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Open AccessArticle

Material-Oriented Shape Functions for FGM Plate Finite Element Formulation

Faculty of Civil Engineering, Warsaw University of Technology, 00-637 Warsaw, Poland
Author to whom correspondence should be addressed.
Materials 2020, 13(3), 803;
Received: 16 December 2019 / Revised: 27 January 2020 / Accepted: 6 February 2020 / Published: 10 February 2020
(This article belongs to the Special Issue Advances in Structural Mechanics Modeled with FEM)
A four-noded finite element of a moderately thick plate made of functionally graded material (FGM) is presented. The base element is rectangular and can be extended to any shape using a transformation based on NURBS functions. The proposed 2D shape functions are consistent with the physical interpretation and describe the states of element displacement caused by unit displacements of nodes. These functions depend on the FGM’s material parameters and are called material-oriented. The shape function matrix is based on a superposition displacement field of two plate strips with 1D exact shape functions. A characteristic feature of the proposed formulation is full coupling of the membrane and bending states in the plate. The analytical form of the stiffness matrix and the nodal load vector was obtained, which leads to the numerical efficiency of the formulation. The element has been incorporated into Abaqus software with the use of Maple program. The finite element shows good convergence properties for different FGM models in the transverse direction to the middle plane of the plate. During derivation of the 2D plate element the formally exact 1D finite element for transverse nonhomogeneous FGM plate strip was developed. View Full-Text
Keywords: finite element; FGM; plate; material-oriented shape functions; NURBS finite element; FGM; plate; material-oriented shape functions; NURBS
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Gilewski, W.; Pełczyński, J. Material-Oriented Shape Functions for FGM Plate Finite Element Formulation. Materials 2020, 13, 803.

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