A Closed-Form Analytical Solution for Crack Interaction in Orthotropic Plates with Multiple Holes under Combined Load

International Journal of Mechanical Engineering

© 2026 by SSRG - IJME Journal

Volume 13 Issue 1

Year of Publication : 2026

Authors : Lakshminarayana N P, Chandra Mohan Reddy B

10.14445/23488360/IJME-V13I1P101

How to Cite?

Lakshminarayana N P, Chandra Mohan Reddy B, "A Closed-Form Analytical Solution for Crack Interaction in Orthotropic Plates with Multiple Holes under Combined Load," SSRG International Journal of Mechanical Engineering, vol. 13,  no. 1, pp. 1-13, 2026. Crossref, https://doi.org/10.14445/23488360/IJME-V13I1P101

Abstract:

This work presents an analytical solution for the radial cracks emanating from three circular holes in an infinite orthotropic plate under in-plane combined biaxial and shear loading. A closed-form solution that takes into account the interaction effects between cracks is obtained by combining Schwarz's alternating method with the complex variable approach. MATLAB is used to assess the normalized Stress Intensity Factors (SIFs) at the crack tips under combined loading conditions. The impact of important factors on the normalized SIFs is methodically examined, including fiber orientation, crack angle, material orthotropy, crack length, and center-to-center hole spacing. The findings show that longer cracks have higher SIF ratios, with the inner crack tip experiencing greater intensity than the outer one, while an increase in hole spacing results in a decrease in the normalized SIF ratio, which approaches unity. The analytical results demonstrate good agreement with deviations of less than 6% when compared to ANSYS finite element simulations. The suggested analytical framework can be successfully applied to real-world fracture mechanics issues involving composite and orthotropic materials and offers a dependable and effective method for evaluating crack interaction effects in orthotropic plates.

Keywords:

Analytical method, Crack angle, Crack interaction, Orthotropic plate, Stress Intensity Factor (SIF).

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