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This and the next image are from:
Chien H. Thai (1,2), A.J.M. Ferreira (3), M. Abdel Wahab (4,5) and H. Nguyen-Yuan (6,7)
(1) Division of Computational Mechanics, Ton Duc Thang University, Ho Chi Minh City, VietNam
(2) Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City, VietNam
(3) Departamento de Engenharia Mecanica, Faculdade de Engenharia, Universidade do Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal
(4) Institute of Research and Development, Duy Tan University, 03 Quang Trung, Da Nang, Viet Nam
(5) Soete Laboratory, Faculty of Engineering and Architecture, Ghent University, 9000, Ghent, Belgium
(6) Center for Interdisciplinary Research in Technology, Hutech University, Ho Chi Minh City, Viet Nam
(7) Department of Architectural Engineering, Sejong University, 209 Neungdong-ro, Gwangjin-gu,
Seoul 05006, Republic of Korea
“A moving Kriging meshfree method with naturally stabilized nodal integration for analysis of functionally graded material sandwich plates”, Acta Mechanica, March 2018, DOI: 10.1007/s00707-018-2156-9
ABSTRACT: This paper presents a moving Kriging meshfree method based on a naturally stabilized nodal integration (NSNI) for bending, free vibration and buckling analyses of isotropic and sandwich functionally graded (FG) plates within the framework of higher order shear deformation theories. A key feature of present formulation is to develop a NSNI technique for the moving Kriging meshfree method. Using this scheme, the strains are directly evaluated at the same nodes as the direct nodal integration (DNI). Importantly, the computational approach alleviates instability solutions in the DNI and decreases significantly computational cost from using the traditional high-order Gauss quadrature. Being different from the stabilized conforming nodal integration (SCNI) scheme which uses the divergence theorem to evaluate the strains by boundary integrations, the NSNI adopts a naturally implicit gradient expansion. The NSNI is then integrated into the Galerkin weak form for deriving the discrete system equations. Due to satisfying Kronecker delta function property of moving Kriging integration (MKI) shape function, the enforcement of essential boundary conditions in the present method is similar to the finite element method. Through numerical examples, the effects of geometries, stiffness ratios, volume fraction and boundary conditions are studied to prove the efficiency of the present approach.
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