A numerical approach for a special crack problem. (English) Zbl 1372.65343

Junghanns, Peter; Kaiser, Robert

Dolomites Res. Notes Approx. 10, Spec. Iss., 56-67 (2017).

Summary: A collocation-quadrature method is proposed and studied for the numerical solution of a singular integral equation concerned with the two-dimensional elasticity problem of a crack at a circular cavity surface. These investigations are based on an \(C^\ast\)-algebra approach presented in a recent paper [P. Junghanns and R. Kaiser, in: Large truncated Toeplitz matrices, Toeplitz operators, and related topics. Basel: Birkhäuser/Springer. 413–462 (2017; Zbl 1364.65293)] on the numerical solution of an integral equation for the notched half-plane problem.

MSC:

65R20	Numerical methods for integral equations
74R10	Brittle fracture
35Q74	PDEs in connection with mechanics of deformable solids

Citations:

Zbl 1364.65293