• Steel and Composite Structures
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• v.23 no.3
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• pp.263-271
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• 2017

A theoretical study was carried-out of mode II delamination fracture behavior of the End Loaded Split (ELS) functionally graded beam configuration with considering the material non-linearity. The mechanical response of ELS was modeled analytically by using a power-law stress-strain relation. It was assumed that the material is functionally graded transversally to the beam. The non-linear fracture was investigated by using the J-integral approach. Equations were derived for the crack arm curvature and zero axes coordinate that are needed for the J-integral solution. The analysis developed is valid for a delamination crack located arbitrary along the beam height. The J-integral solution was verified by analyzing the strain energy release rate with considering material non-linearity. The effects of material gradient, non-linear material behavior and crack location on the fracture were evaluated. The solution derived is suitable for parametric analyses of non-linear fracture. The results obtained can be used for optimization of functionally graded beams with respect to their mode II fracture performance. Also, such simplified analytical models contribute for the understanding of delamination fracture in functionally graded beams exhibiting material non-linearity.

• Structural Engineering and Mechanics
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• v.91 no.6
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• pp.551-565
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• 2024

This study presents a methodical investigation into improving structural designs through the analytical examination of the dynamic behavior of functionally graded plates (FGPs) resting on viscoelastic foundations. By employing a four variable first-order shear deformation theory, the study computes non-dimensional frequencies for a variety of porous FGPs with diverse graded patterns and porosity distributions. Different gradient patterns of the plates are considered, and three distinct functions-sigmoid (S-FGM), exponential (E-FGM), and power-law (P-FGM)-are utilized to assess material performance in specific directions. The equations of motion are derived and solved using both Navier's method and Hamilton's principle. Analytical solutions for vibration frequency are provided to validate the proposed methodology against existing literature. Furthermore, a comprehensive parametric analysis is conducted, taking into account various factors such as ceramic material, porosity distribution, gradient index, length-to-thickness ratio, gradient pattern, and damping coefficient. The findings suggest that enhancing the damping coefficient of the viscoelastic foundation can significantly improve the free-vibrational response of functionally graded material plates.

• Proceedings of the Materials Research Society of Korea Conference
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• 1994.05a
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• pp.41-41
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• 1994

• Journal of Mechanical Science and Technology
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• v.18 no.9
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• pp.1582-1589
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• 2004

The dynamic response of an eccentric Griffith crack in functionally graded piezoelectric ceramic strip under anti-plane shear impact loading is ana lysed using integral transform method. Laplace transform and Fourier transform are used to reduce the problem to two pairs of dual integral equations, which are then expressed to Fredholm integral equations of the second kind. We assume that the properties of the functionally graded piezoelectric material vary continuously along the thickness. The impermeable crack boundary condition is adopted. Numerical values on the dynamic stress intensity factors are presented for the functionally graded piezoelectric material to show the dependence of the gradient of material properties and electric loadings.

• Coupled systems mechanics
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• v.7 no.4
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• pp.441-453
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• 2018

Longitudinal fracture in a functionally graded beam configuration was studied analytically with taking into account the non-linear behavior of the material. A cantilever beam with two longitudinal cracks located symmetrically with respect to the centroid was analyzed. The material was functionally graded along the beam width as well as along the beam length. The fracture was studied in terms of the strain energy release rate. The influence of material gradient, crack location along the beam width, crack length and material non-linearity on the fracture behavior was investigated. It was shown that the analytical solution derived is very useful for parametric analyses of the non-linear longitudinal fracture behavior. It was found that by using appropriate material gradients in width and length directions of the beam, the strain energy release rate can be reduced significantly. Thus, the results obtained in the present paper may be applied for optimization of functionally graded beam structure with respect to the longitudinal fracture performance.

• Advances in nano research
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• v.13 no.6
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• pp.545-559
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• 2022

This paper studies the buckling response of nonuniform functionally graded micro-sized tubes according to the high-order tube theory (HOTT) and classical beam theory (CBT) in addition to nonlocal strain gradient theory. The microtube is made of axially functionally graded material (AFGM). Both inner and outer tube radiuses are changed along the tube length; the microtube is the truncated conical type of tube. The nonlinear partial differential (PD) the formulations are obtained on the basis of the energy conservation method. Then, the linear and nonlinear results are computed via a powerful numerical approach. Finally, the impact of various parameters on the stability of axially functionally graded (AFG) microtube regarding the buckling analysis is discussed.

• Journal of the Korean Ceramic Society
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• v.31 no.3
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• pp.321-329
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• 1994

Functionally gradient materials(FGM), which have the continuous or stepwise variation in a composition and microstructure, are being noticed as the material that solves problems caused by heterogeneous interface of coating or joining. And these materials also expect new functions occured by gradient composition itself. Therefore, to examine possibility of thermal barrier materials, TZP/Mo·FGM and TZP/Ni·FGM were fabricated by sintering method. As to the sintered specimens, sintering shrinkage, relative density and Vicker's hardness in each composition were examined. The phenomena due to the difference of sintering shrinkage velocity during sintering process and the thermal stress induced through differences of thermal expansion coefficient in FGM were discussed. And the structure changes at interface and microsturcture of FGM were investigated. As a results, the difference of shrinkage between ceramic and metal was about 14% in TZP/Mo and 7% in TZP/Ni. The relative density and hardness were considerably influenced by metal content changes. Owing to unbalance of sintering shrinkage velocity between ceramic and metal, various sintering defects were occured. To control these sintering defects and thermal stress, gradient composition of FGM should be narrow. The microstructure changes of FGM depended on the ceramic or metal volume percents and were analogous to the theoretical design.

• Journal of the Korean Society of Propulsion Engineers
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• v.5 no.1
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• pp.49-59
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• 2001

Functionally gradient materials(FGMs) generally consist of different material components, such as ceramics and metals. Continuous changes in their composition, microstructure, porositys, and so on result in gradients in the properties of FGMs. In this study AlN/Al-$Al_3$Ti FGM cubes were fabricated by the powder metallurgical process, and the characteristics of the FGMs were investigated. Powders of Mg and Ti mixed with Al in different ratios or the stack of the mixed powders having a stepwisely controlled compositional gradient from one plane to another were formed in a steel mold. The more the composition of Mg and sintering temperature are increased, the more the amount of AlN is formed. AlN and $Al_3$Ti distributed with continuously gradient composition were detected by XRD analysis and also revealed in optical microstructures, and microhardness tests.

• Structural Engineering and Mechanics
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• v.71 no.6
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• pp.669-682
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• 2019

We in this article study nonlinear thermal buckling of bi-directional functionally graded beams in the theoretical frameworks of nonlocal strain graded theory. To begin with, it is assumed that the effective material properties of beams vary continuously in both the thickness and width directions. Then, we utilize a higher-order shear deformation theory that includes a physical neutral surface to derive the size-dependent governing equations combining with the Hamilton's principle and the von $K{\acute{a}}rm{\acute{a}}n$ geometric nonlinearity. It should be pointed out that the established model, containing a nonlocal parameter and a strain gradient length scale parameter, can availably account for both the influence of nonlocal elastic stress field and the influence of strain gradient stress field. Subsequently, via using a easier group of initial asymptotic solutions, the corresponding analytical solution of thermal buckling of beams is obtained with the help of perturbation method. Finally, a parametric study is carried out in detail after validating the present analysis, especially for the effects of a nonlocal parameter, a strain gradient length scale parameter and the ratio of the two on the critical thermal buckling temperature of beams.

• Structural Engineering and Mechanics
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• v.86 no.6
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• pp.731-738
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• 2023

This article presents an analytical approach to explore the bending behaviour of of two-dimensional (2D) functionally graded (FG) nanobeams based on a two-variable higher-order shear deformation theory and nonlocal strain gradient theory. The kinematic relations are proposed according to novel trigonometric functions. The material gradation and material properties are varied along the longitudinal and the transversal directions. The equilibrium equations are obtained by using the virtual work principle and solved by applying Navier's technique. A comparative evaluation of results against predictions from literature demonstrates the accuracy of the proposed analytical model. Moreover, a detailed parametric analysis checks for the sensitivity of the bending and stresses response of (2D) FG nanobeams to nonlocal length scale, strain gradient microstructure scale, material distribution and geometry.