Abstract

In recent years, Isogeometric Analysis (IGA) [1] has been proposed as an alternative method to the Finite Element Method (FEM). IGA performs analysis using Non-Uniform Rational B-Splines (NURBS), which are the same basis functions widely used in CAD for designing. IGA is expected to perform analysis more accurately than the FEM does, as it can represent exactly the shape of objects and have the basis functions with higher order continuity.

The S-version Isogeometric Analysis (S-IGA) proposed by the authors [2] is a multiscale analysis method that uses global patches to represent the entire structure and local patches to reproduce localized deformation. The idea of S-IGA is analogous to the s-version Finite Element Analysis (s-FEM) in FEM [3]. S-IGA is expected to be a useful analytical tool in the field of fracture mechanics because the crack can the represented by the local patch only. It is much more tractable to model the crack by the local patch than to do by the IGA model with multi-patch approach.

One of the objectives in linear elastic fracture mechanics analysis is to compute the Stress Intensity Factors (SIFs). Hence, we have focused on investigating the SIFs. To capture the stress singularity in the vicinity of crack tip, the singular patch method [4] was adopted. A plate subject to remote uniform tension with an inclined crack (see Yuuki [5]) was analyzed by S-IGA. The inclination angle was 0, 30 or 45 degrees. The interaction integral method was applied to compute the mixed mode SIFs. It was found that the result of the present S-IGA analysis compared well with the reference solutions. More detailed discussions will be presented in the presentation at ICCM 2023.

Keywords: Isogeometric Analysis (IGA), S-version Isogeometric Analysis (S-IGA), Stress Intensity factor, linear elastic fracture mechanics, Singular Patch Method

Acknowledgement: This work has partly been supported by JSPS KAKENHI Grant Number 22K03879.

References

[1]    Cottrell, J. A., Hughes, T. J. R. and Bazilevs, Y. (2009) Isogeometric Analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement, Computer Methods in Applied Mechanics and Engineering 194, 4135-4195.

[2]    Tsuchiyama, Y., Sunaoka, Y., Okada, H., Otoguro, Y., Machino, T. and Nakahara, N., Optimizing the orders of basis functions for S-version Isogeometric Analysis, The Proceedings of The Computational Mechanics Conference, Japan, 2022.

[3]    Fish, J., (1992) The s-version of the finite element method, Computers and Structures 43, 539–547.

[4]    Okada, H., Nakahara, D., Nagashima, A., Watanabe, R., Sunaoka, Y. Yusa, Y. and Otoguro, Y. (2022) Singular patch method for linear elastic fracture mechanics analysis using isogeometric analysis, Mechanical Engineering Journal 9-6, 22-00291.

[5]    Kitagawa, H. and Yuuki, R. (1977) Analysis of Arbitrarily Shaped Crack in a Finite Plate Using Conformal Mapping, Transactions of the Japan Society of Mechanical Engineers 43, 4354-4362.