Isoparametric Circle And Tube Elements And Their Application In Heat Conduction BEM Analysis

The modern engineering applications have much more need for capabilities of structures, which make the appearance of more and more complex surfaces of structures. Based on this background, the structures with hole and tube shapes were widely used in many fields as they have excellent thermal and mechanical properties. However, the analysis of structures with hole and tube shapes using finite element method (FEM) needs a lot of elements, which is a larger workload because of the particularity and complexity of the structure geometries. The boundary element method (BEM) is an important numerical method after FEM and has been widely used in engineering because its lower dimensions and high precision. However, in order to retain the computational accuracy and reduce the discretization errors in BEM analysis of such type of problems using conventional elements, the computational model needs to be discretized into a large number of boundary elements, and as a result the advantages of BEM cannot be produced.To overcome this problem, an algorithm using isoparametric circle elements in BEM is proposed in this thesis based on the Lagrange interpolation formulation. This type of elements can well model geometries with hole shapes and interpolate physical quantities defined on the hole surfaces. As a result, the discretization error can be reduced considerably. In addition, in order to eliminate singularities involved in the boundary integrals, the strategy adopt in this study is to isolate the logarithmic singularity and integrate it using the Gauss integration rule. Numerical examples on heat conduction show that the proposed elements have the advantages of less element discretization and high computational accuracy.Based on the idea of constructing isoparametric circle elements, a new algorithm using isoparametric tube elements in BEM is proposed based on the Lagrange interpolation formulation. The isoparametric tube elements can well model the geometries with tube shapes and interpolate physical quantities defined on the tube surface. In addition, a new technique for eliminating singularities involved in the boundary integrals is also developed in the intrinsic plane when using the proposed isoparametric tube elements in BEM. Numerical examples show that the proposed algorithm is suitable for tubular structures along arbitrary directions in the three-dimensional space and has the advantages of less mesh discretization and high computational efficiency.