Development of High-Order Infinite Element Method for Stress Analysis of Elastic Bodies with Singularities

• Published in: Journal of Solid Mechanics and Materials Engineering Vol. 4; no. 8; pp. 1131 - 1146
• Main Authors: CHENG, Kuo-Liang, LIU, De-Shin, ZHUANG, Zhen-Wei
• Format: Journal Article
• Language: English
• Published: The Japan Society of Mechanical Engineers 2010
• Subjects: Convergence; Discontinuity; Finite Element Method; Formulations; Infinite Element Method; Materials engineering; Mathematical analysis; Mathematical models; Singularities; Stress Intensity Factor; Stress Singularity
• ISSN: 1880-9871; 1880-9871
• DOI: 10.1299/jmmp.4.1131

Structural analysis problems are traditionally solved using the Finite Element Method (FEM). However, when the structure of interest contains discontinuities such as cracks or re-entrant corners, a large number of elements are required to accurately reproduce the stress characteristics in the region of the discontinuities. As a result, the FEM method requires a large storage space and has a slow convergence speed. It has been shown that the Infinite Element Method (IEM) overcomes these limitations and provides a feasible means of solving various types of elasticity and singularity problems. Previous studies have generally focused on the use of IEM formulations based on low-order elements (2×2). By contrast, this study develops a high-order (3×3) IEM formulation. The solutions obtained using the proposed IEM method for various 2D elasto-static problems are compared with the results obtained using the traditional low-order IEM method and the analytical solutions presented in the literature. It is shown that the results obtained using the proposed method are more accurate than those obtained using the low-order IEM method and are in excellent agreement with the analytical solutions.