PSI - Issue 52

Available online at www.sciencedirect.com ScienceDirect Structural Integrity Procedia 00 (2022) 000 – 000 Available online at www.sciencedirect.com ScienceDirect Structural Integrity Procedia 00 (2022) 000 – 000

www.elsevier.com/locate/procedia

www.elsevier.com/locate/procedia

ScienceDirect

Procedia Structural Integrity 52 (2024) 625–646

© 2023 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 Professor Ferri Aliabadi © 2023 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 Professor Ferri Aliabadi Keywords: Variation method, functionally graded materials, Chebyshev polynomials, finite block method, fracture mechanics, static and dynamic stress intensity factors, Laplace transform. Abstract For linear elastic fracture mechanics, the variational technique with a path independent contour integral is used to determine the stress intensity factors (SIFs) for functionally graded materials (FGMs) under static and dynamic loads in this work. Utilizing the interpolation of the Chebyshev polynomials and the finite block method (FBM) to deal with two-dimensional fracture problems. The Quadratic form block is transformed from Cartesian coordinates to normalized coordinates with 8 nodes by technology of mapping. The new equilibrium equations in terms of displacements are derived in a normalized coordinate system. All coefficients of the Chebyshev polynomials are determined by considering the governing equations, boundary conditions and connecting conditions of the two blocks. The accuracy and convergence of the FBM with Chebyshev polynomials are illustrated through several examples and comparison has been implemented with analytical solutions and different numerical approaches. © 2023 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 Professor Ferri Aliabadi Keywords: Variation method, functionally graded materials, Chebyshev polynomials, finite block method, fracture mechanics, static and dynamic stress intensity factors, Laplace transform. Fracture, Damage and Structural Health Monitoring Meshless variational method applied to Mixed-mode dynamic stress intensity factors J.C. Wen a , L. Ning a , C.G. Zhang b , P.H. Wen a,b, *, M.H. Aliabadi c a Institute of Aeronautics and Astronautics, Nanchang University, China b School of Engineering and Materials Science, Queen Mary, University of London, London, UK, E1 4NS c Department of Aeronautics, Imperial College London, London, UK, SW7 2AZ Abstract For linear elastic fracture mechanics, the variational technique with a path independent contour integral is used to determine the stress intensity factors (SIFs) for functionally graded materials (FGMs) under static and dynamic loads in this work. Utilizing the interpolation of the Chebyshev polynomials and the finite block method (FBM) to deal with two-dimensional fracture problems. The Quadratic form block is transformed from Cartesian coordinates to normalized coordinates with 8 nodes by technology of mapping. The new equilibrium equations in terms of displacements are derived in a normalized coordinate system. All coefficients of the Chebyshev polynomials are determined by considering the governing equations, boundary conditions and connecting conditions of the two blocks. The accuracy and convergence of the FBM with Chebyshev polynomials are illustrated through several examples and comparison has been implemented with analytical solutions and different numerical approaches. Fracture, Damage and Structural Health Monitoring Meshless variational method applied to Mixed-mode dynamic stress intensity factors J.C. Wen a , L. Ning a , C.G. Zhang b , P.H. Wen a,b, *, M.H. Aliabadi c a Institute of Aeronautics and Astronautics, Nanchang University, China b School of Engineering and Materials Science, Queen Mary, University of London, London, UK, E1 4NS c Department of Aeronautics, Imperial College London, London, UK, SW7 2AZ

* Corresponding author. Tel.: +86-18279139637; fax: +0-000-000-0000 . E-mail address: p.h.wen@ncu.edu.cn

2452-3216 © 2023 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 Professor Ferri Aliabadi 2452-3216 © 2023 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 Professor Ferri Aliabadi * Corresponding author. Tel.: +86-18279139637; fax: +0-000-000-0000 . E-mail address: p.h.wen@ncu.edu.cn

2452-3216 © 2023 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 Professor Ferri Aliabadi 10.1016/j.prostr.2023.12.064