• Structural Engineering and Mechanics
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• 제72권5호
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• pp.653-673
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• 2019

This work investigates a novel quasi-3D hyperbolic shear deformation theory is presented to discuss the buckling of new type of sandwich plates. This theory accounts for both shear deformation and thickness stretching effects by a hyperbolic variation of all displacements through the thickness. The enhancement of this formulation is due to the use of only five unknowns by including undetermined integral terms, contrary to other theories where we find six or more unknowns. It does not require shear correction factors and transverse shear stresses vary parabolically across the thickness. A new type of FGM sandwich plates, namely, both FGM face sheets and FGM hard core are considered. The governing equations and boundary conditions are derived using the principle of virtual displacements. Analytical solutions are obtained for a simply supported plate. The accuracy of the present theory is verified by comparing the obtained results with quasi-3D solutions and those predicted by higher-order shear deformation theories. The comparison studies show that the obtained results are not only more accurate than those obtained by higher-order shear deformation theories, but also comparable with those predicted by quasi-3D theories with a greater number of unknowns.

• Structural Engineering and Mechanics
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• 제67권3호
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• pp.277-281
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• 2018

The analytical solution of two functionally graded layers with Volterra type screw dislocation is investigated under anti-plane shear impact loading. The energy dissipation of FGM layers is modeled by viscous damping and the properties of the materials are assumed to change exponentially along the thickness of the layers. In this study, the rate of gradual change ofshear moduli, mass density and damping constant are assumed to be same. At first, the stress fields in the interface of the FGM layers are derived by using a single dislocation. Then, by determining a distributed dislocation density on the crack surface and by using the Fourier and Laplace integral transforms, the problem are reduce to a system ofsingular integral equations with simple Cauchy kernel. The dynamic stress intensity factors are determined by numerical Laplace inversion and the distributed dislocation technique. Finally, various examples are provided to investigate the effects of the geometrical parameters, material properties, viscous damping and cracks configuration on the dynamic fracture behavior of the interacting cracks.

• Composites Research
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• 제23권2호
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• pp.1-9
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• 2010

본 연구는 실린더 내부가 경사가능재료로 코팅된 두꺼운 벽을 가진 실린더의 겉보기 파괴인성치를 해석한 것이다. 실린더는 내부로부터 반경방향의 단일 모서리 균열이 내재되어 있으며, 균열면과 내면에는 내압을 받고 있는 것으로 가정하였다. 소결온도로부터 냉각 결과 균일한 열팽창계수로 인해 실린더에는 비적합 고유스트레인이 생성되었다. 기존의 연구에서 소개된 응력확대계수 평가법에 기초해 겉보기 파괴인성치를 계산하였다. 본 연구에서는 TiC/$Al_{2}O_{3}$ FGM 코팅된 실린더를 사용하였고 겉보기 파괴인성치의 수치적인 결과를 도식화하였다. 재료분포프로파일, 실린더 벽 두께, 적용온도와 코팅두께등이 겉보기 파괴인치에 미치는 영향이 상세히 조사되었으며, 이러한 모든 인자는 실린더의 겉보기 파괴인성치를 조절하는데 중요한 역할을 하는 것으로 밝혀졌다.

• Structural Engineering and Mechanics
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• 제85권2호
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• pp.217-231
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• 2023

The bending analysis of sandwich functionally graded (FG) beams under temperature circumstances is performed in this article utilizing Navier's solution-based parabolic shear deformation theory. For the first time, a comparative study has been carried out between the exponential and sigmoidal sandwich FGM beams under thermal conditions. During this investigation, temperature-dependent material characteristics are postulated. Both symmetric and unsymmetric sandwich examples have been studied. The effect of gradation law, gradation coefficient, and thickness scheme on beam behavior has been thoroughly investigated. Three possible temperature combinations at the top and bottom surfaces of the beam are also investigated. Beams with a higher proportion of ceramic to metal are shown to be more resistant to thermal stresses than beams with a higher proportion of metal.

• Steel and Composite Structures
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• 제47권1호
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• pp.71-77
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• 2023

This paper presents a study on the wave propagation of functionally graded material (FGM) sandwich nanoplates with soft core resting on a Winkler foundation. The structure is modelled by classical theory. Motion equations are derived by the assumption of nonlocal Eringen theory and energy method. Then, the equations are solved using an exact method for finding phase velocity responses. The effects of Winkler foundation, nonlocal parameters, thickness and mode number on the dispersion of elastic waves are shown. With the increase of spring constant, the speed of wave propagation increases and reaches a uniform state at a higher wave number.

• Structural Engineering and Mechanics
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• 제53권4호
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• pp.703-723
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• 2015

In this paper optimization of volume fraction distribution in a thick hollow cylinder with finite length made of two-dimensional functionally graded material (2D-FGM) and subjected to steady state thermal and mechanical loadings is considered. The finite element method with graded material properties within each element (graded finite elements) is used to model the structure. Volume fractions of constituent materials on a finite number of design points are taken as design variables and the volume fractions at any arbitrary point in the cylinder are obtained via cubic spline interpolation functions. The objective function selected as having the normalized effective stress equal to one at all points that leads to a uniform stress distribution in the structure. Genetic Algorithm jointed with interior penalty-function method for implementing constraints is effectively employed to find the global solution of the optimization problem. Obtained results indicates that by using the uniform distribution of normalized effective stress as objective function, considerably more efficient usage of materials can be achieved compared with the power law volume fraction distribution. Also considering uniform distribution of safety factor as design criteria instead of minimizing peak effective stress affects remarkably the optimum volume fractions.

• Composites Research
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• 제13권6호
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• pp.23-29
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• 2000

층상구조재료가 갖는 약점으로는 구성재료층 간의 열.기계적 특성 차이로 인하여 내부응력이 발생되고 비틀림 변형이 유발되어 형상 제어가 매우 어려울 뿐만 아니라, 반복적인 열 하중으로 인해 열이력을 받을 경우 접합부에서의 파손이 생길 수 있다는 것이다. 최근 층상구조에서 조직 혹은 조성이 점차적으로 변하는 계면을 삽입한 경사조성재료는 열.기계적 변형특성 차이에 의한 재료의 손상을 최소화시킬 수 있으나, 용도에 적합한 구조설계를 위해서 열.기계적 해석이 필요하다. 본 연구에서는 전자패키징용 $Al-SiC_p$ 경사조성 복합재료의 기하학적 구조와 온도변화에 따른 곡면화 변형 및 내부응력분포를 해석하고자 하였다. 한편 층상구조 $Al-SiC_p$ 경사조성 복합재료의 열변형량을 측정하고 내부응력분포를 실험적으로 구하여, 이론적으로 계산한 결과와 비교하였다. 본 연구의 해석결과는 경사조성 층상구조재료의 최적구조 설계에 유용하게 적용할 수 있다.

• Structural Engineering and Mechanics
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• 제65권4호
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• pp.453-464
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• 2018

In this paper, an efficient higher-order shear deformation theory is presented to analyze thermomechanical bending of temperature-dependent functionally graded (FG) plates resting on an elastic foundation. Further simplifying supposition are made to the conventional HSDT so that the number of unknowns is reduced, significantly facilitating engineering analysis. These theory account for hyperbolic distributions of the transverse shear strains and satisfy the zero traction boundary conditions on the surfaces of the plate without using shear correction factors. Power law material properties and linear steady-state thermal loads are assumed to be graded along the thickness. Nonlinear thermal conditions are imposed at the upper and lower surface for simply supported FG plates. Equations of motion are derived from the principle of virtual displacements. Analytical solutions for the thermomechanical bending analysis are obtained based on Fourier series that satisfy the boundary conditions (Navier's method). Non-dimensional results are compared for temperature-dependent FG plates and validated with those of other shear deformation theories. Numerical investigation is conducted to show the effect of material composition, plate geometry, and temperature field on the thermomechanical bending characteristics. It can be concluded that the present theory is not only accurate but also simple in predicting the thermomechanical bending responses of temperature-dependent FG plates.

• Steel and Composite Structures
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• 제45권5호
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• pp.729-747
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• 2022

The critical buckling loads and buckling modes of bi-directional functionally graded porous unified higher order shear plate with elastic foundation are investigated. A mathematical model based on neutral axis rather than midplane is developed in comprehensive way for the first time in this article. The material constituents form ceramic and metal are graded through thickness and axial direction by the power function distribution. The voids and cavities inside the material are proposed by three different porosity models through the thickness of plate. The constitutive parameters and force resultants are evaluated relative to the neutral axis. Unified higher order shear plate theories are used to satisfy the zero-shear strain/stress at the top and bottom surfaces. The governing equilibrium equations of bi-directional functionally graded porous unified plate (BDFGPUP) are derived by Hamilton's principle. The equilibrium equations in the form of coupled variable coefficients partial differential equations is solved by using numerical differential integral quadrature method (DIQM). The validation of the present model is presented and compared with previous works for bucking. Deviation in buckling loads for both mid-plane and neutral plane are developed and discussed. The numerical results prove that the shear functions, distribution indices, boundary conditions, elastic foundation and porosity type have significant influence on buckling stability of BDFGPUP. The current mathematical model may be used in design and analysis of BDFGPU used in nuclear, mechanical, aerospace, and naval application.

• Steel and Composite Structures
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• 제47권5호
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• pp.633-644
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• 2023

Taking a look at the previously published papers, it is revealed that there is a porosity index limitation (around 0.35) for the mechanical behavior analysis of the functionally graded porous (FGP) structures. Over mentioned magnitude of the porosity index, the elastic modulus falls below zero for some parts of the structure thickness. Therefore, the current paper is presented to analyze the vibrational behavior of the FGP Timoshenko beams (FGPTBs) using a novel refined formulation regardless of the porosity index magnitude. The silica aerogel foundation and various hydrothermal loadings are assumed as the source of external forces. To obtain the FGPTB's properties, the power law is hired, and employing Hamilton's principle in conjunction with Navier's solution method, the governing equations are extracted and solved. In the end, the impact of the various variables as different beam materials, elastic foundation parameters, and porosity index is captured and displayed. It is revealed that changing hygrothermal loading from non-linear toward uniform configuration results in non-dimensional frequency and stiffness pushing up. Also, Al - Al2O3 as the material composition of the beam and the porosity presence with the O pattern, provide more rigidity in comparison with using other materials and other types of porosity dispersion. The presented computational model in this paper hopes to help add more accuracy to the structures' analysis in high-tech industries.