• Steel and Composite Structures
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• 제23권1호
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• pp.1-16
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• 2017

This paper is presented to solve the buckling problem of functionally graded truncated conical shells subjected to displacement-dependent pressure which remains normal to the shell middle surface throughout the deformation process by the semi-analytical finite strip method. Material properties are assumed to be temperature dependent, and varied continuously in the thickness direction according to a simple power law distribution in terms of the volume fraction of a ceramic and metal. The governing equations are derived based on first-order shear deformation theory which accounts for through thickness shear flexibility with Sanders-type of kinematic nonlinearity. The element linear and geometric stiffness matrices are obtained using virtual work expression for functionally graded materials. The load stiffness also called pressure stiffness matrix which accounts for variation of load direction is derived for each strip and after assembling, global load stiffness matrix of the shell which may be un-symmetric is formed. The un-symmetric parts which are due to load non-uniformity and unconstrained boundaries have been separated. A detailed parametric study is carried out to quantify the effects of power-law index of functional graded material and shell geometry variations on the difference between follower and non-follower lateral buckling pressures. The results indicate that considering pressure stiffness which arises from follower action of pressure causes considerable reduction in estimating buckling pressure.

• Structural Engineering and Mechanics
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• 제74권1호
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• pp.83-90
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• 2020

Several classical and higher order plate theories were used to study the buckling of functionally graded material (FGM) plates. In the great majority of research, a power function is used to represent metal and ceramic material transverse distribution (P-FGM). Therefore, the effect of having other transverse variation of material properties on the buckling behavior of thick rectangular FGM plates was not properly addressed. In the present work, this effect is investigated using the Third order Shear Deformable Theory (TSDT) for the case of simply supported FGM plate. Both a sigmoid function and an exponential functions are used to represent the transverse gradual property variation. The plate governing equations are combined with a Navier type expanded solution of the unknown displacements to derive the buckling equation in terms of the pre-buckling in-plane loads. Finally, the critical in-plane load is calculated for the different buckling modes. The model is verified by a comparison of the calculated buckling loads with available published results of Al-SiC P-FGM plates. The conducted parametric study shows that manufacturing FGM plates with sigmoid variation of properties in the thickness direction increases the buckling load considerably. This improvement is found to be more significant for the case of thick plates than that of thin plates. Results also show that this stiffening-like effect of the sigmoid function profile is more evident for cases where the in-plane loads are applied along the shorter edge of the plate.

• Steel and Composite Structures
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• 제45권6호
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• pp.839-850
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• 2022

This paper presents an analytical solution to study the combined effect of non-local and stretching effect on the vibration of advanced functionally graded (FG) nanoplates. A new quasi-3D plate theory is presented; there are only five unknowns and any shear correction factor is used. A new displacement field with a new shear warping function is proposed. The equilibrium equations of the FG nanoplates are obtained using the Hamilton principle and solved numerically using the Navier technique. The material properties of functionally graded nanoplates are presumed to change according to the power-law distribution of ceramic and metal constituents. The numerical results of this work are compared with those of other published results to indicate the accuracy and convergence of this theory. Hence, a profound parameterstudy is also performed to show the influence of many parameters of the functionally graded nanoplates on the free vibration responses is investigated.

• Structural Engineering and Mechanics
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• 제56권1호
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• pp.137-156
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• 2015

In this paper, an analytical solution of displacement, strain and stress field for rotating thick-walled cylinder made of functionally graded material subjected to the uniform external magnetic field and thermal field in plane strain state has been studied. Stress, strain and displacement field as a function of radial coordinates considering magneto-thermo-elasticity are derived analytically. According to the Maxwell electro-dynamic equations, Lorentz force in term of displacement is obtained in cylindrical coordinates. Also, symmetric temperature distribution along the thickness of hollow cylinder is obtained by solving Fourier heat transfer equation in cylindrical coordinates. Using equation of equilibrium and thermo-mechanical constitutive equations associated with Lorentz force, a second-order inhomogeneous differential equation in term of displacement is obtained and will be solved analytically. Except Poisson's ratio, other mechanical properties such as elasticity modulus, density, magnetic permeability coefficient, heat conduction coefficient and thermal expansion coefficient are assumed to vary through the thickness according to a power law. In results analysis, non-homogeneity parameter has been chosen arbitrary and inner and outer surface of cylinder are assumed to be rich metal and rich ceramic, respectively. The effect of rotation, thermal, magnetic field and non-homogeneity parameter of functionally graded material which indicates percentages of cylinder's constituents are studied on displacement, Von Mises equivalent stress and Von Mises equivalent strain fields.

• Steel and Composite Structures
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• 제30권6호
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• pp.567-576
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• 2019

Time-dependent creep analysis of a rotating functionally graded cantilever beam with trapezoidal longitudinal cross section subjected to thermal and inertia loading is investigated using first-order shear deformation theory (FSDT). The model described in this paper is a simple simulation of a turbine blade working under creep condition. The material is a metal based composite reinforced by a ceramic where the creep properties of which has been described by the Sherby's constitutive model. All mechanical and thermal properties except Poisson's ratio are assumed to be variable longitudinally based on the volume fraction of constituent. The principle of virtual work as well as first order shear deformation theory is used to derive governing equations. Longitudinal distribution of displacements and stresses are investigated for various volume fractions of reinforcement. Method of successive elastic solution is employed to obtain history of stresses and creep deformations. It is found that stresses and displacements approach their steady state values after 40000 hours. The results presented in this paper can be used for selection of appropriate longitudinal distribution of reinforcement to achieve the desired stresses and displacements.

• Steel and Composite Structures
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• 제39권5호
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• pp.493-509
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• 2021

There is not enough mixed finite element method (MFEM) model developed for static and dynamic analysis of functionally graded material (FGM) beams in the literature. The main purpose of this study is to develop a reliable and efficient computational modeling using an efficient functional in MFEM for free vibration and static analysis of FGM composite beams subject to high order shear deformation effects. The modeling of material properties was performed using mixture rule and Mori-Tanaka scheme which are more realistic determination techniques. This method based on the assumption that a two phase composite material consisting of matrix reinforced by spherical particles, randomly distributed in the beam. To explain the displacement components of the shear deformation effects, it was accepted that the shear deformation effects change sinusoidal. Partial differential field equations were obtained with the help of variational methods and then these equations were transformed into a novel functional for FGM beams with the help of Gateaux differential derivative operator. Thanks to the Gateaux differential method, the compatibility of the field equations was checked, and the field equations and boundary conditions were reflected to the function. A MFEM model was developed with a total of 10 degrees of freedom to apply the obtained functional. In the numerical applications section, free vibration and flexure problems solutions of FGM composite beams were compared with those predicted by other theories to show the effects of shear deformation, thickness changing and boundary conditions.

• Structural Engineering and Mechanics
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• 제86권3호
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• pp.373-384
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• 2023

The main objective of this research work is to present analytical solutions for the thermoelastic bending analysis of sandwich plates made of functionally graded materials with an arbitrary gradient. The governing equations of equilibrium are solved for a functionally graded sandwich plates under the effect of thermal loads. The transverse shear and normal strain and stress effects on thermoelastic bending of such sandwich plates are considered. Field equations for functionally graded sandwich plates whose deformations are governed by either the shear deformation theories or the classical theory are derived. Displacement functions that identically satisfy boundary conditions are used to reduce the governing equations to a set of coupled ordinary differential equations with variable coefficients. The results of the shear deformation theories are compared together. Numerical results for deflections and stresses of functionally graded metal-ceramic plates are investigated.

• Steel and Composite Structures
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• 제49권4호
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• pp.431-440
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• 2023

The functionally graded (FG) porous plates are usually characterized by the non-symmetric elastic modulus distribution through the thickness so that the plate neutral surface does not coincide with the mid-surface. Nevertheless, the conventional analysis models were mostly based on the plate mid-surface so that the accuracy of resulting numerical results is questionable. In this context, this paper presents the neutral surface-based static and free vibration analysis of FG porous plates and investigates the differences between the mid- and neutral surface-based analysis models. The neutral surface-based numerical method is formulated using the (3,3,2) hierarchical model and approximated by the last introduced natural element method (NEM). The volume fractions of metal and ceramic are expressed by the power-law function and the cosine-type porosity distributions are considered. The proposed numerical method is demonstrated through the benchmark experiment, and the differences between two analysis models are parametrically investigated with respect to the thickness-wise material and porosity distributions. It is found from the numerical results that the difference cannot be negligible when the material and porosity distributions are remarkably biased in the thickness direction.

• 터널과지하공간
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• 제22권1호
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• pp.69-76
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• 2012

본 논문은 폭약의 폭발현상을 이용한 폭발용접, 폭발성형과 충격분말고화기술의 기본적 원리와 실험방법, 실험결과에 대하여 기술한다. 타이타늄(Ti)과 스테인레스 강(Stainless steel, SUS 304) 판재의 폭발용접 실험결과, 두 재료 접촉면의 단면에서는 연속적인 젯(jet)모양의 파형이 관찰되었고, 두 금속판재의 설치 경사각도가 $15{\sim}20^{\circ}$ 이고 접착속도가 2,100~2,800 m/s인 경우에 최적의 접합조건을 보였다. 알루미늄(Al) 판재를 이용한 폭발성형 실험과 전형적인 가압성형 실험 결과를 비교분석하여, 폭발성형의 경우가 큰 곡률변형을 보여 가공성이 우수한 것으로 확인되었다. 끝으로 금속과 세라믹의 혼합분말($Fe_{11.2}La_2O_3Co_{0.7}Si_{1.1}$)에 대한 충격고화 실험법을 제안하고 실험을 수행한 결과, 고화체의 표면과 내부에 균열이 확인되지 않았으며 세라믹입자와 금속입자들의 강한 미세조직 결합이 형성되었다. 또한 충격분말고화실험에서 발생되는 폭약의 폭발에 의한 폭굉파와 수중 충격파의 전파 및 간섭현상을 분석하기 위하여 LS-Dyna 3D를 이용한 동적해석을 수행하였다. 그 결과, 물용기 내 벽면에서 반사된 수중충격파가 중앙부에서 중첩되어 폭약의 폭발압력보다 높은 20 GPa의 수중 충격압을 보여, 물용기 내부형상의 중요성을 입증하였다.

• Steel and Composite Structures
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• 제43권6호
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• pp.821-837
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• 2022

This research is devoted to study the effects of humidity and temperature on the bending behavior of functionally graded (FG) ceramic-metal porous plates resting on Pasternak elastic foundation using a quasi-3D hyperbolic shear deformation theory developed recently. The present plate theory with only four unknowns, takes into account both transverse shear and normal deformations and satisfies the zero traction boundary conditions on the surfaces of the functionally graded plate without using shear correction factors. Material properties of porous FG plate are defined by rule of the mixture with an additional term of porosity in the through-thickness direction. The governing differential equations are obtained using the "principle of virtual work". Analytically, the Navier method is used to solve the equations that govern a simply supported FG porous plate. The obtained results are checked by comparing the results determined for the perfect and imperfect FG plates with those available in the scientific literature. Effects due to material index, porosity factors, moisture and thermal loads, foundation rigidities, geometric ratios on the FG porous plate are all examined. Finally, this research will help us to design advanced functionally graded materials to ensure better durability and efficiency for hygro-thermal environments.