Abstract
This paper presents a novel approach for fracture analysis in two-dimensional orthotropic domain. The proposed method is based on consecutive-interpolation procedure (CIP) and enrichment functions. The CIP were recently introduced as an improvement for standard Finite Element method, such that higher-accurate and higher-continuous solution can be obtained without smoothing operation and without increasing the number of degrees of freedom. To avoid re-meshing, the enrichment functions are employed to mathematically describe the jump in displacement fields and the singularity of stress near crack tip. The accuracy of the method for analysis of cracked body made of orthotropic materials is studied. For that purpose, various examples with different geometries and boundary conditions are considered. The results of stress intensity factors, a key quantity in fracture analysis, are validated by comparing with analytical solutions and numerical solutions available in literatures.
Highlights
Thanks to its specific high strength and stiffness per unit weight, orthotropicManuscript Received on July 13th, 2016
Nguyen Ngoc Minh, Nguyen Thanh Nha, Truong Tich Thien are with Department of Engineering Mechanics, Faculty of Applied Sciences, Ho Chi Minh City University of Technology, VNU-HCM
Analytical investigation on fracture mechanics of orthotropic materials have been presented for some particular problems with relatively simple geometries and boundary conditions [1, 2, 3]
Summary
The enriched functions are proposed based on knowledge of closed form asymptotic fields at crack tip, see [4] for isotropic material and [5] for orthotropic materials. A general formulation to determine auxiliary functions for a wide range of finite elements from one to three dimensions has been recently proposed by [9], resolving the bottleneck. Given an element e with ne number of nodes, the auxiliary functions associated with the local ith node (i = 1, 2, 3,..., ne) is calculated by [13]. Once the sets Si, Sj, Sk, Sm are determined, the consecutive-interpolation shape functions can be calculated through (2).
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