Symmetric coupling of Galerkin boundary elements with finite elements

The boundary element method and the finite element method are the two most prominent techniques to solve problems in continuum mechanics. However, both of these methods have their advantages and disadvantages for specific category of problems. The Finite Element Method (FEM) is a well known and well used method to solve solid mechanics problems. FEM is well suited for finite domain problems, thin plates and shells, built up structures, domains in which material properties are inhomogeneous and domains where non-linear behavior occurs. Compared to this, the Boundary Element Method (BEM) is a fairly recent development that uses an integral approach to solving PDE problems. BEM is well-suited for infinite domains, reducing the dimensionality and simplifying the modelling considerably because of its boundary only approach. It is preferable to FEM for satisfying traction compatibility across laminar interfaces. It also requires very fine meshes in areas of high stress gradients which becomes more acute when constant remeshing is used to capture the stress singularities in problems like fracture mechanics or contact problems. However, FEM is very useful for non-linear structures and for irregularities. Thus, each method performs better than the other in some domains or some parts of the same domain. Therefore, a combined analysis approach which models high stress gradient regions with the BEM while using FEM for the rest of the structure would be both accurate and efficient.; Past efforts at integrating boundary elements and finite elements have been problematic and inefficient due to the unsymmetric nature of the boundary element technique used. Consequently, the usefulness of the combined approach is limited. The present thesis derives a formulation which symmetrically combines a Finite Element Approach (FEA) with a symmetric multi-zone Boundary Element Approach (BEA). The symmetric Galerkin approach has been extended for multi-zones, ultimately leading to a fully symmetric formulation. This multi-zone Galerkin Boundary Element formulation is then combined with a finite element based approach by transforming it to an equivalent finite element. This method has also been extended to a problem in fracture mechanics to capture the stress intensity factors.