Material-Oriented Shape Functions for FGM Plate Finite Element Formulation

Abstract

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.

The stress analysis effect on structural health monitoring in functionally graded shell

“…A numerical solution was applied to explore the free vibration of power distributed over length and thickness of the beam [16][17]. For nonlinear free flexural vibrations, eight-node rectangular elements were used [18]. The in-plane shear stress, direct stress, displacement and transverse stress of a simply supported rectangular shell are examined [19].…”

Structural Analysis of Functionally Graded Material Using Sigmioadal and Power Law

“…Other studies described the sigmoid-law in distribution of different material properties such as ceramic and metal through thickness of beam. Stiffness and buckling matrices were built by the finite element model and solved free vibration analysis numerically [16]. In addition, other researches investigate the dynamic response of functionally graded for axi-symmetric plate and cylinders under thermo-mechanical and finite element formulation under thermal load using theory of first order shear (FSDT) [17].…”

Special Issue: “Advances in Structural Mechanics Modeled with FEM”

“…Gilewski and Pełczyński developed a four-noded finite element for the analysis of thick plates made of (FG) materials [ 5 ]. A coordinate change based on NURBS functions was used to describe arbitrarily shaped domains.…”