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The purpose of this paper is to develop a new multi-objective optimization procedure for crashworthiness optimization of thin-walled structures especially circular tubes with functionally graded thickness.

The proposed optimization approach is based on finite element analyses for construction of sample design space and verification; gene-expression programming (GEP) for generating algebraic equations (meta-models) to compute objective functions values (peak crash force and specific energy absorption) for design parameters; multi-objective genetic algorithms for generating design parameters alternatives and determining optimal combination of them. The authors have also utilized linear and non-linear least square regression meta-models as a benchmark for GEP.

It is shown that the proposed approach is able to generate Pareto optimal designs which are in a very good agreement with the actual results.

The paper presents the application of a genetic programming-based method, namely, GEP first time in the literature. The proposed approach can be used to all kinds of related crashworthiness problems.

The purpose of this paper is to investigate the characterizations of high energy thick-walled functionally graded (FG) cylinder containing Al-26%Cu fabricated by horizontal centrifugal casting technique.

Field emission scanning electron microscopy in conjunction with image analyser software and energy dispersion spectroscopy is applied to measure the variations of constituent phase’s content and elemental ratios along the radial direction, respectively. Distributions of the FG properties are measured through hardness, CTE, E and σ_y along the radial direction to investigate the mechanical and physical properties corresponding to the variations in microstructure. In addition, the variations of wear rate along the thickness are evaluated through a series of dry sliding wear tests using the pin-on-disk wear machine. Moreover, scanning electron microscopy is employed to characterize the worn-out surfaces and morphology of wear debris in order to clarify the dominant operative wear mechanism.

Results showed that Al₂Cu content gradually decreases from the inner wall containing 33.3 vol.% to outer wall containing 26.4 vol.% in the FG cylindrical shell. The elastic modulus and yield strength measured through compression tests reveal that these mechanical properties are limited up to certain value of Al₂Cu. The obtained optimum value of Al₂Cu content for studied Al-Al₂Cu FG is almost 31 vol.%.

The obtained optimum value of Al₂Cu content for studied Al-Al₂Cu FG was almost 31 vol.%.

This paper aims to study the energy absorption properties of the thin-walled square tube with lateral piecewise variable thickness under axial crashing and the influence of the tube parameters on energy absorption.

In this work, the energy absorption properties of the thin-walled square tube were analyzed by theoretical, numerical and experimental approach. The numerical results are obtained based on the finite element method. The explicit formulation for predicting the mean crushing force of the tube with lateral piecewise variable thickness was derived based on Super Folding Element method. The limitation of the prediction formulation was analyzed by numerical calculation. The numerical calculation was also used to compare the energy absorption between the tube with lateral piecewise variable thickness and other tubes, and to carry out the parametric analysis.

Results indicate that the thin-walled tube with lateral piecewise variable thickness has higher energy absorption properties than the uniform thickness tubes and the tubes with lateral linear variable thickness. The thickness of the corner is the key factor for the energy absorption of the tubes. The thickness of the non-corner region is the secondary factor. Increasing the corner thickness and decreasing the non-corner thickness can make the energy absorption improved. It is also found that the prediction formulation of the mean crushing force given in this paper can quickly and accurately predict the energy absorption of the square tube.

The outcome of the present research provides a design idea to improve the energy absorption of thin-walled tube by designing cross-section thickness and gives an explicit formulation for predicting the mean crushing force quickly and accurately.

The purpose of this paper is to investigate creep in an internally pressurized thick-walled, closed ends cylinder made of functionally graded composite, having linear and non-linear distribution of reinforcement, using finite element (FE) analysis.

FE-based Abaqus software is used to investigate creep behavior of a functionally graded cylinder. The cylinder is made of composite containing linear and non-linearly varying distributions of reinforcement along the radius. The creep behavior has been described by Norton's power law. The creep stresses and strains have been estimated in linear and non-linear functionally graded materials (FGM) cylinders and compared with those estimated for a similar composite cylinder but having uniform distribution of reinforcement.

The radial stress in the composite cylinder is observed to decreases over the entire radius upon imposing linear or non-linear reinforcement gradients. However, the tangential stress in the cylinder increases near the inner radius but decreases toward the outer radius, on imposing linear or non-linear reinforcement gradients. The creep strains in the FGM cylinders are significantly lower than those observed in a uniform composite cylinder.

The creep strains in an internally pressurized functionally graded thick composite cylinder could be reduced significantly by employing non-linear distribution of reinforcement along the radial direction.

This paper seeks to obtain the dynamic behavior of cylinders made of functionally graded materials (FGMs). The cylinder should be analyzed subjected to dynamic and shock loads.

The functionally graded cylinder is assumed to be made of many subcylinders. The material properties within a subcylinder are assumed to vary linearly in the thickness direction. The material properties in subcylinders are chosen as linear functions. The properties are controlled by volume fraction that is an exponential function of radius. The shell is assumed to be in plane strain condition, and is subjected to axisymmetric dynamic loading. The Navier Equation is solved by Galerkin finite element and Newmark methods. By using the Fast Fourier Transform, the time response is transferred to frequency domain and natural frequencies are illustrated.

The dynamic behavior of functionally graded thick hollow cylinder is discussed. The radial wave propagation due to an internal pressure unloading is studied. The time history of radial stresses are discussed and the mean velocity of radial stress wave propagation for different exponent “n” of FGM are determined.

This paper presents the high strength technique to studying and analyzing the functionally graded thick hollow cylinders subjected to dynamic loads and the mean velocity of radial wave propagation is obtained using the proposed method.

The purpose of this study is to distinguish the difference in tribological behavior of functionally graded composites in two sliding modes, namely, unidirectional and reciprocating.

A356-(10 Wt.%)SiCp functionally graded composite material (FGM) was prepared by vertical centrifugal casting and then a comparison was made between the tribological characteristics using pin-on-disk and pin-on-reciprocating plate configurations under identical operating conditions (sliding distance (s): 350 m; load (W): 30 = W = 120 N, in steps of 30 N; and velocity (v): 0.2 = v = 1.2 m/s, in steps of 0.2 m/s). Two types of test pins were considered, namely, a test pin taken from the outer zone of the FGM with maximum particle concentration and a test pin taken from the inner zone of the FGM in a matrix-rich region.

The study revealed that, for the test pin taken from the outer zone of the FGM in the low-velocity range (0.2–0.4 m/s), the reciprocating wear of the friction pair was dominant, while unidirectional wear was dominant in the velocity range of 0.6–0.8 m/s for the entire load range investigated. However, when the velocity was increased from 1.0 to 1.2 m/s, conflicting nature of dominancy in the wear characteristics of the friction pair was observed, depending on the loading condition. In addition, the inner zone FGM pin underwent seizure in the reciprocating mode, whereas this phenomenon was not seen in the unidirectional mode.

Differences in wear and friction characteristics of FGM friction pairs in two different sliding modes were investigated over a wide range of operating parameters.

This paper gives a bibliographical review of the finite element methods (FEMs) applied to the analysis of ceramics and glass materials. The bibliography at the end of the paper contains references to papers, conference proceedings and theses/dissertations on the subject that were published between 1977‐1998. The following topics are included: ceramics – material and mechanical properties in general, ceramic coatings and joining problems, ceramic composites, ferrites, piezoceramics, ceramic tools and machining, material processing simulations, fracture mechanics and damage, applications of ceramic/composites in engineering; glass – material and mechanical properties in general, glass fiber composites, material processing simulations, fracture mechanics and damage, and applications of glasses in engineering.

This study aims to explain the characterization of cyclic behavior of a tube made of functionally graded material (FGM) under different combinations of internal pressure and cyclic through-thickness temperature gradients.

The normality rule, nonlinear kinematic hardening Chaboche model and Von Mises yield criterion were used to model the constitutive behavior of an FG tube in the incremental form. The material properties and hardening parameters of the Chaboche model vary according to the power-law function in the radial direction. The backward Euler integration scheme combined with return mapping algorithm which relies on the solution of a nonlinear equation performs the numerical procedure. The algorithm is implemented within the user subroutine UMAT in ABAQUS/standard.

The published works on FG components considering only the mechanical and physical properties as a function of spatial coordinate and nonlinear kinematic hardening parameters have not been considered to be changed continuously from one surface to another. Motivated by this, the present paper has deliberately been targeted to tackle this kind of problem to simulate the cyclic behavior of an FG tube as accurately as possible. In addition, to classify various behaviors the FG tube under cyclic thermomechanical loadings, Bree’s interaction diagram as an essential tool in designing of the FG pressure vessels in many engineering sectors is presented.

Provides a detailed description of the FG parameters of Chaboche kinematic hardening parameters in the adopted constitutive equations. In this paper, the significant effects of internal pressure values, kinematic hardening models and also FG inhomogeneity index related to the hardening rule parameters on plastic deformation of the FG tube are illustrated. Finally, the various cyclic behaviors of the FG tube under different combinations of thermomechanical loading are fully explored.

When the temperature of an air conditioning unit’s fin surface goes below its dew point temperature, condensation forms on the unit’s surface. As a result, the cooling coil’s performance is compromised. By altering the cross-section and heat conductivity of the fins, the performance of such systems can be improved. This study aims to analyze the thermal performance of longitudinal fins made up of a variable thickness (assuming constant weight) and functionally graded material.

Different grading parameters are considered for an exponential variation of thermal conductivity. The humidity ratio and the corresponding fin temperatures are assumed to follow a cubic relationship. The Bvp4c solver in MATLAB^® is used to solve the differential heat transfer equation resulting from balancing heat transfer in a small segment.

Validation of the methodology is provided by previous research presented in this area. For different combinations of grading parameters, geometry parameters and relative humidity, the normalized temperature distribution along the fin length and fin efficiency contours are plotted, and the results are very promising.

When compared to the efficiency of an isotropic homogenous rectangular longitudinal fin with optimal geometry and grading parameters, a 17% increase in efficiency under fully wet conditions is measured. When it comes to fin design, these efficiency contour plots are extremely useful.

The purpose of this paper is to propose a hybrid mesh-free method based on generalized finite difference (GFD) and Newmark finite difference methods to study the elastic wave propagation in functionally graded nanocomposite reinforced by carbon nanotubes (FGNRCN). The presented hybrid mesh-free method is applied for a thick hollow cylinder, which is made of FGNRCN and excited by various mechanical shock loadings.

The FG nanocomposite cylinder is assumed to be under shock loading. The elastic wave propagation is obtained and studied for various nonlinear grading patterns and distributions of the aligned carbon nanotubes. The distribution of carbon naotubes in FG nanocomposite are considered to vary as nonlinear function of radius, which varies with various nonlinear grading patterns continuously through radial direction. The effective material properties of functionally graded carbon nanotube are estimated using a micro-mechanical model.

The mechanical shock analysis of FGNRCN thick hollow cylinder is carried out and the dynamic behavior of displacement field and the time history of radial displacement are obtained for various grading patterns. An effective hybrid mesh-free method based on GFD and Newmark finite difference methods is presented to calculate the average velocity of elastic wave propagation in FGNRCN. The average velocity of elastic wave propagation is obtained for various grading patterns and various kinds of volume fraction. The effects of some parameters on average velocity of elastic wave propagation are obtained and studied in detail.

The calculation of elastic radial wave propagation in a FGNRCN thick hollow cylinder is presented using a hybrid mesh-free method. The effects of some parameters on wave propagation such as various grading patterns of distribution of carbon nanotubes are studied in details.