The Axially Symmetric Displacement Problem in the Transversely Isotropic Elasticity

TL;DR

This paper addresses the axially symmetric displacement problem in transversely isotropic elastic materials with hexagonal symmetry, reducing it to a system of Fredholm integral equations for bounded axially symmetric solids.

Contribution

It introduces a novel reduction of the displacement problem to integral equations specifically for transversely isotropic materials with hexagonal symmetry.

Findings

Reduction to Fredholm integral equations

Applicable to bounded axially symmetric solids

Provides a basis for solving displacement problems

Abstract

In the assumption of hexagonal symmetry of an elastic material the axially symmetric displacement problem in a bounded axially symmetric solid with a Lyapunov boundary is reduced to a system of regular (Fredholm) integral equations.