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Article
Publication date: 6 October 2021

Kaveh Salmalian, Ali Alijani and Habib Ramezannejad Azarboni

The purpose of this study is to investigate the post-buckling analysis of functionally graded columns by using three analytical, approximate and numerical methods. A pre-defined…

Abstract

Purpose

The purpose of this study is to investigate the post-buckling analysis of functionally graded columns by using three analytical, approximate and numerical methods. A pre-defined function as an initial assumption for the post-buckling path is introduced to solve the differential equation. The finite difference method is used to approximate the lateral deflection of the column based on the differential equation. Moreover, the finite element method is used to derive the tangent stiffness matrix of the column.

Design/methodology/approach

The non-linear buckling analysis of functionally graded materials is carried out by using three analytical, finite difference and finite element methods. The elastic deformation and Euler-Bernoulli beam theory are considered to establish the constitutive and kinematics relations, respectively. The governing differential equation of the post-buckling problem is derived through the energy method and the calculus variation.

Findings

An incremental iterative solution and the perturbation of the displacement vector at the critical buckling point are performed to determine the post-buckling path. The convergence of the finite element results and the effects of geometric and material characteristics on the post-buckling path are investigated.

Originality/value

The key point of the research is to compare three methods and to detect error sources by considering the derivation process of relations. This comparison shows that a non-incremental solution in the analytical and finite difference methods and an initial assumption in the analytical method lead to an error in results. However, the post-buckling path in the finite element method is traced by the updated tangent stiffness matrix in each load step without any initial limitation.

Details

Journal of Engineering, Design and Technology , vol. 21 no. 3
Type: Research Article
ISSN: 1726-0531

Keywords

Article
Publication date: 20 December 2018

Igor V. Andrianov, Jan Awrejcewicz and Alexander A. Diskovsky

The purpose of this paper is to define and solve the problem of an optimized structural topology of the simply supported beam made from functionally graded material (FGM) enabling…

Abstract

Purpose

The purpose of this paper is to define and solve the problem of an optimized structural topology of the simply supported beam made from functionally graded material (FGM) enabling achievement of a maximum buckling load.

Design/methodology/approach

Two kinds of inclusions are considered: regular distribution of inclusions of different rigidities and non-uniform distribution of identical inclusions. It is shown that the optimal conditions are similar for both structural designs. The optimization problems are solved by using the homogenization method, and the target functions belong to the class of piece-wise continuous functions. Both optimized structures exhibit border zones free of any inclusions, and the largest amount of inclusions is localized in the central zone of the beams.

Findings

It has been shown that the final result of the carried out optimization of the internal structure for both studied types of FGM are similar. The relative increase in the buckling force of the FG beam with the optimized internal structure is on amount of 20 per cent while comparing it with the regular structure beam.

Originality/value

In contrary to a standard approach, this paper is aimed to detect and study a scenario of transition from heterogeneous to its counterpart homogeneous beam structure based on the consideration of the FGM inclusions. In addition, the problem of inversed transition from the optimized homogeneous structure to the optimal heterogeneous one is solved.

Details

Engineering Computations, vol. 36 no. 1
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 4 September 2019

Mohammad Rezaiee-Pajand and Amir R. Masoodi

The purpose of this study is dedicated to use an efficient mixed strain finite element approach to develop a three-node triangular shell element. Moreover, large deformation…

Abstract

Purpose

The purpose of this study is dedicated to use an efficient mixed strain finite element approach to develop a three-node triangular shell element. Moreover, large deformation analysis of the functionally graded material shells is the main contribution of this research. These target structures include thin or moderately thick panels.

Design/methodology/approach

Due to reach these goals, Green–Lagrange strain formulation with respect to small strains and large deformations with finite rotations is used. First, an efficient three-node triangular degenerated shell element is formulated using tensorial components of two-dimensional shell theory. Then, the variation of Young’s modulus through the thickness of shell is formulated by using power function. Note that the change of Poisson’s ratio is ignored. Finally, the governing linearized incremental relation was iteratively solved using a high potential nonlinear solution method entitled generalized displacement control.

Findings

Some well-known problems are solved to validate the proposed formulations. The suggested triangular shell element can obtain the exact responses of functionally graded (FG) shell structures, without any shear locking, instabilities and ill-conditioning, even by using fewer numbers of the elements. The obtained outcomes are compared with the other reference solutions. All findings demonstrate the accuracy and capability of authors’ element for analyzing FG shell structures.

Research limitations/implications

A mixed strain finite element approach is used for nonlinear analysis of FG shells. These structures are curved thin and moderately thick shells. Small strains and large deformations with finite rotations are assumed.

Practical implications

FG shells are mostly made curved thin or moderately thick, and these structures have a lot of applications in the civil and mechanical engineering.

Social implications

The social implication of this study is concerned with how technology impacts the world. In short, the presented scheme can improve structural analysis ways.

Originality/value

Developing an efficient three-node triangular element, for geometrically nonlinear analysis of FG doubly-curved thin and moderately thick shells, is the main contribution of the current research. Finite rotations are considered by using the Taylor’s expansion of the rotation matrix. Mixed interpolation of strain fields is used to alleviate the locking phenomena. Using fewer numbers of shell elements with fewer numbers of degrees of freedom can reduce the computational costs and errors significantly.

Details

World Journal of Engineering, vol. 16 no. 5
Type: Research Article
ISSN: 1708-5284

Keywords

Article
Publication date: 12 June 2017

W.X. Zhang, R.G. Liu and Y. Bai

For general quasi-static problems of viscoelastic functionally graded materials (VFGMs), the correspondence principle can be applied only for simple structures with a closed form…

Abstract

Purpose

For general quasi-static problems of viscoelastic functionally graded materials (VFGMs), the correspondence principle can be applied only for simple structures with a closed form solution of the corresponding elastic problem exists. In this paper, a new symplectic approach, according to the correspondence principle between linearly elastic and viscoelastic solids, is proposed for quasi-static VFGMs.

Design/methodology/approach

Firstly, by employing the method of separation of variables, all the fundamental eigenvectors of the governing equations are obtained analytically. Then, the satisfactions of boundary conditions prescribed on the ends and laterals are discussed based on the variable substitution and the eigenvector expansion methods.

Findings

In the numerical examples, some boundary condition problems are given. The results show the local effects due to the displacement constraints.

Originality/value

The paper provides an innovative technique for quasi-static problems of VFG Ms. Its correctness and the efficiency are well suported by numerical results.

Details

Engineering Computations, vol. 34 no. 4
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 9 July 2020

Mehmet Eker, Durmuş Yarımpabuç and Kerimcan Çelebi

This paper aims to present thermal and mechanical stresses in solid and hollow thick-walled cylinders and spheres made of functionally graded materials (FGMs) under the effect of…

Abstract

Purpose

This paper aims to present thermal and mechanical stresses in solid and hollow thick-walled cylinders and spheres made of functionally graded materials (FGMs) under the effect of heat generation.

Design/methodology/approach

Constant internal temperature and convective external conditions in hollow bodies along with internal heat generation with a combination of outer convective conditions in solid bodies are investigated individually. The effect of the heat convection coefficient on solid bodies is additionally discussed. The variation of the FGM properties in the radial direction is adapted to the Mori–Tanaka homogenization schemes, which produces irregular and two-point linear boundary value problems that are numerically solved by the pseudospectral Chebyshev method.

Findings

It has been shown that the selection of the mixtures of FGMs has to be made correctly to keep the thermal and mechanical loads acting on objects at low levels.

Originality/value

In this study, both solid and hollow functionally graded cylinders and spheres for different boundary conditions that are as their engineering applications are examined with the proposed method. The results have demonstrated that the pseudospectral Chebyshev method has high accuracy, low calculation costs and ease of application and can be easily adapted to such engineering problems.

Article
Publication date: 30 August 2022

Bo Chen, Tao Wang, Xin Xi, Caiwang Tan and Xiaoguo Song

Ti-Al composite plates have been used in aerospace and other important fields for specific purposes in recent years. However, relatively few studies have concentrated on Ti-Al…

Abstract

Purpose

Ti-Al composite plates have been used in aerospace and other important fields for specific purposes in recent years. However, relatively few studies have concentrated on Ti-Al additive manufacturing because during additive manufacturing process the local fusion and mixing of Ti/Al are inevitable. These areas where Ti and Al are mixed locally, especially interface, could easily generate high residual stresses and cracks. This study aims to manufacture Ti-Al functionally graded material and investigate the interaction of interface.

Design/methodology/approach

In this study, Ti6Al4V/AlSi10Mg functionally graded materials were fabricated by laser based directed energy deposition (L-DED) and a strategy using V interlayer to relieve interfacial stress was investigated.

Findings

The area between the two materials was divided into transition zone (TZ) and remelting zone (RZ). The phase distribution, microstructure and micro-Vickers hardness of the TZ and RZ were investigated. Typical intermetallic compounds (IMCs) such as TiAl3, Ti3Al and Ti5Si3 were found in both composites. The addition of V interlayer promoted the homogenization of IMCs near interface and led to the formation of new phases like V5Si3 and Al3V.

Originality/value

The solidification process near the interface of Ti-Al functionally graded material and the possible generation of different phases were described. The result of this paper proved the feasibility of manufacturing Ti-Al functionally graded material by L-DED.

Details

Rapid Prototyping Journal, vol. 29 no. 3
Type: Research Article
ISSN: 1355-2546

Keywords

Article
Publication date: 1 August 1999

Jaroslav Mackerle

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…

2604

Abstract

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.

Details

Engineering Computations, vol. 16 no. 5
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 9 November 2015

Mokhtar Bouazza and Noureddine Benseddiq

The purpose of this paper is to investigate an analytical modeling for the thermoelastic buckling behavior of functionally graded (FG) rectangular plates (FGM) under thermal…

Abstract

Purpose

The purpose of this paper is to investigate an analytical modeling for the thermoelastic buckling behavior of functionally graded (FG) rectangular plates (FGM) under thermal loadings. The material properties of FGM are assumed to vary continuously through the thickness of the plate, according to the simple power-law distribution. Derivations of equations are based on novel refined theory using a new hyperbolic shear deformation theory. Unlike other theories, there are only four unknown functions involved, as compared to five in other shear deformation theories. The theory presented is variationally consistent and strongly similar to the classical plate theory in many aspects. It does not require the shear correction factor, and gives rise to the transverse shear stress variation so that the transverse shear stresses vary parabolically across the thickness to satisfy free surface conditions for the shear stress. In addition, numerical results for a variety of FG plates with simply supported edge are presented and compared with those available in the literature. Moreover, the effects of geometrical parameters of dimension the length to width aspect ratio (a/b), the plate width to thickness ratio (b/h), and material properties index (k) on the FGM buckling temperature difference are determined and discussed.

Design/methodology/approach

In the current paper, the application of the refined theory proposed by Shimpi is based on the assumption that the in-plane and transverse displacements consist of bending and shear components in which the bending components do not contribute toward shear forces and, likewise, the shear components do not contribute toward bending moments. The most interesting feature of this theory is that it accounts for a quadratic variation of the transverse shear strains across the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. It is extended to the analysis of buckling behavior of ceramic-metal FG plates subjected to the three types of thermal loadings, namely; uniform temperature rise, linear temperature change across the thickness, and nonlinear temperature change across the thickness. The material properties of the FG plates are assumed to vary continuously through the thickness of the plate, according to the simple power-law distribution. Numerical results for a variety of FG plates with simply supported edges are given and compared with the available results, wherever possible. Additionally, the effects of geometrical parameters and material properties on the buckling temperature difference of FGM plates are determined and discussed.

Findings

Unlike any other theory, the theory presented gives rise to only four governing equations. Number of unknown functions involved is only four, as against five in case of simple shear deformation theories of Mindlin and Reissner (first shear deformation theory). The plate properties are assumed to be varied through the thickness following a simple power-law distribution in terms of volume fraction of material constituents. The theory presented is variationally consistent, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions.

Originality/value

To the best of the authors’ knowledge, there are no research works for thermal buckling analysis of FG rectangular plates based on new four-variable refined plate theory (RPT). The novelty of this paper is extended the use of the above-mentioned RPT with the addition of a new function proposed by Shimpi for thermal buckling analysis of plates made of FG materials. Unlike any other theory, the number of unknown functions involved is only four, as against five in the case of other shear deformation theories. The theory takes account of transverse shear effects and parabolic distribution of the transverse shear strains through the thickness of the plate, hence it is unnecessary to use shear correction factors. The plates subjected to the two types of thermal loadings, namely; uniform temperature rise and nonlinear temperature change across the thickness. Numerical results for a variety of FG plates with simply supported edges are given and compared with the available results.

Details

Multidiscipline Modeling in Materials and Structures, vol. 11 no. 4
Type: Research Article
ISSN: 1573-6105

Keywords

Article
Publication date: 15 October 2018

Mohammad Azadi

The purpose of this paper is to analyze and control the flutter vibrations of a thermoelastic functionally graded material (FGM) beam subjected to follower force using the…

Abstract

Purpose

The purpose of this paper is to analyze and control the flutter vibrations of a thermoelastic functionally graded material (FGM) beam subjected to follower force using the piezoelectric sensors/actuators.

Design/methodology/approach

The beam is made of FGM properties which are functionally graded in the thickness direction according to the volume fraction power law distribution and change with temperature. As the two sides of the beam are located in two different temperatures, the thermoelastic effects are considered in the governing equation of motion. The beam is fixed from one end and a follower force is applied to the free end of it. An active control is applied to the system to suppress the flutter vibration of the beam.

Findings

After the simulation, the effects of the temperature gradient, magnitude of the follower force and piezoelectric lengths on the dynamic stability and the response of the system are studied. Simulation results show that the vibration of the system has been damped rapidly by applying the controller to the system.

Originality/value

Stability analysis and robust control of a thermoelastic FGM beam subjected to a follower force using piezoelectric sensors and actuators is the novelty of this study.

Details

Aircraft Engineering and Aerospace Technology, vol. 90 no. 9
Type: Research Article
ISSN: 1748-8842

Keywords

Article
Publication date: 1 February 2005

M.S. Domack and J.M. Baughman

Three layer‐additive manufacturing methods were evaluated to producing nickel‐titanium graded composition material. One potential application is fabrication of attachment clips…

9372

Abstract

Purpose

Three layer‐additive manufacturing methods were evaluated to producing nickel‐titanium graded composition material. One potential application is fabrication of attachment clips that join thermal protection systems to launch vehicle structure. Thermal gradients during flight generate excessive bending and shear loads that limit the service lifetime of the Inconel clips currently used. It is envisioned that a graded composition component could be tailored to reduce the stress concentrations.

Design/methodology/approach

Deposits with nearly continuous composition grade were built from Ti‐6‐4 and Inconel 718 powder using laser direct metal deposition. Layered deposits were produced by flat wire welding from Ti‐6‐4 and Inconel 718 wire. Ultrasonic consolidation was used to produce layered deposits from pure nickel and commercially pure titanium foils. Microstructure, bond line morphology, chemical composition, and reaction phases were characterized.

Findings

All three manufacturing methods require further development before graded composition material can be reliably produced. Laser direct metal deposition samples exhibited coarse dendritic microstructures and significant elemental segregation. Chemistries varied from calculated targets by up to 20 percent and macroscopic cracking occurred for chemistries greater than 60 percent Inconel 718. Flat wire welded deposits exhibited good mixing between the wire layers, however brittle cracking occurred adjacent to a 5 μm thick reaction layer. Ultrasonically‐consolidated samples demonstrated metallurgical bonding between pure Ni and commercially pure (CP) Ti foils, with material reaction limited to a 1 μm layer.

Originality/value

Producing nickel‐titanium graded composition materials had not been attempted by the selected manufacturing methods. A refined experimental program is needed to resolve the remaining technical issues.

Details

Rapid Prototyping Journal, vol. 11 no. 1
Type: Research Article
ISSN: 1355-2546

Keywords

1 – 10 of 195