• 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.

• Journal of Mechanical Science and Technology
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• 제14권3호
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• pp.298-305
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• 2000

The functionally graded material (FGM) is the new concept for a heat resisting material. FGM consists of ceramics on one side and metal on the other. A composition and microstructure of an intermediate layer change continuously from ceramics to metal at the micron level. This study is carried out to analyze the thermal shock characteristics of functionally graded PSZ/ metal composites. Heat-resistant property was evaluated by gas burner heating test using $C_2H_2/O_2$ combustion flame. The ceramic surface was heated with burner flame and the bottom surface cooled with water flow. Also, the composition profile and the thickness of the graded layer were varied to study the thermo mechanical response. Furthermore, this study carried out the thermal stress analysis to investigate the thermal characteristics by the finite element method. Acoustic emission (AE) monitoring was performed to detect the microfracture process in a thermal shock test.

• Structural Engineering and Mechanics
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• 제56권6호
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• pp.1003-1020
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• 2015

In this study, free vibration analysis of an edge cracked multilayered symmetric sandwich beams made of functionally graded materials are investigated. Modelling of the cracked structure is based on the linear elastic fracture mechanics theory. Material properties of the functionally graded beams change in the thickness direction according to the power and exponential laws. To represent functionally graded symmetric sandwich beams more realistic, fifty layered beam is considered. Composition of each layer is different although each layer is isotropic and homogeneous. The considered problem is carried out within the Timoshenko first order shear deformation beam theory by using finite element method. A MATLAB code developed to calculate natural frequencies for clamped and simply supported conditions. The obtained results are compared with published studies and excellent agreement is observed. In the study, the effects of crack location, depth of the crack, power law index and slenderness ratio on the natural frequencies are investigated.

• Structural Engineering and Mechanics
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• 제20권4호
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• pp.435-450
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• 2005

Here, the dynamic instability characteristics of aero-thermo-mechanically stressed functionally graded plates are investigated using finite element procedure. Temperature field is assumed to be a uniform distribution over the plate surface and varied in thickness direction only. Material properties are assumed to be temperature dependent and graded in the thickness direction according to simple power law distribution. For the numerical illustrations, silicon nitride/stainless steel is considered as functionally graded material. The aerodynamic pressure is evaluated based on first-order high Mach number approximation to the linear potential flow theory. The boundaries of the instability region are obtained using the principle of Bolotin's method and are conveniently represented in the non-dimensional excitation frequency-load amplitude plane. The variation dynamic instability width is highlighted considering various parameters such as gradient index, temperature, aerodynamic and mechanical loads, thickness and aspect ratios, and boundary condition.

• Structural Engineering and Mechanics
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• 제81권2호
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• pp.179-194
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• 2022

The bending, buckling and free vibration responses of functionally graded material (FGM) beams are investigated semi-analytically by the scaled boundary finite element method (SBFEM) in this paper. In the concepts of the SBFEM, the dimension of computational domain can be reduced by one, therefore only the axial dimension of the beam is discretized using the higher order spectral element, which reduces the amount of calculation and greatly improves the calculation efficiency. The governing equation of FGM beams is derived in detail by the means of the principle of virtual work. Compared with the higher-order beam theory, fewer parameters and simpler control equations are used. And the governing equation is transformed into a first-order ordinary differential equation by introducing intermediate variables. Analytical solutions of the governing equation can be obtained by pade series expansion in the direction of thickness. Numerical example are compared with the numerical solutions provided by the previous researchers to verify the accuracy and applicability of the proposed method. The results show that the proposed formulations can quickly converge to the reference solutions by increasing the order of higher order spectral elements, and high accuracy can be achieved by using a small number of the elements. In addition, the influence of the structural sizes, material properties and boundary conditions on the mechanical behaviors of FG beams subjected to different load types is discussed.

• 한국도로학회논문집
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• 제14권4호
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• pp.29-36
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• 2012

PURPOSES : Plastic deformation is frequently made in intersection asphalt pavement at its early age due to deceleration and stoppage of vehicles. This study has been performed to provide a mechanistic basis for reasonable selection of paving method to minimize the plastic deformation at intersection. METHODS : Pavement layer, temperature, traffic volume of the intersections managed by the Daejeon Regional Construction and Management Administration were collected to calculate asphalt dynamic modulus with pavement depth by using a prediction equation suggested by the Korean pavement design guide. Performance of ordinary dense-graded asphalt pavement, polymer modified asphalt pavement, and fiber reinforced asphalt pavement was analyzed by finite element method and the results were used in a performance model to predict the plastic deformation. RESULTS : In aspect of performance, the three paving methods were usable under low traffic while the fiber reinforced asphalt pavement was the most suitable under heavy traffic. CONCLUSIONS : Reasonable paving method suitable for traffic characteristics in the intersection might be decided by considering economic feasibility.

• Structural Engineering and Mechanics
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• 제85권4호
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• pp.445-459
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• 2023

The current investigation is the first endeavor to apply the full layerwise finite element method (FEM) in free vibration analysis of functionally graded (FG) composite plates reinforced with graphene nanoplatelets (GPLs) in thermal environment. Unlike the equivalent single-layer (ESL) theories, the layerwise FEM focuses on all three-dimensional (3D) effects. The GPLs weight fraction is presumed invariable in each layer but varies through the plate thickness in a layerwise model. The modified Halpin-Tsai model is employed to acquire the effective Young's modulus. The rule of mixtures is applied to specify the effective Poisson's ratio and mass density. First, the current method is validated by comparing the numerical results with those stated in the available works. Next, a thorough numerical study is performed to examine the influence of various factors involving the pattern of distribution, weight fraction, geometry, and size of GPLs, together with the thickness-to-span ratio, thermal environment, and boundary conditions of the plate, on its free vibration behaviors. Numerical results demonstrate that employing a small percentage of GPL as reinforcement considerably grows the natural frequencies of the pure epoxy. Also, distributing more square-shaped GPLs, involving a smaller amount of graphene layers, and vicinity to the upper and lower surfaces make it the most efficient method to enhance the free vibration behaviors of the plate.

• Steel and Composite Structures
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• 제16권1호
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• pp.77-96
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• 2014

In this paper, magneto-thermo-elastic problem of a thick truncated conical shell immersed in a uniform magnetic field and subjected to internal pressure is investigated. Material properties of the shell including the elastic modulus, magnetic permeability, coefficients of thermal expansion and conduction are assumed to be isotropic and graded through the thickness obeying the simple power law distribution, while the poison's ratio is assumed to be constant. The temperature distribution is assumed to be a function of the thickness direction. Governing equations of the truncated conical shell are derived in terms of components of displacement and thermal fields and discretised with the help of differential quadrature (DQ) method. Results are obtained for different values of power law index of material properties and effects of thermal load on displacement, stress, temperature and magnetic fields are studied. Results of the present method are compared with those of the finite element method.

• Smart Structures and Systems
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• 제25권6호
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• pp.669-678
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• 2020

This paper focuses on the free vibration analysis of axially functionally graded (FG) Euler-Bernoulli beams. The material properties of the beams are assumed to obey the linear law distribution. The complexities in solving differential equation of transverse vibration of composite beams which limit the analytical solution to some special cases are overcome using the Differential Transformation Method (DTM). Natural frequencies and corresponding normalized mode shapes are calculated. Validation targets are experimental data or finite element results. Different parameters such as reinforcement distribution, ratio of the reinforcement Young's modulus to the matrix Young's modulus and ratio of the reinforcement density to the matrix density are taken into investigation. The delivered results prove the capability and the robustness of the applied method. The studied parameters are demonstrated to be very crucial for the normalized natural frequencies and mode shapes.

• Steel and Composite Structures
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• 제48권1호
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• pp.73-88
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• 2023

This paper presents a novel implicit level set method for topology optimization of functionally graded (FG) structures with pre-existing discontinuities (pre-cracks) using radial basis functions (RBF). The mathematical formulation of the optimization problem is developed by incorporating RBF-based nodal densities as design variables and minimizing compliance as the objective function. To accurately capture crack-tip behavior, crack-tip enrichment functions are introduced, and an eXtended Finite Element Method (X-FEM) is employed for analyzing the mechanical response of FG structures with strong discontinuities. The enforcement of boundary conditions is achieved using the Hamilton-Jacobi method. The study provides detailed mathematical expressions for topology optimization of systems with defects using FG materials. Numerical examples are presented to demonstrate the efficiency and reliability of the proposed methodology.