scholarly journals On the Finite Element Implementation of Functionally Graded Materials

Materials ◽  
2019 ◽  
Vol 12 (2) ◽  
pp. 287 ◽  
Author(s):  
Emilio Martínez-Pañeda
Keyword(s):  
Finite Element ◽  
Functionally Graded Materials ◽  
Functionally Graded ◽  
The Finite Element Method ◽  
Element Level ◽  
Graded Materials ◽  
Property Variation ◽  
User Subroutine ◽  
Finite Element Package ◽  
Fracture Assessment

We investigate the numerical implementation of functionally graded properties in the context of the finite element method. The macroscopic variation of elastic properties inherent to functionally graded materials (FGMs) is introduced at the element level by means of the two most commonly used schemes: (i) nodal based gradation, often via an auxiliary (non-physical) temperature-dependence, and (ii) Gauss integration point based gradation. These formulations are extensively compared by solving a number of paradigmatic boundary value problems for which analytical solutions can be obtained. The nature of the notable differences revealed by the results is investigated in detail. We provide a user subroutine for the finite element package ABAQUS to overcome the limitations of the most popular approach for implementing FGMs in commercial software. The use of reliable, element-based formulations to define the material property variation could be key in fracture assessment of FGMs and other non-homogeneous materials.

Parametric Formulation of the Finite-Volume Theory for Functionally Graded Materials—Part II: Numerical Results

2006 ◽  
Vol 74 (5) ◽  
pp. 946-957 ◽  
Author(s):  
Marcio A. A. Cavalcante ◽  
Severino P. C. Marques ◽  
Marek-Jerzy Pindera
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Volume ◽  
Functionally Graded Materials ◽  
Exact Analytical Solution ◽  
Functionally Graded ◽  
Structural Components ◽  
The Finite Element Method ◽  
Graded Materials ◽  
Element Method

In Part I of this communication, the finite-volume theory for functionally graded materials was further extended to enable efficient analysis of structural components with curved boundaries, as well as efficient modeling of continuous inclusions with arbitrarily-shaped cross sections of a graded material’s microstructure, previously approximated using discretizations by rectangular subcells. This was accomplished through a parametric formulation based on mapping of a reference square subcell onto a quadrilateral subcell resident in the actual microstructure. In Part II, the parametric formulation is verified through comparison with analytical solutions for homogeneous and graded curved structural components subjected to transient thermal and steady-state thermomechanical loading. Grading is modeled using piecewise uniform thermoelastic moduli assigned to each discretized region. Results for a heterogeneous microstructure in the form of a single inclusion embedded in the matrix phase of large dimensions are also generated and compared with the exact analytical solution, as well as with the results obtained using the standard version of the finite-volume theory based on rectangular discretization and the finite-element method. It is demonstrated that the parametric finite-volume theory is a very competitive alternative to the finite-element method based on the quality of results and execution time.

Model Development of the Application of Finite Element – Eigenvalue Method to the Determination of Transient Temperature Field in Functionally Graded Materials

2007 ◽  
Vol 18-19 ◽  
pp. 253-261
Author(s):  
John A. Akpobi ◽  
C.O. Edobor
Keyword(s):  
Finite Element ◽  
Temperature Field ◽  
Functionally Graded Materials ◽  
Model Development ◽  
Element Model ◽  
Steady State Solution ◽  
Functionally Graded ◽  
Transient Temperature ◽  
Graded Materials ◽  
Eigenvalue Method

In this paper, a finite elment-eigenvalue method is formulated to solve the finite element models of time dependent temperature field problems in non-homogeneous materials such as functionally graded materials (FGMs). The method formulates an eigenvalue problem from the original finite element model and proceeds to calculate the associated eigenvectors from which the solution can be obtained. The results obtained highly accurate and are exponential functions of time which when compared with the exact solution tended fast to the steady state solution.

scholarly journals Analysis of the Functionally Step-Variable Graded Plate Under In-Plane Compression

Materials ◽  
2019 ◽  
Vol 12 (24) ◽  
pp. 4090 ◽  
Author(s):  
Leszek Czechowski ◽  
Zbigniew Kołakowski
Keyword(s):  
Mechanical Properties ◽  
Finite Element Method ◽  
Finite Element ◽  
Functionally Graded ◽  
The Finite Element Method ◽  
Graded Materials ◽  
Number Of Layers ◽  
Critical Equilibrium ◽  
Post Buckling ◽  
Plane Compression

A study of the pre- and post-buckling state of square plates built from functionally graded materials (FGMs) and pure ceramics is presented. In contrast to the theoretical approach, the structure under consideration contains a finite number of layers with a step-variable change in mechanical properties across the thickness. An influence of ceramics content on a wall and a number of finite layers of the step-variable FGM on the buckling and post-critical state was scrutinized. The problem was solved using the finite element method and the asymptotic nonlinear Koiter’s theory. The investigations were conducted for several boundary conditions and material distributions to assess the behavior of the plate and to compare critical forces and post-critical equilibrium paths.

Contact Analysis of Functionally Graded Materials Using Smoothed Finite Element Methods

2019 ◽  
Vol 17 (05) ◽  
pp. 1940012 ◽  
Author(s):  
Y. F. Zhang ◽  
J. H. Yue ◽  
M. Li ◽  
R. P. Niu
Keyword(s):  
Finite Element ◽  
Functionally Graded Materials ◽  
Contact Point ◽  
Linear Complementarity Problems ◽  
Contact Problems ◽  
Contact Analysis ◽  
Functionally Graded ◽  
Numerical Results ◽  
Graded Materials ◽  
Stiffness Matrices

In the paper, the smoothed finite element method (S-FEM) based on linear triangular elements is used to solve 2D solid contact problems for functionally graded materials. Both conforming and nonconforming contacts algorithms are developed using modified Coulomb friction contact models including tangential strength and normal adhesion. Based on the smoothed Galerkin weak form, the system stiffness matrices are created using the formulation procedures of node-based S-FEM (NS-FEM) and edge-based S-FEM (ES-FEM), and the contact interface equations are discretized by contact point-pairs. Then these discretized system equations are converted into a form of linear complementarity problems (LCPs), which can be further solved efficiently using the Lemke method. The singular value decomposition method is used to deal with the singularity of the stiffness matrices in the procedure constructing the standard LCP, which can greatly improve the stability and accuracy of the numerical results. Numerical examples are presented to investigate the effects of the various parameters of functionally graded materials and comparisons have been made with reference solutions and the standard FEM. The numerical results demonstrate that the strain energy solutions of ES-FEM have higher convergence rate and accuracy compared with that of NS-FEM and FEM for functionally graded materials through the present contact analysis approach.

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