is proposed,and the corresponding 2D and 3D high performance computational programs are designed and developed by FORTRAN programming language.The developed programs can efficiently solve multiphase solid problems with hundreds of thousands or even millions of unknowns on a personal computer.Due to the unknowns appear only on the boundary of the solution domain in the present model,the coefficient matrix of the system equations is small and only need to be calculated once.Therefore,compared with the traditional BEM subdomain method,the computational model presented in this paper has high computational efficiency.2)The analysis of the 3D solids with a large number of fluid-filled pores base on the computation model of eigenstrain BIE.Under the constant assumption of eigenstrain,the eigenstrain BIE with corresponding iterative solution procedures is used to solve the 3D solids with a large number of fluid-filled pores.Numerical results verify the feasibility and efficiency of the computational model.Moreover,the application range of the model extends from solid inclusions/holes to fluid inclusions.In the numerical examples,the relationship between the internal structure of material and the overall mechanical property parameters is studied,and the internal details of the material are also solved accurately.3)The construction of high-order smooth ellipsoid element and its application in the computation model of eigenstrain BIE.In order to reduce the number of boundary nodes needed for the discretization of subdomains,the high-order smooth ellipsoid elements are constructed based on the Lagrange interpolation polynomial.It is realized that a closed surface of ellipsoid inclusion/hole can be discrete by only using a single element.Moreover,the coefficients of shape functions can be generated automatically to get rid of the manual long derivation process encountered in the construction of a variety of high-order elements.The smoothness of the element is realized by repeated use of real nodes as auxiliary nodes,and the interpolation range of the interpolation nodes of the element is increased,so that the calculation accuracy is improved by one or two orders of magnitude.On the basis of Cauchy principal value(CPV)integral and Hadamard finite-part(HFP)integral,various singular and near singular integral evaluating methods are given for arbitrary high-order elements.Numerical results show that the high-order smooth ellipsoid elements can greatly improve the efficiency of the computational model of the eigenstrain BIE.4)The establishment of the non-uniform eigenstrain BIE and its application to rectangular inclusion problem.A computational model of the non-uniform eigenstrain BIE is developed by removing the constant assumption of eigenstrain,and which is applied to the analysis of rectangular inclusions.The local Eshelby matrix,reflecting the intrinsic properties of the near field group and the interaction between subdomains,is constructed in a new way,and the relationships among non-uniform eigenstrain,local Eshelby matrix and external load are derived.In addition,the numerical iteration procedure reflected the influence of the far field group is also studied.The accuracy and effectiveness of the model are verified by numerical examples,so that it further expands the application range of the computational model of the eigenstrain BIE.5)The construction of high-order smooth crack element and its application to3 D crack problem.Based on the smooth ellipsoid element,the high-order smooth penny-shaped crack elements and elliptic crack elements are constructed and applied to solve the 3D crack problem.It is realized that an embedded circular or elliptic shaped crack can be discrete by only using a single crack element.Moreover,the evaluated methods are proposed for the hypersingular and near hypersingular integral in the high-order crack element.In addition,the calculation method is given over crack elements for crack-related parameters.The numerical examples show that the accuracy,efficiency and effectiveness of the proposed high-order smooth crack element can be guaranteed under various complex load modes,which lays a foundation for the future work of the multi cracks problem. |
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