Theory And Application Of Hybrid Boundary Node Method Based On Dual Reciprocity Method

As an improvement of the conventional numerical methods, meshless method has been developed in the past decades. They have the advantages that there no element is needed totally or partly, and the pre-process is quite easy. Therefore, meshless method can be widely applied to elasto-plastic analysis, crack propagation problemand large scale three-dimensional problem analysis. As a truly boundary-type meshless method, the hybrid boundary node method (HBNM) is the main research object in this dissertation, and the theory of the HBNM is thoroughly introduced. The HBNM, which combine modified variational theory and moving least square (MLS) method, is a truly meshless method with many excellent characteristics, such as simple pre-process and high accuracy. However, when it is applied to the inhomogeneous problems, such as elasticity problems with body force and dynamic loading and so on, it is evitable to need domain integral. In this dissertation, the dual reciprocity method (DRM) is combined with the HBNM, which successfully avoids domain integral, and expands the application scope of this method to inhomogeneous problems, such as transient eddy current and elasto-dynamic problems. The dissertation includes the following contents:Firstly, the HBNM for solving fracture mechanics is presented. The basis function enrichment in MLS is used for simulating the singularity of the stress field on the tip of the crack. Several nodes are located on the edge of the crack and higher accuracy of the stress field can be obtained. The preprocess can be simplified.Secondly, combine the DRM with the HBNM. The relationship of the unknown parameters between DRM and HBNM is presented and the theory formula is established for solving Poisson equation. In this method, the solution is divided into two parts, i. e., the complementary solution and the particular solution. The particular solution is obtained by radial basis function interpolation. The complementary one is solved by HBNM. At the same time, the modified boundary conditions are applied in hybrid boundary node method. This method requires a substantial number of internal points to interpolate particular solution by radial basis function, which approximation based only on boundary nodes may not guarantee sufficient accuracy. But the points in the domain are used only to interpolate particular solutions and it is not necessary for the intergration and approximation of the solution variable. Therefore, this method still is a truly boundary-type meshless method. Thirdly, the HBNM for solving transient eddy current in engineering problems is presented. The formulation of this method in this problem is developed, and the numerical implementation scheme is obtained. The correspondence programs are complied. The numerical results show that the present method possesses not only good performance of convergence, but also high accuracy, and it can be very suitable to solve the transient eddy current problems.Fourthly, the HBNM for solving Helmholtz problems is presented. The Helmholtz equation is an elliptic partial differential equation which is a time-harmonic solution of the wave equation. Obtaining an efficient and more accurate numerical solution for the Helmholtz equation has been the subject of many studies. In this dissertation, the system formulations are established for solving the Helmholtz equation. Two vibrating beams with different boundary conditions are analysized. The numerical results show that high accuracy and convergence are achieved with the present method.Fifthly, the HBNM for solving elasto-dynamic problems is presented. Combine the HBNM and the DRM, the theory formulations for elasto-dynamic problems are given. The formulations can.be applied non-linear problems. The relative programs are complied. The numerical examples are shown that the present method is adapted to solve the dynamic problems.Sixthly, the sensitivity of the number of the boundary node and the inner node for the accuracy is analysized. For simple problem, the influence of the number and location of inner node for accuracy is small. For complicated problems, the accuracy is more sensitive to the number of the inner node. Based on the numerical examples, the number of inner node is half of the number of boundary nodes, provides solutions which are satisfactory for all problems.The study shows that the present method possesses the not only excellent performance of convergence, but also high accuracy, and the preprocess is also very simple. It can be widely applied to the practical problems, such as crack propagation, adaptive problem and contact analysis and so on.