Stress Analysis of Elastic Plates with Circular Holes

Stress analysis of elastic plates containing circular apertures has been a cornerstone of elasticity theory for more than a century. The presence of a hole introduces local stress amplification, characterised by a stress concentration factor that depends on hole size, plate geometry and loading conditions. Classical solutions, such as the Kirsch problem, employ the Airy stress function in polar coordinates to yield closed-form fields for an infinite plate under remote tension. In practical settings, finite plate dimensions and complex boundary conditions necessitate numerical approaches, most commonly finite element modelling, to capture three-dimensional effects and interactions between multiple cut-outs. Recent work has extended analytical techniques through conformal mapping and superposition of singular solutions, enabling efficient evaluation of plates with several holes. These advances underpin design in aerospace, mechanical and civil engineering, where weight reduction via perforations must be balanced against structural integrity. Contemporary research focuses on dynamic loads, multi-hole interactions and coupling between in-plane and out-of-plane responses, reflecting the global demand for optimised perforated structures in lightweight architectures, pressure vessels and offshore platforms.

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Stress Analysis of Elastic Plates with Circular Holes publication trend

The graph below shows the total number of articles in stress analysis of elastic plates with circular holes across all publications each year (not limited to Nature Index journals).

Technical terms

Stress concentration factor: Ratio of peak local stress near a discontinuity to nominal far-field stress.

Airy stress function: Scalar potential whose biharmonic equation solution yields planar stress fields in elasticity.

Finite element method (FEM): Numerical technique that discretises a continuous domain into elements to approximate stress and displacement fields.

Conformal mapping: Analytical transformation that maps complex geometries into simpler domains while preserving boundary conditions.

Superposition method: Analytical strategy that constructs complex solutions by summing simpler, singular stress fields to satisfy multiple boundary conditions.

References

1. Theoretical and simulation of central elliptical hole with rectangular plate. Journal of Emerging Science and Engineering (2024).
2. Three-Dimensional Stress Concentration Factor in Finite Width Plates with a Circular Hole. World Journal of Mechanics (2013).
3. Using Refined Theory to Studied Elastic Wave Scattering and Dynamic Stress Concentrations in Plates with Two Cutouts. Journal of Applied Mathematics and Physics (2020).
4. The stress state of a plate with several holes under the action of axial tensile load. E3S Web of Conferences (2024).