Stochastic Extended Finite Element Implementation for Natural Frequency of Cracked Functionally Gradient and Bi-Material Structures

2020 ◽  
pp. 2150044
Author(s):  
Ahmed Raza ◽  
Himanshu Pathak ◽  
Mohammad Talha
Keyword(s):  
Finite Element ◽  
Natural Frequency ◽  
Material Properties ◽  
Perturbation Technique ◽  
Vibration Characteristics ◽  
Functionally Graded ◽  
Extended Finite Element ◽  
Material Interface ◽  
Level Set Function ◽  
Graded Material

In this work, stochastic perturbation-based vibration characteristics of cracked bi-material and functionally graded material (FGM) domain with uncertain material properties are investigated using the extended finite element method. The level set function is implemented to track the geometrical discontinuities. The partition of unity-based extrinsic enrichment technique is employed to model the crack and material interface. The exponential law is used to model the graded material properties of FGM. The First-order perturbation technique (FOPT) is implemented to predict the standard deviation of natural frequency for the given uncertainties in the material properties. The numerical results are presented to show the effect of geometrical discontinuities and material randomness on vibration characteristics.

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.

Finite Element Analysis of Human Tibia Modeled as a Functionally Graded Material

2019 ◽  
Vol 2 (3) ◽  
Author(s):  
Ashish Tiwari ◽  
Pankaj Wahi ◽  
Niraj Sinha
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Stress Distribution ◽  
Functionally Graded Material ◽  
Material Properties ◽  
Functionally Graded ◽  
Element Analysis ◽  
Cross Sectional ◽  
Human Tibia ◽  
Graded Material

Human tibia, the second largest bone in human body, is made of complex biological material having inhomogeneity and anisotropy in such a manner that makes it a functionally graded material. While analyses of human tibia assuming it to be made of different material regions have been attempted in past, functionally graded nature of the bone in the mechanical analysis has not been considered. This study highlights the importance of functional grading of material properties in capturing the correct stress distribution from the finite element analysis (FEA) of human tibia under static loading. Isotropic and orthotropic material properties of different regions of human tibia have been graded functionally in three different manners and assigned to the tibia model. The nonfunctionally graded and functionally graded models of tibia have been compared with each other. It was observed that the model in which functional grading was not performed, uneven distribution and unrealistic spikes of stresses occurred at the interfaces of different material regions. On the contrary, the models with functional grading were free from this potential artifact. Hence, our analysis suggests that functional grading is essential for predicting the actual distribution of stresses in the entire bone, which is important for biomechanical analysis. We find that orthotropic nature of the bone tends to increase the maximum von Mises stress in the entire tibia, while inclusion of cross-sectional inhomogeneity typically increases the stresses across normal cross section. Accordingly, our analysis suggests that both orthotropy as well as cross-sectional inhomogeneity should be included to correctly capture the stress distribution in the bone.

scholarly journals Elastostatic Analysis of the Spatial FGM Structures

2015 ◽  
Vol 65 (1) ◽  
pp. 27-56 ◽  
Author(s):  
J. Murín ◽  
M. Aminbaghai ◽  
J. Hrabovský
Keyword(s):  
Finite Element ◽  
Material Properties ◽  
Stiffness Matrix ◽  
Displacement Vector ◽  
Longitudinal Direction ◽  
Functionally Graded ◽  
Beam Structures ◽  
The Real ◽  
Graded Material ◽  
Local Stiffness

Abstract In this contribution, results of elastostatic analysis of spatial composite beam structures are presented using our new beam finite element of double symmetric cross-section made of a Functionally Graded Material (FGM). Material properties of the real beams vary continuously in the longitudinal direction while variation with respect to the transversal and lateral directions is assumed to be symmetric in a continuous or discontinuous manner. Continuously longitudinal varying spatial Winkler elastic foundations (except the torsional foundation) and the effect of axial and shear forces are considered as well. Homogenization of spatially varying material properties to effective quantities with a longitudinal variation is done by the multilayer method (MLM). For the homogenized beam finite element the local stiffness matrix is established by means of the transfer matrix method. By the conventional finite element procedure, the global element stiffness matrix and the global system of equation for the beam structure are established for calculation of the global displacement vector. The secondary variables (internal forces and moments) are then calculated by means of the transfer relations on the real beams. Further, the mechanical stress in the real beams are calculated. Finally, the numerical experiments are carried out concerning the elastic-static analysis of the single FGM beams and beam structures in order to show the possibilities of our approach.

scholarly journals Free vibration characteristics of sectioned unidirectional/bidirectional functionally graded material cantilever beams based on finite element analysis

2020 ◽  
Vol 41 (12) ◽  
pp. 1787-1804
Author(s):  
N. V. Viet ◽  
W. Zaki ◽  
Quan Wang
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Free Vibration ◽  
Functionally Graded Material ◽  
Material Properties ◽  
Rapid Development ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Element Analysis ◽  
Graded Material

AbstractAdvancements in manufacturing technology, including the rapid development of additive manufacturing (AM), allow the fabrication of complex functionally graded material (FGM) sectioned beams. Portions of these beams may be made from different materials with possibly different gradients of material properties. The present work proposes models to investigate the free vibration of FGM sectioned beams based on one-dimensional (1D) finite element analysis. For this purpose, a sample beam is divided into discrete elements, and the total energy stored in each element during vibration is computed by considering either Timoshenko or Euler-Bernoulli beam theories. Then, Hamilton’s principle is used to derive the equations of motion for the beam. The effects of material properties and dimensions of FGM sections on the beam’s natural frequencies and their corresponding mode shapes are then investigated based on a dynamic Timoshenko model (TM). The presented model is validated by comparison with three-dimensional (3D) finite element simulations of the first three mode shapes of the beam.

Influence of Material Uncertainty on Vibration Characteristics of Higher-Order Cracked Functionally Gradient Plates Using XFEM

2021 ◽  
Vol 13 (05) ◽  
Author(s):  
Ahmed Raza ◽  
Mohammad Talha ◽  
Himanshu Pathak
Keyword(s):  
Perturbation Technique ◽  
Shear Deformation Theory ◽  
Partition Of Unity ◽  
Higher Order ◽  
Vibration Characteristics ◽  
Functionally Graded ◽  
Element Formulation ◽  
Power Law Distribution ◽  
Graded Materials ◽  
Level Set Function

In this study, the influence of material uncertainty on the vibration characteristics of the cracked functionally graded materials (FGM) plates is investigated. Extended stochastic finite element formulation is implemented to model the cracked FGM plate with material uncertainty using higher-order shear deformation theory (HSDT). The level set function is employed to track the crack in the FGM domain. The concept of partition of unity technique is implemented to enrich the primary variable with additional functions. The gradation of the material properties along the thickness direction is done using the power-law distribution. The first-order perturbation technique (FOPT) is incorporated in the methodology for stochastic vibration analysis. The convergence and validation study has been performed to verify the efficacy and accuracy of the formulation. Numerical results are obtained to show the effects of various influential parameters like crack length, gradient index, thickness ratio, and boundary condition on the covariance of the square of natural frequencies. The presented computational approach is accurate, efficient, and robust enough to investigate the vibration response of cracked FGM plates with material randomness.

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