An edge-based smoothed finite element for buckling analysis of functionally graded material variable-thickness plates

Tran Trung Thanh, Tran Van Ke, Pham Quoc Hoa, Tran The Van, Nguyen Thoi Trung
Author affiliations


  • Tran Trung Thanh Le Quy Don Technical University, Hanoi, Vietnam
  • Tran Van Ke Le Quy Don Technical University, Hanoi, Vietnam
  • Pham Quoc Hoa Tran Dai Nghia University, Ho Chi Minh City, Vietnam
  • Tran The Van Tran Dai Nghia University, Ho Chi Minh City, Vietnam
  • Nguyen Thoi Trung Ton Duc Thang University, Ho Chi Minh City, Vietnam



buckling analysis, critical load, variable thickness plate, edge-based finite element method, ES-MITC3


The paper aims to extend the ES-MITC3 element, which is an integration of the edge-based smoothed finite element method (ES-FEM) with the mixed interpolation of tensorial components technique for the three-node triangular element (MITC3 element), for the buckling analysis of the FGM variable-thickness plates subjected to mechanical loads. The proposed ES-MITC3 element is performed to eliminate the shear locking phenomenon and to enhance the accuracy of the existing MITC3 element. In the ES-MITC3 element, the stiffness matrices are obtained by using the strain smoothing technique over the smoothing domains formed by two adjacent MITC3 triangular elements sharing the same edge. The numerical results demonstrated that the proposed method is reliable and more accurate than some other published solutions in the literature. The influences of some geometric parameters, material properties on the stability of FGM variable-thickness plates are examined in detail.


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