Nonstationary torsion problems for the finite cylinder partly coupled with rigid base

Abstract

The axisymmetric dynamic problems of determining the stress state in the vicinity of the delamination in a finite cylinder partly coupled with the rigid base were solved. In contrast to the traditional solution methods based on the use of the integral Laplace transform, the proposed method consists in the difference approximation only of the time derivative. As a result, the original problem is replaced by a sequence of homogeneous boundary value problems for the Helmholtz equation that reduce to the Fredholm integral equation of the second kind. The numerical solution found made it possible to obtain an approximate formula for calculating the stress intensity factor.

Modelling and investigation of the stress state in a finite cylinder with a circular crack under sudden torsional loading

“…Consequently, for these borderline cases, it is necessary to solve individual problems. They are given in [25].…”

“…Until now, such a problem has been considered for the harmonic moment [18]. The authors of this paper also solved problems with a similar statement for a cylinder with a ring-shaped crack [24] and a cylinder with different types of delamination [25].…”

“…The solution to this boundary value problem is constructed by the integral transform method, analogous to papers [24,25] and it has the form:…”

“…where Next, equation ( 12) was reduced to the Fredholm equation of the second kind in accordance with the known method used in [25].…”

“…Equation ( 13) contains unknown A ν , equation ( 8) should be used to determine it. An approximate solution to equation (13), as in [24,25], is sought in the form of an interpolation polynomial.…”