scholarly journals Natural frequencies of cracked functionally graded material plates by the extended finite element method

2011 ◽  
Vol 93 (11) ◽  
pp. 3082-3092 ◽  
Author(s):  
S. Natarajan ◽  
P.M. Baiz ◽  
S. Bordas ◽  
T. Rabczuk ◽  
P. Kerfriden
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Functionally Graded Material ◽  
Extended Finite Element Method ◽  
Natural Frequencies ◽  
Functionally Graded ◽  
Extended Finite Element ◽  
Graded Material ◽  
Element Method

scholarly journals Extended finite -element method for modeling the mechanical behavior of functionally graded material plates with multiple random inclusions

2017 ◽  
Vol 20 (K3) ◽  
pp. 119-125
Author(s):  
Bang Kim Tran ◽  
Huy The Tran ◽  
Tinh Quoc Bui ◽  
Thien Tich Truong
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Level Set Method ◽  
Level Set ◽  
Functionally Graded Material ◽  
Extended Finite Element Method ◽  
Functionally Graded ◽  
Extended Finite Element ◽  
Graded Material ◽  
Element Method

Functionally graded material is of great importance in many engineering problems. Here the effect of multiple random inclusions in functionally graded material (FGM) is investigated in this paper. Since the geometry of entire model becomes complicated when many inclusions with different sizes appearing in the body, a methodology to model those inclusions without meshing the internal boundaries is proposed. The numerical method couples the level set method to the extended finite-element method (X-FEM). In the X-FEM, the finite-element approximation is enriched by additional functions through the notion of partition of unity. The level set method is used for representing the location of random inclusions. Numerical examples are presented to demonstrate the accuracy and potential of this technique. The obtained results are compared with available refered results and COMSOL, the finite element method software.

scholarly journals Extended finite element method for simulating the mechanical behavior of multiple random holes and inclusions in functionally graded material

2017 ◽  
Vol 20 (K2) ◽  
pp. 141-147
Author(s):  
Bang Kim Tran ◽  
Huy The Tran ◽  
Tinh Quoc Bui ◽  
Thien Tich Truong
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Mechanical Behavior ◽  
Functionally Graded Material ◽  
Extended Finite Element Method ◽  
Functionally Graded ◽  
The Finite Element Method ◽  
Extended Finite Element ◽  
Graded Material ◽  
Element Method

Analysis of mechanical behavior of a structure containing defects such as holes and inclusions is essential in many engineering applications. In many structures, the discontinuities may have a significant influence on the reduction of the structural stiffness. In this work, we consider the effect of multiple random holes and inclusions in functionally graded material (FGM) plate and apply the extended finite element method with enrichment functions to simulate the mechanical behavior of those discontinuous interfaces. The inclusions also have FGM properties. Numerical examples are considered and their obtained results are compared with the COMSOL, the finite element method software.

Fracture analysis of plastically graded material with thermo-mechanical J-integral

2021 ◽  
pp. 146442072199158
Author(s):  
Margi Gajjar ◽  
Himanshu Pathak
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Extended Finite Element Method ◽  
Isotropic Hardening ◽  
Fracture Parameter ◽  
J Integral ◽  
Extended Finite Element ◽  
Graded Material ◽  
Plastically Graded ◽  
Element Method

In this paper, the influence of plasticity graded property and thermal boundary conditions have been investigated on the fracture parameter, i.e. J-integral using the extended finite element method. A complete computational methodology has been presented to model elasto-plastic fracture problems with geometrical and material nonlinearities. For crack discontinuity modeling, a partition of unity enrichment concept was employed with additional mathematical functions like Heaviside and branch enrichment for crack discontinuity and stress field gradient, respectively. The modeling of the stress–strain relationship of the material is implemented using the Ramberg–Osgood material model and geometric nonlinearity is modeled using an updated Lagrangian approach. The isotropic hardening and von-Mises yield criteria are considered to check the plasticity condition. The elastic predictor–plastic corrector algorithm is employed to capture elasto-plastic stress in a cracked domain. The variation in plasticity properties for plastically graded material is modeled by exponential law. Furthermore, the nonlinear discrete equations are numerically solved using a Newton–Raphson iterative scheme. Various cracked problem geometries subjected to thermal (adiabatic and isothermal conditions) and thermo-mechanical loads are simulated for stress contours and J-integrals using the elasto-plastic fracture mechanics approach. A comparison of the results obtained using extended finite element method with literature and the finite element analysis (FEA) package shows the accuracy and effectiveness of the presented computational approach. A component-based problem, i.e. a Brazilian disc subjected to thermo-mechanical loading, has been solved to show the adaptability of this work.

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