tailieunhanh - About the edge - based smoothed finite element method for the reissner - mindlin plate - bending problem
The paper further develops the edge-based smoothed finite element method (ES-FEM) for analysis of Reissner - Mindlin plates using triangular meshes. The bending and shearing stiffness matrices are obtained using strain smoothing technique over the smoothing domains associated with edges of elements. | Vietnam Journal of Mechanics, VAST, Vol. 31, No. 2 (2009) , pp. 75-86 ABOUT THE EDGE-BASED SMOOTHED FINITE ELEMENT METHOD FOR THE REISSNER-MINDLIN PLATE-BENDING PROBLEM Nguyen Xuan Hung 1 '2 , Nguyen Thoi. Trung 1 '3 1 Department of Mechanics, Faculty of Mathematics and Computer Science, University of Science- VNU-HCM, Vietnam 2 Singapore-MIT Alliance (SMA), E4-04 -10, 4 Engineering Drive 3, Singapore 3 Center for Advanced Computations in Engineering Science (ACES), Department of Mechanical Engineering, NatiOnal University of Singapore, 9 Engineering Drive 1, Singapore Abstract. The paper further develops the edge-based smoothed finite element method (ES-FEM) for analysis of Reissner - Mindlin plates using triangular meshes . The bending and shearing stiffness matrices are obtained using strain smoothing technique over the smoothing domains associated with edges of elements. Transverse shear locking can be avoided with help of the discrete shear gap (DSG) method. The numerical examples show that the present ES-FEM-DSG method obtains y accurate results compared to the exact solution and other existing elements. 1. INTRODUCTION In the practical applications, lower-order plate finite elements are the most preferred due to its simplicity and efficiency. However, using the Reissner-Mindlin plate theory, these elements often suffer from one intrinsic difficulty: shear locking phenomenon in the limitation of thin plates. In order to eliminate shear locking, early methods tried to avoid shear locking by using reduced integration or a selective reduced integration [1]. For example, based on a four node quadrilateral element, a single Gauss point is utilized to compute shear strain energy while a 2x2 Gauss point scheme is used for the bending energy. Unfortunately, reduced integration often causes the instability due to rank deficiency of and results in zero-energy modes [1]. Various improvements of formulations as well as numerical techniques have been developed .
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