Displacement and Stress Analysis of an Elastic Hollow Disk: Comparison with Strength of Materials' Prediction

TL;DR

This study investigates the stress distribution in elastic hollow disks under diametric loading, comparing dynamic elasticity theory predictions with classical strength of materials, to improve understanding of material behavior and address shear stress issues.

Contribution

It introduces a dynamic elasticity approach to analyze stress in elastic disks with holes, extending classical methods and addressing shear stress problems near loading points.

Findings

Dynamic elasticity provides detailed stress distribution insights.

Hollow disks exhibit different stress patterns compared to solid disks.

The approach improves predictions over traditional strength of materials methods.

Abstract

This paper analyzes the stress distribution in a two-dimensional elastic disk under diametric loading, with a focus on enhancing the understanding of concrete and rock materials' mechanical behavior. The study revisits the Brazilian test and addresses its high shear stress issue near loading points by exploring the ring test, which introduces a central hole in the disk. Using dynamic elasticity theory, we derive stress distributions over time and extend the analysis to static conditions. This approach distinguishes between longitudinal and transverse wave effects, providing a detailed stress field analysis. By drawing parallels with curved beam theories, we demonstrate the applicability of dynamic elasticity theory to complex stress problems, offering improved insights into the stress behavior in elastic disks.