| As a new numerical method,BEM(boundary element method) has beenobtained more and more attention inpractical engineering applications. In the past20years, BEM has shown the unique advantages in dealing with problems in infinitedomains; and BEM has been more and more used in solving the geotechnicalengineering problems, such as interactionof foundation-subsoil, excavation andblasting etc..However, BEM used as an artificial boundary to deal with wavepropagation in the infinite domain has not been fully studied. So far, there is not anypublicly acepted artificial boundary based on BEM algorithm proposed.In this thesis,BEMin time domain is used to deal with the dynamic problems in infinite media;and the artificial boundary based onBEM algorithm is established. The researchscope are as follows:(1) BEM is used to solve the two-dimensional potential problems. Thepotential problem is one of theclassical issueswith whichBEMcan be used to dealwith. The method to deal with potential problems using BEMalgorithm is alsoapplicable in the other problems where BEM algorithm are used. Based on the twodimentional Laplase equationand the initial boundary values, the boundary integralequation is established. Several kinds of element, including the constant element,linear element and thequadratic element,are used to discrete the boundary of thecomputational domain. The expressions of the various parameters involved in theboundary integral equation are analytically derived.The boundary integral equationis solved to get all of the unknown variables on the boundary. BEM algorithm isvalidated by a practical engineering potential example. In the course of the study ondeveloping BEM algorithm in the potential problem, the general process for theboundary element method dealing with practical problems are probed. Meanwhile,also in the course of the study, the numerical computation accuracy is studied byusing different calculation methods.(2) BEM is also used to solve the two-dimensional elastostatics problem. Fristof all, according to elastostatics fundamental equation and weighted residual method,boundary integral equation is established for the fundamental elastostatics problem.Then the equation is discreted and solved. In the course of solving the boundaryintegral equation for the elastostatics problem, the effective computation methodsare probed to deal with the singularity for the fundamental solution and roughness ofthe boundary, and also to calculate the values for every element in several kinds ofmatrix.A case study for the foundamental elastostatics problem is carried out. In the case study, the BEM algorithm is validated, and the numerical accuracy in the BEMalgorithm is also studied. The main idea in the BEM algorithm in thefundamentalelastostatics problem is the important base for sloving morecomplicated dynamic problem in time domain. The discretization method fordealing with the sigularity and the methods for establishing several sets of equationsbasically similar for the fundamental elastostatics problem and the dynamic problemin time domain.(3)BEM algorithm in the time domain is used to dealwith wave propagation inan infinite medium. Thefundamental solution for BEM algorithm foratwo-dimensional isotropic medium is used to establish the boundary integralequation. Numerical methods are usedto discretethe boundary integral equationinspace and time domains. The values of the elements of the coefficient matrix in theboundary integral equation are obtained by analytical method in time domain.In thecourse of the calculation of the element values, Gaussian integration method isusedto solve the integral equation in the space on each unit, and coefficient matrixfor all formulasare developed. The analytical approach is usedto deal with thesingularity; the Kobayashi methodis used to apply the wave input. Matlabprogramiscodedaccording tothe numerical algorithm. |
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