• Structural Engineering and Mechanics
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• v.91 no.2
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• pp.197-209
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• 2024

The vibration of elastically supported bidirectional functionally graded (BDFG) sandwich beams on an elastic foundation is investigated. The sandwich structure is composed of upper and lower layers of BDFG material and the core layer of isotropic material. Material properties of upper and lower layers are assumed to vary continuously along the length and thickness of the beam with a power-law function. Hamilton's principle is used to deduce the vibration equations of motion of the sandwich Timoshenko beam. Then, the partial differential equation of motion is spatially discretized into a time-varying ordinary differential equation in terms of Chebyshev differential matrices. The eigenvalue equation associated with the free vibration is formulated to study the influence of various slenderness ratios, material gradient indexes, thickness ratios, foundation and support spring constants on the vibration frequency of BDFG sandwich beams. The present method can provide researchers with deep insight into the impact of various geometric, material, foundation and support parameters on the vibration behavior of BDFG sandwich beam structures.

• Smart Structures and Systems
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• v.20 no.6
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• pp.709-728
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• 2017

This disquisition proposes a nonlocal strain gradient beam theory for thermo-mechanical dynamic characteristics of embedded smart shear deformable curved piezoelectric nanobeams made of porous electro-elastic functionally graded materials by using an analytical method. Electro-elastic properties of embedded curved porous FG nanobeam are assumed to be temperature-dependent and vary through the thickness direction of beam according to the power-law which is modified to approximate material properties for even distributions of porosities. It is perceived that during manufacturing of functionally graded materials (FGMs) porosities and micro-voids can be occurred inside the material. Since variation of pores along the thickness direction influences the mechanical and physical properties, so in this study thermo-mechanical vibration analysis of curve FG piezoelectric nanobeam by considering the effect of these imperfections is performed. Nonlocal strain gradient elasticity theory is utilized to consider the size effects in which the stress for not only the nonlocal stress field but also the strain gradients stress field. The governing equations and related boundary condition of embedded smart curved porous FG nanobeam subjected to thermal and electric field are derived via the energy method based on Timoshenko beam theory. An analytical Navier solution procedure is utilized to achieve the natural frequencies of porous FG curved piezoelectric nanobeam resting on Winkler and Pasternak foundation. The results for simpler states are confirmed with known data in the literature. The effects of various parameters such as nonlocality parameter, electric voltage, coefficient of porosity, elastic foundation parameters, thermal effect, gradient index, strain gradient, elastic opening angle and slenderness ratio on the natural frequency of embedded curved FG porous piezoelectric nanobeam are successfully discussed. It is concluded that these parameters play important roles on the dynamic behavior of porous FG curved nanobeam. Presented numerical results can serve as benchmarks for future analyses of curve FG nanobeam with porosity phases.

• Structural Engineering and Mechanics
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• v.64 no.4
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• pp.487-494
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• 2017

The present paper deals with a theoretical study of delamination fracture in the Crack Lap Shear (CLS) functionally graded beam configuration. The basic purpose is to analyze the fracture with taking into account the material non-linearity. The mechanical behavior of CLS was described by using a non-linear stress-strain relation. It was assumed that the material is functionally graded along the beam height. The fracture was analyzed by applying the J-integral approach. The curvature and neutral axis coordinate of CLS beam were derived in order to solve analytically the J-integral. The non-linear solution of J-integral obtained was verified by analyzing the strain energy release rate with considering material non-linearity. The effects of material gradient, crack location along the beam height and material non-linearity on fracture behavior were evaluated. The J-integral non-linear solution derived is very suitable for parametric studies of longitudinal fracture in the CLS beam. The results obtained can be used to optimize the functionally graded beam structure with respect to the fracture performance. The analytical approach developed in the present paper contributes for the understanding of delamination fracture in functionally graded beams exhibiting material non-linearity.

• Proceedings of the Materials Research Society of Korea Conference
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• 1996.05a
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• pp.104-104
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• 1996

• Proceedings of the Materials Research Society of Korea Conference
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• 1996.05a
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• pp.52-52
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• 1996

• Proceedings of the Korean Ceranic Society Conference
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• 2002.10a
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• pp.126.1-126
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• 2002

• Proceedings of the Materials Research Society of Korea Conference
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• 1993.05a
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• pp.12-12
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• 1993

• Structural Engineering and Mechanics
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• v.64 no.5
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• pp.591-610
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• 2017

This paper is concerned with the static analysis of variable thickness of two directional functionally graded porous materials (FGPM) circular plate resting on a gradient hybrid foundation (Horvath-Colasanti type) with friction force and subjected to compound mechanical loads (e.g., transverse, in-plane shear traction and concentrated force at the center of the plate).The governing state equations are derived in terms of displacements based on the 3D theory of elasticity, assuming the elastic coefficients of the plate material except the Poisson's ratio varying continuously throughout the thickness and radial directions according to an exponential function. These equations are solved semi-analytically by employing the state space method (SSM) and one-dimensional differential quadrature (DQ) rule to obtain the displacements and stress components of the FGPM plate. The effect of concentrated force at the center of the plate is approximated with the shear force, uniformly distributed over the inner boundary of a FGPM annular plate. In addition to verification study and convergence analysis, numerical results are displayed to show the effect of material heterogeneity indices, foundation stiffness coefficients, foundation gradient indices, loads ratio, thickness to radius ratio, compressibility, porosity and friction coefficient of the foundation on the static behavior of the plate. Finally, the responses of FG and FG porous material circular plates to compound mechanical loads are compared.

• Steel and Composite Structures
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• v.18 no.1
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• pp.1-28
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• 2015

In this paper, the dynamic response of functionally gradient steel (FGS) composite cylindrical panels in steady-state thermal environments subjected to impulsive loads is investigated for the first time. FGSs composed of graded ferritic and austenitic regions together with bainite and martensite intermediate layers are analyzed. Thermo-mechanical material properties of FGS composites are predicted according to the microhardness profile of FGS composites and approximated with appropriate functions. Based on the three-dimensional theory of thermo-elasticity, the governing equations of motionare derived in spatial and time domains. These equations are solved using the hybrid Fourier series expansion-Galerkin finite element method-Newmark approach for simply supported boundary conditions. The present solution is then applied to the thermo-elastic dynamic analysis of cylindrical panels with three different arrangements of material compositions of FGSs including ${\alpha}{\beta}{\gamma}M{\gamma}$, ${\alpha}{\beta}{\gamma}{\beta}{\alpha}$ and ${\gamma}{\beta}{\alpha}{\beta}{\gamma}$ composites. Benchmark results on the displacement and stress time-histories of FGS cylindrical panels in thermal environments under various pulse loads are presented and discussed in detail. Due to the absence of similar results in the specialized literature, this paper is likely to fill a gap in the state of the art of this problem, and provide pertinent results that are instrumental in the design of FGS structures under time-dependent mechanical loadings.

• Nuclear Engineering and Technology
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• v.52 no.8
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• pp.1706-1713
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• 2020

Functionally gradient material (FGM) is promisingly effective in mitigating the thermal stress between plasma facing materials (PFM) and structural materials. However, the corresponding research with respect to W/V FGM has not been reported yet. In this work, we firstly report the successful fabrication of W/V FGM by a combined technology of mechanical alloying (MA) and spark plasma sintering (SPS). The microhardness and microstructure of the consolidated sample were both investigated. W/V stacks show significantly enhanced microhardness (>100%) compared with pure W plate, which is beneficial to the integral strength of the hybrid structure. Furthermore, we clarify that the different ductility of W and V should be carefully considered, otherwise W/V powder might aggregate and lead to the formation of compositional segregation, and simultaneously unmask the impact of V proportion on the distribution of second phase in W-V binary alloy system. This work provides an innovative approach for obtaining W-V connections with much better performance.