PSI - Issue 79

Available online at www.sciencedirect.com

ScienceDirect

Procedia Structural Integrity 79 (2026) 404–412

© 2025 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Abstract Bi-directional functionally graded materials (BDFGMs), where properties vary in both in-plane and thickness directions, are in creasingly used in aerospace components / structures to improve vibration performance through tailored sti ff ness and mass distri bution. However, cracks inevitably develop during in-service conditions and can significantly influence their vibration behavior, making their consideration essential in vibration analysis and design. To address this, an extended isogeometric analysis (XIGA) in conjunction with higher-order shear deformation theory (HDST) is employed for the first time to investigate the vibration behavior of BDFG plates containing the through-the-thickness crack. HSDT naturally captures the shear deformation e ff ect, whereas the NURBS basis functions of XIGA inherently satisfy the higher-order requirement of the HSDT plate kinematics. The materials are graded in two directions, and e ff ective properties are obtained using the rule of mixtures. The proposed method is first validated against benchmark solutions for FGM plates with property variation only in the thickness direction. Subsequently, a parametric study is conducted to analyze the e ff ects of crack length, orientation, boundary conditions, and material gradation on the natural frequencies and mode shapes. The results show excellent agreement with reference data and emphasize the critical role of both cracks and material gradation in the vibrational response. The developed HDST-XIGA framework o ff ers a reliable and accurate tool for the dynamic analysis of BDFGMs. 28th International Conference on Fracture and Structural Integrity - 3rd Mediterranean Conference on Fracture and Structural Integrity An HDST based XIGA Approach for Vibration Analysis of Cracked Bi-Directional Functionally Graded Plates Pranaw Parihar a , Sunil Kumar Singh a, ∗ a Department of Mechanical Engineering, Indian Institute of Technology Patna, Bihta, 801106, India

Peer-review under responsibility of IGF28 - MedFract3 organizers Keywords: HSDT; NURBS; XIGA; Vibration; Bi-directional FGM

1. Introduction

A functionally graded material (FGM) is a type of composite whose properties vary gradually in a specific direction, depending on design requirements. Similar to conventional fibrous composites, FGM o ff er a high strength-to-weight ratio; however, they also eliminate interlaminar stress. Owing to these advantages, FGM are widely used across various engineering disciplines.

∗ Corresponding author. Tel.: + 91-6115-233974 E-mail address: sunils@iitp.ac.in

2452-3216 © 2025 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of IGF28 - MedFract3 organizers 10.1016/j.prostr.2025.12.351