Green's functions and boundary element methods for the analysis of bimaterials with imperfect interfaces
Chen, Ei Lene
Date of Issue2014
School of Mechanical and Aerospace Engineering
This thesis is concerned with the numerical solution of several important classes of boundary value problems involving bimaterials with imperfect interfaces. The use of imperfect interfaces in the analysis of layered materials is in line with the current research trends in engineering science. Problems in steady state axisymmetric heat conduction and plane elastostatics are considered in this thesis. The imperfect interfaces of the bimaterials in the axisymmetric heat conduction analysis are either low or high conducting. For the plane elastostatic analysis, the interfaces are assumed to be either soft or stiff. For both the axisymmetric heat conduction and plane elastostatic problems considered, special Green's functions are derived for cases where the imperfect interfaces are flat (planar). The Green's functions are chosen to satisfy the relevant imperfect interfacial conditions and employed to derive boundary integral equations that do not involve integrals over the imperfect interfaces. Boundary element procedures based on the boundary integral equations, which do not require the interfaces to be discretized into elements, are then proposed for solving numerically the boundary value problems for the bimaterials. An alternative boundary element approach based on hypersingular integral formulation of the imperfect interfacial conditions is also proposed for the numerical solution of axisymmetric heat conduction problems involving bimaterials with low and high conducting interfaces. Unlike the special Green's function boundary element approaches for flat interfaces, the hypersingular boundary integral method may be used to solve problems involving curved interfaces. Together with a corrective-predictor procedure, it is applied too to solve an axisymmetric heat conduction problem involving nonlinear interfacial conditions. The validity and the accuracy of all the boundary element approaches proposed in this thesis are examined by solving numerically specific test problems that have known analytical solutions. The numerical solutions are found to agree well with the analytical ones. For some problems that may be of practical interest, the effects of the interfacial parameters on the heat conduction or elastic deformation of bimaterials with imperfect interfaces are studied using the boundary element procedures. The results obtained appear to be intuitively and qualitatively acceptable.