Research On Boundary Element Analysis Of Coating-structures And Interfacial Strength Of V-notched Structures

Based on the review of the analytic methods of coating-structures and V-notched structures, boundary element analysis of the coating-structures and V-notched structures are studied in detail by the author. The main work and contribution in this thesis are given as follows:1) The evaluation of the temperature field and two-dimensional stress field in the coating-structures is studied by boundary element method. Because the thickness of the coatings is very thin, the nearly singular integrals will occur in the boundary element analysis of the coating-structures. Here, a completely analytic algorithm has been raised to deal with the nearly singular integral. Consequently, the boundary element method can be used to efficiently calculate the temperature field, the stress and displacement fields of the coating-structure with multilayer materials. Then, the present method is adopted to determine the strength of the carbon fiber reinforced structures and the stress intensity factors of the sub-surface cracks.2) The semi-analytic algorithm of the nearly singular integral is introduced to the boundary element analysis of three-dimensional thin laminated structures. By using the semi-analytic formulation, the boundary element method can not only calculate the mechanical parameter of the inner points very close to the boundary in each layer, but also analyze the stress and displacement fields of multilayer thin-walled structures.3) The evaluation of the hyper-singular integral in the stress boundary integral equations (BIE) is studied. A series of transformations are performed to the conventional displacement derivative BIE in order to eliminate the hyper-singular principal value integrals. Hence,a new stress natural BIE is developed, in which there only exist the strongly singular integrals instead of the hyper-singular integrals in the conventional stress BIE. Furthermore, when a source point tends to the boundary, the small dominant factor leading to the nearly strongly singular integrals in the natural BIE is shifted out of the integral representations by the integration by parts, so that the singular integrals are accurately calculated. As a result, the present method is extended to the thermo-elasticity and multi-domain boundary element method by the author. Numerical examples demonstrate that the natural BIE can successfully determine the stress distributions in the domain very closer to the boundary in comparison with the conventional BIE.4) A new technique about the evaluation of the stress singularity orders of the V-notches by boundary element method is firstly proposed. Based on the theory of linear elasticity, the asymptotic displacement and stress fields in the V-notch tip region are expressed as a series expansion with respect to the radial coordinate from the tip. The series expansion of the asymptotic field is then substituted into the equations of the boundary element analysis of the V-notched structure. After the discretization, the boundary integral equation is transformed to the eigen equation with the stress singularity orders. By the use of the QR method to solve the eigen equation, the eigenvalues which are the singularity orders can be obtained: Hence, the use of very fine elements near the V-notch tip in the conventional boundary element method is unnecessary in the present new method. The multiple singularity orders of the V-notch can be obtained simultaneously in the present method. 5) A new way to determinate the singularity stress field near the V-notch tip by the boundary element method is established. Firstly, the V-notched structure is divided into two parts, a small sector around the V-notch tip and the other. Based on the computed multiple stress singularity orders and the corresponding eigen functions of the displacements and stresses, the displacements and stresses in the small sector are expressed as the linear combinations of the finite terms of the series expansion with all the singularity orders. Secondly, the boundary element method is used to model the V-notched structure removed the small sector, in which the boundary conditions along the arc edge from cutting the sector are expressed by the above linear combinations. Finally, the displacement and stress field at the V-notch tip and the multiple stress intensity factors are obtained through the boundary element analysis. This new method reflects the completely analytic character of the singular stress field near the V-notch tip. The accurate stress fields obtained by the present method are very useful in the analysis of the fatigue and fracture of the V-notched structures.