Galerkin boundary element modeling of three-dimensional functionally graded material systems

Recent advances in material processing technology have enabled the design and manufacture of new functionally graded material systems that can withstand Very high temperature and large thermal gradient. Galerkin boundary element method is a powerful numerical method with good efficiency and accuracy which uses C0 elements for hypersingular integrals which are essential for solving fracture problem. Novel Galerkin boundary element method formulations for steady state and transient heat conduction, and fracture problems involving multiple interacting cracks in three-dimensional graded material systems are developed.; In the boundary element formulation, treatment of the singular and hypersingular integrals is one of the main challenges. A direct treatment of the hypersingular integral using a hybrid analytical/numerical approach is presented. Symmetric Galerkin formulation for exponentially graded material using the Green's function approach is developed. In the Green's function approach, each material variation requires different fundamental solution to be derived and consequently, new computer codes to be developed. In order to alleviate this constraint a "simple" Galerkin boundary element method is proposed where the nonhomogeneous problems can be transformed to known homogeneous problems for a class of variations (quadratic, exponential and trigonometric) of thermal conductivity. The material property can have a functional variation in one, two and three dimensions. Recycling existing codes for homogeneous media, the problems in nonhomogeneous media can be solved maintaining a pure boundary only formulation. This method can be used for any problem governed by potential theory. The transient heat conduction is carried out using a Laplace transform Galerkin formulation whereas the crack problem is formulated using the dual boundary element method approach. The implementations of all the techniques involved in this work are discussed and several numerical examples are presented to demonstrate the accuracy and efficiency of the methods.; Finally, new techniques of scientific visualization, which is an integral part of computational science research, are explored in the context of boundary element method. This investigation includes developing new modules for viewing the boundary and the domain data using modern visualization tools, developing virtual reality based visualization and concluding with web based interactive visualization.