| Computational tools like finite element method (FEM) and boundary element method (BEM) have become integral part of engineering design. Bonded joints, inclusion in materials, fibers in epoxy of polymer composites, steel wire in tires, plastic encapsulation of micro circuits, medical implants, are among the growing list of the modern engineering applications requiring accurate stress analysis near material interface. BEM has proven to have very good resolution of stress gradients such as those that appear in front of cracks or in regions of stress concentrations. Successful application of BEM for fracture mechanics problem is primarily due to the fact that the stress singularity is in front of the crack, a region that is not discretized in BEM. The efforts to improve the accuracy of the analysis by refining the mesh have been going on since late seventies. The mesh refinements schemes in the literature do well for smooth density functions but have difficulties when density functions have singularities, particularly when the location and order of singularities are not known. However, problems such as lap joints contain strong gradients in the density function along the interface and the location of the maximum value cannot be prescribed during mesh construction. Inclusions with corners contain singularities in the density function at the corner that have to be accurately modelled to obtain accurate stresses. An adaptive hpr-mesh refinement method that can model the smooth as well singular nature of the density function while minimizing the degrees of freedom to achieve accuracy specified by the user is presented. The mesh refinement scheme is independent of BEM methodology and can be used for approximation of any mathematical function of one variable. Numerical results demonstrate the viability of the algorithm for smooth and singular density functions in Indirect and Direct BEM. The mesh refinement method was extended to interface boundaries. The mesh refinement scheme was validated using tests with known analytical stress solutions near interface boundaries. The method was also applied to BEM multiple material applications like inclusions with corners and adhesively bonded lap joints. |
