scholarly journals Optimization of Functionally Graded Structural Members by Means of New Effective Properties Estimation Method

Materials ◽  
2019 ◽  
Vol 12 (19) ◽  
pp. 3139
Author(s):  
Anna Wiśniewska ◽  
Halina Egner
Keyword(s):  
Volume Fraction ◽  
Effective Properties ◽  
Estimation Method ◽  
Functionally Graded ◽  
Structural Members ◽  
Structural Element ◽  
Composite Configuration ◽  
Analytical Formulae ◽  
Circular Bar ◽  
Composite Properties

An innovative method of effective composite mechanical properties estimation is applied to optimize the distribution of reinforcement in a functionally graded structural element. The concept is based on the assumption of the mechanical equivalence between two configurations: The real heterogeneous composite configuration and the fictitious quasi-homogeneous one. It allows to obtain the analytical formulae describing the dependence of the effective elastic composite properties on the volume fraction of reinforcing inclusions. As an example of application, a circular bar subjected to torsion is considered.

scholarly journals Higher-Order Thermo-Elastic Analysis of FG-CNTRC Cylindrical Vessels Surrounded by a Pasternak Foundation

Nanomaterials ◽  
2019 ◽  
Vol 9 (1) ◽  
pp. 79 ◽  
Author(s):  
Masoud Mohammadi ◽  
Mohammad Arefi ◽  
Rossana Dimitri ◽  
Francesco Tornabene
Keyword(s):  
Deformation Theory ◽  
Volume Fraction ◽  
Effective Properties ◽  
Shear Deformation Theory ◽  
Pressure Vessels ◽  
Functionally Graded ◽  
Elastic Response ◽  
Governing Equations ◽  
Third Order ◽  
Reinforced Composite

This study analyses the two-dimensional thermo-elastic response of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) cylindrical pressure vessels, by applying the third-order shear deformation theory (TSDT). The effective properties of FG-CNTRC cylindrical pressure vessels are computed for different patterns of reinforcement, according to the rule of mixture. The governing equations of the problem are derived from the principle of virtual works and are solved as a classical eigenproblem under the assumption of clamped supported boundary conditions. A large parametric investigation aims at showing the influence of some meaningful parameters on the thermo-elastic response, such as the type of pattern, the volume fraction of CNTs, and the Pasternak coefficients related to the elastic foundation.

Designing Optimal Volume Fractions For Functionally Graded Materials With Temperature-Dependent Material Properties

2006 ◽  
Vol 74 (5) ◽  
pp. 861-874 ◽  
Author(s):  
Florin Bobaru
Keyword(s):  
Functionally Graded Materials ◽  
Material Properties ◽  
Volume Fraction ◽  
Effective Properties ◽  
Functionally Graded ◽  
Dominant Factor ◽  
Temperature Dependent ◽  
Graded Materials ◽  
Critical Stresses ◽  
Non Linear

We present a numerical approach for material optimization of metal-ceramic functionally graded materials (FGMs) with temperature-dependent material properties. We solve the non-linear heterogeneous thermoelasticity equations in 2D under plane strain conditions and consider examples in which the material composition varies along the radial direction of a hollow cylinder under thermomechanical loading. A space of shape-preserving splines is used to search for the optimal volume fraction function which minimizes stresses or minimizes mass under stress constraints. The control points (design variables) that define the volume fraction spline function are independent of the grid used in the numerical solution of the thermoelastic problem. We introduce new temperature-dependent objective functions and constraints. The rule of mixture and the modified Mori-Tanaka with the fuzzy inference scheme are used to compute effective properties for the material mixtures. The different micromechanics models lead to optimal solutions that are similar qualitatively. To compute the temperature-dependent critical stresses for the mixture, we use, for lack of experimental data, the rule-of-mixture. When a scalar stress measure is minimized, we obtain optimal volume fraction functions that feature multiple graded regions alternating with non-graded layers, or even non-monotonic profiles. The dominant factor for the existence of such local minimizers is the non-linear dependence of the critical stresses of the ceramic component on temperature. These results show that, in certain cases, using power-law type functions to represent the material gradation in FGMs is too restrictive.

TORSIONAL BUCKLING OF FUNCTIONALLY GRADED CYLINDRICAL SHELLS WITH TEMPERATURE-DEPENDENT PROPERTIES

2013 ◽  
Vol 14 (01) ◽  
pp. 1350048 ◽  
Author(s):  
JIABIN SUN ◽  
XINSHENG XU ◽  
C. W. LIM
Keyword(s):  
Boundary Conditions ◽  
Volume Fraction ◽  
Effective Properties ◽  
Thermal Environment ◽  
Cylindrical Shells ◽  
Accurate Solution ◽  
Functionally Graded ◽  
Torsional Buckling ◽  
Temperature Dependent Properties ◽  
Transverse Boundary

Based on Hamilton's principle, a new accurate solution methodology is developed to study the torsional bifurcation buckling of functionally graded cylindrical shells in a thermal environment. The effective properties of functionally graded materials (FGMs) are assumed to be functions of the ambient temperature as well as the thickness coordinate of the shell. By applying Donnell's shell theory, the lower-order Hamiltonian canonical equations are established, from which the eigenvalues and eigenvectors are solved as the critical loads and buckling modes of the shell of concern, respectively. The effects of various aspects, including the combined in-plane and transverse boundary conditions, dimensionless geometric parameters, FGM parameters and changing thermal surroundings, are discussed in detail. The results reveal that the in-plane axial edge supports do have a certain influence on the buckling loads. On the other hand, the transverse boundary conditions only affect extremely short shells. With increasing thermal loads, the material volume fraction has a different influence on the critical stresses. It is concluded that the optimized FGM mixtures to withstand thermal torsional buckling are Si 3 N 4/SUS304 and Al 2 O 3/SUS304 among the materials studied in this paper.

The Thermal Instability Analysis of Functionally Graded Carbon Nanotube Composite Plates Using Finite Element Method

2014 ◽  
Vol 695 ◽  
pp. 285-288 ◽  
Author(s):  
Z.A. Rasid ◽  
Hafizal Yahaya
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Carbon Nanotube ◽  
Critical Temperature ◽  
Thermal Instability ◽  
Volume Fraction ◽  
Effective Properties ◽  
Functionally Graded ◽  
Parametric Studies ◽  
Element Method

In recent years carbon nanotube (CNT) has been combined with polymers to take advantage of the extremely high strength and stiffness of the CNT. This paper reports a study on the thermal instability of carbon nanotube reinforced composites (CNTRC) plate subjected to uniform temperature rise. Finite element method (FEM) formulation was developed based on the first order shear deformation theory. The extended rule of mixture was used to determine the effective properties of the CNTRC plate. The CNTRC plate was functionally graded in its thickness direction. The results of the thermal instability were validated using past results and several parametric studies were then conducted using the developed formulation. The parametric studies showed that the critical temperature of the CNTRC was increased with the increase of the CNT volume fraction and the FG-4 configuration gave the highest critical temperature.

Vibration Reduction of Laminated Plates With Various Piezoelectric Functionally Graded Actuators

2008 ◽  
Author(s):  
Marek Pietrzakowski
Keyword(s):  
Numerical Simulations ◽  
Volume Fraction ◽  
Effective Properties ◽  
Plate Theory ◽  
Functionally Graded ◽  
Laminated Plates ◽  
Dynamic Responses ◽  
Electromechanical Properties ◽  
Classical Plate Theory ◽  
Fraction Distribution

The aim of the present study is to develop models of active laminated plates containing monolithic piezopolymer sensor layers and a new type of actuator layers made of Piezoelectric Functionally Graded (PFG) material, which is a mixture of piezoceramics and polymer or epoxy matrix. The electromechanical properties of the PFG layers can be tailored varying continuously the piezoceramic volume fraction across the thickness during the manufacturing process. The analysis and numerical simulations are focused on the relationship between the material compositional gradient and electromechanical properties and also dynamic responses of the structure obtained. Three types of functions, which describe the volume fraction distribution of constituents, are considered: exponential, parabolic and sigmoid. The effective properties of the PFG material, i.e. the Young’s modulus and piezoelectric coefficient gradations, are determined using to the rule of mixtures. A constant velocity feedback algorithm is used for the active damping of transverse plate vibration. The dynamic analysis concerns steady-state behavior of rectangular symmetrically laminated plates and is based on hypothesis of the classical plate theory. The numerical simulations are performed to recognize the influence of the applied pattern of the piezoceramic fraction distribution and its parameters on the gradient of elastic and piezoelectric properties within the PFG actuators and, as the final result, the active plate structural response presented in terms of amplitude-frequency characteristics. The changes in both the natural frequencies and resonant amplitudes are compared and the influence of the piezoceramic gradation on the control system operational effectiveness is also indicated and discussed.

scholarly journals Transient Analysis of a Functionally Graded Ceramic/Metal Layer considering Lord-Shulman Theory

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Antonios M. Nikolarakis ◽  
Efstathios E. Theotokoglou
Keyword(s):  
Finite Element ◽  
Volume Fraction ◽  
Effective Properties ◽  
Metal Layer ◽  
Time Integration ◽  
Maximum Tensile Stress ◽  
Functionally Graded ◽  
Sigmoid Function ◽  
The One ◽  
Functionally Graded Layer

The transient displacement, temperature, and stress fields in a functionally graded ceramic/metal layer under uniform thermal shock conditions at the upper surface are numerically studied based on the Lord-Shulman model, employing a direct finite element method. The Newmark method is employed for the time integration of the problem. A Matlab finite element code is developed for the numerical analysis of the one-dimensional problem under consideration. The Voigt model (rule of mixture) is used for the estimation of the effective properties inside the functionally graded layer and the variation of the volume fraction of the materials follows the sigmoid function in terms of the introduced parameter p. Furthermore, a parametric study with respect to the parameter p follows, where three different combinations of ceramic/metal materials are considered. It is concluded that the value p=1, which corresponds to a linear variation of the properties, minimizes the maximum (tensile) stress applied at the middle of the functionally graded layer.

scholarly journals Buckling and postbuckling of axially-loaded CNT-reinforced composite cylindrical shell surrounded by an elastic medium in thermal environment

2018 ◽  
Author(s):  
Hoang Van Tung
Keyword(s):  
Carbon Nanotubes ◽  
Elastic Medium ◽  
Volume Fraction ◽  
Effective Properties ◽  
Thermal Environment ◽  
Cylindrical Shells ◽  
Functionally Graded ◽  
Environment Temperature ◽  
Classical Shell Theory ◽  
Walled Carbon Nanotubes

Buckling and postbuckling behaviors of nanocomposite cylindrical shells reinforced by single walled carbon nanotubes (SWCNTs), surrounded by an elastic medium, exposed to a thermal environment and subjected to uniform axial compression are investigated in this paper. Material properties of carbon nanotubes (CNTs) and isotropic matrix are assumed to be temperature dependent, and effective properties of nanocomposite are estimated by extended rule of mixture. The CNTs are embedded into matrix via uniform distribution (UD) or functionally graded (FG) distribution along the thickness direction. Governing equations are based on Donnell’s classical shell theory taking into account von Karman-Donnell nonlinear terms and interaction between the shell and surrounding elastic medium. Three-term form of deflection and stress function are assumed to satisfy simply supported boundary conditions and Galerkin method is applied to obtain load-deflection relation from which buckling and postbuckling behaviors are analyzed. Numerical examples are carried out to analyze the effects of CNT volume fraction and distribution types, geometrical ratios, environment temperature and surrounding elastic foundation on the buckling loads and postbuckling strength of CNTRC cylindrical shells.

The Effective Properties of Composite Materials With Constant Reinforcement Density by the Linear Mori-Tanaka Method

1994 ◽  
Vol 116 (3) ◽  
pp. 428-437 ◽  
Author(s):  
J. R. Zuiker ◽  
G. J. Dvorak
Keyword(s):  
Composite Materials ◽  
Volume Fraction ◽  
Effective Properties ◽  
Functionally Graded ◽  
Local Fields ◽  
Original Form ◽  
Constant Field ◽  
Inhomogeneous Materials ◽  
Reinforcement Density ◽  
Variable Reinforcement

In its original form, the Mori-Tanaka method estimates constant overall properties of statistically homogeneous composite materials subjected to uniform overall stresses, strain or temperature changes, from averages of local fields in the phases. To permit applications involving large overall stress and/or temperature gradients, and functionally graded materials with a variable reinforcement density, the method has been extended to linearly variable overall and local fields by Zuiker and Dvorak (Composites Engineering, Vol. 4, 19–35, 1994) as a first step toward application of the method to statistically inhomogeneous materials with variable reinforcement density. Here, the effective properties are examined in detail. Non-zero components of the stiffness matrix are shown to satisfy invariance requirements and to vary with reinforcement volume fraction and size of the representative volume. It is shown that the linear and constant field approaches provide different estimates of overall properties for small representative volumes, but nearly identical estimates for large volumes.

scholarly journals An Intrinsic Material Tailoring Approach for Functionally Graded Axisymmetric Hollow Bodies Under Plane Elasticity

2021 ◽  
Author(s):  
Hassan Mohamed Abdelalim Abdalla ◽  
Daniele Casagrande
Keyword(s):  
Optimization Problem ◽  
Volume Fraction ◽  
Minimum Principle ◽  
Equivalent Stress ◽  
Micromechanical Model ◽  
Plane Elasticity ◽  
Functionally Graded ◽  
Pontryagin Minimum Principle ◽  
Volume Fractions ◽  
Material Tailoring

AbstractOne of the main requirements in the design of structures made of functionally graded materials is their best response when used in an actual environment. This optimum behaviour may be achieved by searching for the optimal variation of the mechanical and physical properties along which the material compositionally grades. In the works available in the literature, the solution of such an optimization problem usually is obtained by searching for the values of the so called heterogeneity factors (characterizing the expression of the property variations) such that an objective function is minimized. Results, however, do not necessarily guarantee realistic structures and may give rise to unfeasible volume fractions if mapped into a micromechanical model. This paper is motivated by the confidence that a more intrinsic optimization problem should a priori consist in the search for the constituents’ volume fractions rather than tuning parameters for prefixed classes of property variations. Obtaining a solution for such a class of problem requires tools borrowed from dynamic optimization theory. More precisely, herein the so-called Pontryagin Minimum Principle is used, which leads to unexpected results in terms of the derivative of constituents’ volume fractions, regardless of the involved micromechanical model. In particular, along this line of investigation, the optimization problem for axisymmetric bodies subject to internal pressure and for which plane elasticity holds is formulated and analytically solved. The material is assumed to be functionally graded in the radial direction and the goal is to find the gradation that minimizes the maximum equivalent stress. A numerical example on internally pressurized functionally graded cylinders is also performed. The corresponding solution is found to perform better than volume fraction profiles commonly employed in the literature.

Flexural behavior of functionally graded polymeric composite beams

2021 ◽  
pp. 152808372110003
Author(s):  
M Atta ◽  
A Abu-Sinna ◽  
S Mousa ◽  
HEM Sallam ◽  
AA Abd-Elhady
Keyword(s):  
Flexural Strength ◽  
Volume Fraction ◽  
Stress Gradient ◽  
Polymeric Composite ◽  
Composite Beams ◽  
Functionally Graded ◽  
Flexural Behavior ◽  
Bending Test ◽  
Polymeric Composite Material ◽  
Fiber Volume

The bending test is one of the most important tests that demonstrates the advantages of functional gradient (FGM) materials, thanks to the stress gradient across the specimen depth. In this research, the flexural response of functionally graded polymeric composite material (FGM) is investigated both experimentally and numerically. Fabricated by a hand lay-up manufacturing technique, the unidirectional glass fiber reinforced epoxy composite composed of ten layers is used in the present investigation. A 3-D finite element simulation is used to predict the flexural strength based on Hashin’s failure criterion. To produce ten layers of FGM beams with different patterns, the fiber volume fraction ( Vf%) ranges from 10% to 50%. A comparison between FGM beams and conventional composite beams having the same average Vf% is made. The experimental results show that the failure of the FGM beams under three points bending loading (3PB) test is initiated from the tensioned layers, and spread to the upper layer. The spreading is followed by delamination accompanied by shear failures. Finally, the FGM beams fail due to crushing in the compression zone. Furthermore, the delamination failure between the layers has a major effect on the rapidity of the final failure of the FGM beams. The present numerical results show that the gradient pattern of FGM beams is a critical parameter for improving their flexural behavior. Otherwise, Vf% of the outer layers of the FGM beams, i.e. Vf% = 30, 40, or 50%, is responsible for improving their flexural strength.

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