A novel crack-tip singular element for extended finite element analysis
Xingxing Wang
Tianjin Key Laboratory of Integrated Design and On-line Monitoring for Light Industry & Food Machinery and Equipment, Tianjin, China
School of Mechanical Engineering, Tianjin University of Science and Technology, Tianjin, China
Search for more papers by this authorCorresponding Author
Xuecheng Ping
Tianjin Key Laboratory of Integrated Design and On-line Monitoring for Light Industry & Food Machinery and Equipment, Tianjin, China
School of Mechanical Engineering, Tianjin University of Science and Technology, Tianjin, China
Correspondence
Xuecheng Ping, Tianjin Key Laboratory of Integrated Design and On-line Monitoring for Light Industry and Food Machinery and Equipment, Tianjin 300222, China.
Email: [email protected]
Search for more papers by this authorCongman Wang
Tianjin Key Laboratory of Integrated Design and On-line Monitoring for Light Industry & Food Machinery and Equipment, Tianjin, China
School of Mechanical Engineering, Tianjin University of Science and Technology, Tianjin, China
Search for more papers by this authorHongxia Zheng
School of Transportation, Ludong University, Yantai, Shandong, China
Search for more papers by this authorXingxing Wang
Tianjin Key Laboratory of Integrated Design and On-line Monitoring for Light Industry & Food Machinery and Equipment, Tianjin, China
School of Mechanical Engineering, Tianjin University of Science and Technology, Tianjin, China
Search for more papers by this authorCorresponding Author
Xuecheng Ping
Tianjin Key Laboratory of Integrated Design and On-line Monitoring for Light Industry & Food Machinery and Equipment, Tianjin, China
School of Mechanical Engineering, Tianjin University of Science and Technology, Tianjin, China
Correspondence
Xuecheng Ping, Tianjin Key Laboratory of Integrated Design and On-line Monitoring for Light Industry and Food Machinery and Equipment, Tianjin 300222, China.
Email: [email protected]
Search for more papers by this authorCongman Wang
Tianjin Key Laboratory of Integrated Design and On-line Monitoring for Light Industry & Food Machinery and Equipment, Tianjin, China
School of Mechanical Engineering, Tianjin University of Science and Technology, Tianjin, China
Search for more papers by this authorHongxia Zheng
School of Transportation, Ludong University, Yantai, Shandong, China
Search for more papers by this authorAbstract
The traditional extended finite element method (XFEM) is suitable for simulating crack growth, but the crack-tip stress field analysis still depends on the enriched function. In this paper, based on the numerical eigensolution of the singular displacement and stress field together with the Hellinger–Reissner (H–R) variational principle, a novel crack-tip singular element is established to replace the enriched element in the crack-tip region in the traditional XFEM. The stress field inside the element adopts a series expression instead of only including the leading-order terms. The element only requires Gaussian integration at the element boundary and avoids mesh refinement in the crack-tip region. The element can be used to analyze cracks in anisotropic materials, interface cracks, and cracks terminating at the bimaterial interface. The numerical solutions of the singular stress field in various crack forms are presented through numerical examples, which proves the effectiveness and versatility of the novel crack-tip singular element.
Highlights
- An extended finite element method with a novel crack-tip singular element is proposed.
- The convergence speed of the present extended finite element method is satisfactory.
- The compatibility between the singular element and other elements is good.
- The singular element has the feature of multifunction.
Open Research
DATA AVAILABILITY STATEMENT
The data that support the findings of this study are available from the corresponding author upon reasonable request.
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