Contour integrals in nonlinear fracture mechanics for mixed forms of deformation

Nonlinear eigenvalue problems and contour integrals

Beyn’s algorithm for solving nonlinear eigenvalue problems is given a new interpretation and a variant is designed in which the required information is extracted via the canonical polyadic decomposition of a Hankel tensor. A numerical example shows that the choice of the filter function is very important, particularly with respect to where it is positioned in the complex plane.

Probabilistic Fracture Mechanics for Nonlinear Structures

A probabilistic methodology has been developed for fracture-mechanics analysis of nonlinear cracked structures. The methodology involves nonlinear ®nite element analysis using well-known commercial codes; statistical models for uncertainty in material constitutive law, fracture toughness, and loads; and standard reliability methods for evaluating probabilistic characteristics of elastic±plastic...

The mixed mode fracture mechanics in a hole plate bonded with two dissimilar plane

In the present research, the mixed-mode fracture mechanics analysis in a plate with central hole under tensile loading is considered. It is assumed that a plate containing two symmetrical hole-edge cracks is bonded with two dissimilar planes. The stress intensity factors at the crack tips are calculated. The problem is modeled in Casca software and this model is analyzed with Franc software. Th...

Computation of contour integrals

The Analysis of Contour Integrals

Recommended by Stephen L. Clark For any n, the contour integral y cosh x ∮ C cosh zs / sinh z − sinhx n 1 dz, s2 −λ, is associated with differential equation d2y x /dx2 λ n n 1 /coshx y x 0. Explicit solutions for n 1 are obtained. For n 1, eigenvalues, eigenfunctions, spectral function, and eigenfunction expansions are explored. This differential equation which does have solution in terms of t...