Singular Integral Equations: Applications to Elasticity and Numerical Solution

Abstract: The purpose of this thesis is to develop stable, accurate, and efficient numerical algorithms for the solution of certain problems in materials science using integral equations. All the appearing integral equations are of the second kind. Such equations are typically well suited for numerical solution. The second kind equations are obtained from first kind equations through analytical regularizations. Several modifications and generalizations of earlier numerical schemes for the solution of the appearing equations are presented. The obtained integral equations and numerical schemes are applied to the solution of problems from, for instance, linear elastic fracture mechanics. Using an ordinary workstation, fairly complex setups can be simulated accurately. As a final application, quasi-static crack growth is simulated in a linearly elastic material. The growing crack is approximated by a piecewise smooth curve in such a way that the computed crack path converges quadratically to the true path.