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In this study, elastic-plastic fracture mechanics analysis are carried out for two-dimensional (2D) solids using the wavelet Galerkin method (WGM) and the extended finite element method (X-FEM). In the proposed approach, severe stress concentration near crack tip is approximated by multilevel wavelet basis functions. In addition, discontinuous enrichment functions and tip enrichment functions of the X-FEM are introduced to represent crack geometry in the WGM. To discuss elastic-plastic stress field near crack tip, J-integral and HRR (Hutchinson-Rice-Rosengren) singular stress fields are evaluated. In numerical examples, elastic-plastic fracture mechanics analyses of 2D solids are analyzed to verify the proposed approach, and accuracy of the numerical results is critically examined. 1. 諸 言 Element Free Galerkin Method (EFGM) (Belytschko, et al., 1994) や Reproducing Kernel Particle Method (RKPM) (Liu, et al., 1995)などのメッシュフリー法,Partition of Unity (PU)条件 (Melenk and Babǔ ska, 1996)を満足するよう に近似関数を構成する Extended Finite Element Method (X-FEM) (Belytschko and Black, 1999),(Mo ës, et al., 1999) , SmoothedParticle Hydrodynamics (SPH) (Monaghan, 1988) や,Moving Particle Semi-implicit (MPS) 法 (Koshizuka and Oka, 1996) に代表される粒子法などの新しい数値解析手法の提案や確立,その工学的応用に関する研究が行わ れている.これらの数値解析手法では,従来の差分法や有限要素法では取り扱うことが困難な大変形問題や,構 造物中のき裂進展挙動などの物理現象を効率的に解析できると期待されており,精力的な研究が進んでいる.こ れらのメッシュフリー/粒子法の分類は,文献 (野口, 2004)に詳しい. 著者らのグループでは,これらの新しい数値解析手法の一つとして,ウェーブレットガラーキン法を用いた固 体/構造解析法に関する研究 (Tanaka, et al., 2012) を行っている.ウェーブレットガラーキン法では,ボクセル法 ウェーブレットガラーキン法を用いた弾塑性破壊力学解析に関する研究 上田 秀哉,田中 智行,山王丸 将吾,岡澤 重信,岡田 裕 Shuya UEDA, Satoyuki TANAKA, Shogo SANNOMARU, Shigenobu OKAZAWA and Hiroshi OKADA *1,*2 Graduate School of Engineering, Hiroshima University 1-4-1 Kagamiyama, Higashi-Hiroshima-shi, Hiroshima 739-8527, Japan *3 Department of Mechanical Engineering, Faculty of Science and Technology, Tokyo University of Science 2641 Yamazaki, Noda-shi, Chiba 278-8510, Japan Received 16 Feburary 2014

Elastic-plastic fracture mechanics analysis using wavelet Galerkin method