Finite Element Implementation of the Uncoupled Theory of Functionally Graded Plates

This study starts with defining generalized displacements. Together with the assumptions and shear-stress-free conditions, the in-plane displacements of a functionally graded (FG) plate are first mathematically assumed, and then orthogonally decomposed into three terms with the aid of a neutral surf...

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Bibliographic Details
Published in:AIAA journal 2020-02, Vol.58 (2), p.918-928
Main Authors: Pei, Y. L, Geng, P. S, Li, L. X
Format: Article
Language:English
Subjects:
Bending
Constitutive relationships
Couplings
Displacement
Functionally gradient materials
Mathematical analysis
Shear forces
Stresses
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Summary:This study starts with defining generalized displacements. Together with the assumptions and shear-stress-free conditions, the in-plane displacements of a functionally graded (FG) plate are first mathematically assumed, and then orthogonally decomposed into three terms with the aid of a neutral surface. The generalized stresses are accordingly defined, and the constitutive relations are derived for an FG plate after the generalized strains are measured. The principles of virtual work (PVW) are eventually expressed for FG plate problems. Compared with the previous work in this field, due to the use of frame-indifferent generalized displacements, the in-plane displacements are physically interpreted as tension part, bending part, and high-order bending part. Because of the use of frame-indifferent generalized stresses and generalized strains, mutual couplings of tension, bending, and higher-order bending are removed in the constitutive relations. More important, the lower-order theory of an FG plate is mathematically correlated with the higher-order theory from the viewpoint of PVW. With these fundamentals, finite element formulations are derived and two kinds of plate elements are constructed. Typical examples show that the elements can yield satisfactory deflection and rotation, whereas the high-order element can also capture the boundary effect of shear force at the clamped edge.
ISSN:0001-1452
1533-385X
DOI:10.2514/1.J058413