• Structural Engineering and Mechanics
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• 제66권1호
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• pp.97-111
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• 2018

Cracking can lead to unexpected sudden failure of normally ductile metals subjected to a tensile stress, especially at elevated temperature. This article is raised to study the application of a composite material instead of the traditional carbon steel material used in the natural gas transmission pipeline because the cracks occurs in the pipeline initiate at its internal surface which is subjected to internal high fluctuated pressure and unsteady temperature according to actual operation conditions. Functionally graded material (FGM) is proposed to benefit from the ceramics durability and its surface hardness against erosion. FGM properties are graded at the radial direction. Finite element method (FEM) is applied and solved by ABAQUS software including FORTRAN subroutines adapted for this case of study. The stress intensity factor (SIF), temperatures and stresses are discussed to obtain the optimum FGM configuration under the actual conditions of pressure and temperature. Thermoelastic analysis of a plane strain model is adopted to study SIF and material response at various crack depths.

• Wind and Structures
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• 제23권6호
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• pp.543-558
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• 2016

The response of functionally graded ceramic-metal plates is investigated using theoretical formulation, Navier's solutions, and a new displacement based on the high-order shear deformation theory are presented for static analysis of functionally graded plates. The theory 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. The plates are assumed to have isotropic, two-constituent material distribution through the thickness, and the modulus of elasticity of the plate is assumed to vary according to a power-law distribution in terms of the volume fractions of the constituents. Numerical results of the new refined plate theory are presented to show the effect of the material distribution on the deflections, stresses and fundamental frequencies. It can be concluded that the proposed theory is accurate and simple in solving the static and free vibration behavior of functionally graded plates.

• Structural Engineering and Mechanics
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• 제60권2호
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• pp.313-335
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• 2016

In this article, a four-variable refined plate theory is presented for buckling analysis of functionally graded plates subjected to uniform, linear and non-linear temperature rises across the thickness direction. The theory accounts for parabolic distribution of the transverse shear strains, and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factor. Young's modulus and Poisson ratio of the FGM plates are assumed to remain constant throughout the entire plate. However, the coefficient of thermal expansion of the FGM plate varies according to a power law form through the thickness coordinate. Equilibrium and stability equations are derived based on the present theory. The influences of many plate parameters on buckling temperature difference such ratio of thermal expansion, aspect ratio, side-to-thickness ratio and gradient index will be investigated.

• Steel and Composite Structures
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• 제53권1호
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• pp.91-101
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• 2024

A cost-effective fabrication method suitable for research purposes is proposed in this study. The elastic modulus of the fabricated functionally graded materials is evaluated and compared using two experimental methods: the three-point bending test and the tensile test, with a focus on the fiber volume fraction of the FGM layers. New methods for computing the elastic modulus are introduced, which are based on Castigliano's theorem and the secant modulus concept, incorporating the non-linear behavior of the material. Additionally, the mode I fracture toughness of the FGM layers is measured accurately using the three-point bending test and finite element analysis, and the influence of varying fiber volume fractions on this parameter is investigated through statistical analysis. Results indicate that while an increase in fiber volume fraction correlates with a rise in elastic modulus, it does not necessarily lead to an enhancement in mode I fracture toughness, highlighting the complex interactions between material composition and mechanical properties.

• Structural Engineering and Mechanics
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• 제88권4호
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• pp.355-368
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• 2023

Employing the non-local strain gradient theory (NSGT), this paper investigates the nonlinear resonance characteristics of functionally graded material (FGM) nanoshells with initial geometric imperfection for the first time. The effective material properties of the porous FGM nanoshells with even distribution of porosities are estimated by a modified power-law model. With the guidance of Love's thin shell theory and considering initial geometric imperfection, the strain equations of the shells are obtained. In order to characterize the small-scale effect of the nanoshells, the nonlocal parameter and strain gradient parameter are introduced. Subsequently, the Euler-Lagrange principle was used to derive the motion equations. Considering three boundary conditions, the Galerkin principle combined with the modified Lindstedt Poincare (MLP) method are employed to discretize and solve the motion equations. Finally, the effects of initial geometric imperfection, functional gradient index, strain gradient parameters, non-local parameters and porosity volume fraction on the nonlinear resonance of the porous FGM nanoshells are examined.

• Advances in nano research
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• 제13권4호
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• pp.351-368
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• 2022

Recently, promising structural technologies like multi-function, ultra-load bearing capacity and tailored structures have been put up for discussions. Finite Element (FE) modelling is probably the best-known option capable of treating these superior properties and multi-domain behavior structures. However, advanced materials such as Functionally Graded Material (FGM) and nanocomposites suffer from problems resulting from variable material properties, reinforcement aggregation and mesh generation. Motivated by these factors, this research proposes a unified shape function for FGM, nanocomposites, graded nanocomposites, in addition to traditional isotropic and orthotropic structural materials. It depends not only on element length but also on the beam's material properties and geometric characteristics. The systematic mathematical theory and FE formulations are based on the Timoshenko beam theory for beam structure. Furthermore, the introduced element achieves C1 degree of continuity. The model is proved to be convergent and free-off shear locking. Moreover, numerical results for static and free vibration analysis support the model accuracy and capabilities by validation with different references. The proposed technique overcomes the issue of continuous properties modelling of these promising materials without discarding older ones. Therefore, introduced benchmark improvements on the FE old concept could be extended to help the development of new software features to confront the rapid progress of structural materials.

• 한국전산구조공학회논문집
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• 제21권1호
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• pp.13-20
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• 2008

기능경사 소재(FGM)에는 서로 다른 두 가지 구성입자들이 혼합되어 있는 경사층(graded layer)이 삽입되어, 소재 전 영역에 걸쳐 구성입자의 체적분율이 연속적이고 기능적으로 변화하도록 되어있다. 이러한 이상(dual-phase) 입자복합재의 열 기계적 거동을 해석함에 있어 필수적인 경사층의 물성치는 전통적으로 균질화 기법을 이용하여 예측되었다. 하지만, 이러한 균질화 기법은 구성입자의 형태, 분산구조 등과 같은 상세 형상을 반영하지 못하지 때문에 복합재의 총체적인 등가 물성치 예측에만 국한 되어왔다. 이러한 맥락에서 본 연구에서는 경사층을 미시역학적으로 이산화 모델링하고, 다양한 체적분율과 외부 하중조건에 대해 유한요소해석을 실시하여 이러한 균질화 기법들의 특성을 분석하였다.

• Smart Structures and Systems
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• 제13권1호
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• pp.111-135
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• 2014

Based on the Reissner mixed variational theorem (RMVT), finite rectangular layer methods (FRLMs) are developed for the three-dimensional (3D) linear buckling analysis of simply-supported, fiber-reinforced composite material (FRCM) and functionally graded material (FGM) sandwich plates subjected to bi-axial compressive loads. In this work, the material properties of the FGM layers are assumed to obey the power-law distributions of the volume fractions of the constituents through the thickness, and the plate is divided into a number of finite rectangular layers, in which the trigonometric functions and Lagrange polynomials are used to interpolate the in- and out-of-plane variations of the field variables of each individual layer, respectively, and an h-refinement process is adopted to yield the convergent solutions. The accuracy and convergence of the RMVT-based FRLMs with various orders used for expansions of each field variables through the thickness are assessed by comparing their solutions with the exact 3D and accurate two-dimensional ones available in the literature.

• Earthquakes and Structures
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• 제17권3호
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• pp.329-336
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• 2019

An efficient shear deformation beam theory is developed for thermo-elastic vibration of FGM beams. The theory accounts for parabolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the on the surfaces of the beam without using shear correction factors. The material properties of the FGM beam are assumed to be temperature dependent, and change gradually in the thickness direction. Three cases of temperature distribution in the form of uniformity, linearity, and nonlinearity are considered through the beam thickness. Based on the present refined beam theory, the equations of motion are derived from Hamilton's principle. The closed-form solutions of functionally graded beams are obtained using Navier solution. Numerical results are presented to investigate the effects of temperature distributions, material parameters, thermal moments and slenderness ratios on the natural frequencies. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions.

• Structural Engineering and Mechanics
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• 제68권3호
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• pp.299-312
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• 2018

In this paper, an extended finite element method is proposed to analyze both geometric and material non-linear behavior of general Functionally Graded Material (FGM) plate-shell type structures. A user defined subroutine (UMAT) is developed and implemented in Abaqus/Standard to study the elastoplastic behavior of the ceramic particle-reinforced metal-matrix FGM plates-shells. The standard quadrilateral 4-nodes shell element with three rotational and three translational degrees of freedom per node, S4, is extended in the present study, to deal with elasto-plastic analysis of geometrically non-linear FGM plate-shell structures. The elastoplastic material properties are assumed to vary smoothly through the thickness of the plate-shell type structures. The nonlinear approach is based on Mori-Tanaka model to underline micromechanics and locally determine the effective FGM properties and self-consistent method of Suquet for the homogenization of the stress-field. The elasto-plastic behavior of the ceramic/metal FGM is assumed to follow Ludwik hardening law. An incremental formulation of the elasto-plastic constitutive relation is developed to predict the tangent operator. In order to to highlight the effectiveness and the accuracy of the present finite element procedure, numerical examples of geometrically non-linear elastoplastic functionally graded plates and shells are presented. The effects of the geometrical parameters and the volume fraction index on nonlinear responses are performed.