Journal
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
Volume 85, Issue 3, Pages 269-288Publisher
WILEY
DOI: 10.1002/nme.2962
Keywords
strain gradient theory; couple stress theory; C0-1 patch test; finite element method
Funding
- National Natural Sciences Foundation of China [10672032]
- China Postdoctoral Science Foundation [20100470069]
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C0-1 patch test (Int. J. Numer. Meth. Engng 2004; 61: 433-454) proposed by Soh and Chen is a reliable method to ensure convergence of nonconforming finite element for the couple stress/strain gradient elasticity. The C0-1 patch test function is a complete quadratic polynomial that satisfies the equilibrium equations. To pass the C0-1 patch test, the element displacement functions used to calculate strains must satisfy C-0 continuity (or weak C-0 continuity) and quadratic completeness. In this paper, a 24-DOF (degrees of freedom) quadrilateral element (CQ12+RDKQ) for the couple stress/strain gradient elasticity is developed by combining the refined thin plate element RDKQ and the nonconforming element CQ12. The element RDKQ, which satisfies weak C-1 continuity, is used to calculate strain gradients, whereas strains are computed by the element CQ12, which is established based on an extended variational functional and satisfies weak C-0 continuity and quadratic completeness. Numerical examples show that the element (CQ12+RDKQ) passes the C0-1 patch test and it is also more efficient than the existing available triangular and quadrilateral elements in stress concentration problems with size effects. Copyright (C) 2010 John Wiley & Sons, Ltd.
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