• Advances in aircraft and spacecraft science
• /
• 제6권3호
• /
• pp.189-206
• /
• 2019

In this work, a novel first-order shear deformation beam theory is applied to explore the vibration and buckling characteristics of thick functionally graded beams. The material properties are assumed to vary across the thickness direction in a graded form and are estimated by a power-law model. A Fourier series-based solution procedure is implemented to solve the governing equation derived from Hamilton's principle. The obtained results of natural frequencies and buckling loads of functionally graded beam are checked with those supplied in the literature and demonstrate good achievement. Influences of several parameters such as power law index, beam geometrical parameters, modulus ratio and axial load on dynamic and buckling behaviors of FGP beams are all discussed.

• Coupled systems mechanics
• /
• 제13권1호
• /
• pp.43-60
• /
• 2024

This work presents an analytical approach to investigate wave propagation in bi-directional functionally graded cantilever porous beam. The formulations are based on Touratier's higher-order shear deformation beam theory. The physical properties of the porous functionally graded material beam are graded through the width and thickness using a power law distribution. Two porosities models approximating the even and uneven porosity distributions are considered. The governing equations of the wave propagation in the porous functionally graded beam are derived by employing the Hamilton's principle. Closed-form solutions for various parameters and porosity types are obtained, and the numerical results are compared with those available in the literature.The numerical results show the power law index, number of wave, geometrical parameters and porosity distribution models affect the dynamic of the FG beam significantly.

• Steel and Composite Structures
• /
• 제43권1호
• /
• pp.117-127
• /
• 2022

This study investigates the wave propagation in porous functionally graded (FG) sandwich plates subjected to hygrothermal environments. A new simple three-unknown first-ordershear deformation theory (FSDT) incorporating an integral term is utilized in this paper. Only three unknowns are used to formulate the governing differential equation by applying the Hamilton principle. The FG layer of the sandwich plate is modeled using the power-law function with evenly distributed porosities to represent the defects of the manufacturing process. The plate is subjected to nonlinear hygrothermal changes across the thickness. The effects of the power-law exponent, core to thickness ratios, porosity volume, and the relations between volume fraction and wave properties of porous FG plate under the hygrothermal environment are investigated. The results showed that the waves' phase velocities increase linearly with the waves number in the FGM plate. The porosity of the FG materials plate has a noticeable impact on the phase velocity when considering the high ratios of the core layer. It has a negligible effect on small core layers. Finally, it is observed that changing temperatures and moistures do not influence the relationship between the power law and the phase velocity.

• 한국재료학회지
• /
• 제19권12호
• /
• pp.674-679
• /
• 2009

Yttria stabilized zirconia single crystals show plastic deformation at high temperatures by activating dislocations. The plastic deformation is highly dependent on crystallographic orientation. When the samples were deformed at different orientations, stress-strain curves changed by operating different slip systems. The strength of samples was also highly dependent on crystallographic orientation, i.e., samples without yield drop showed higher strength than that of samples exhibiting yield drop. The slip systems in the sample deformed along <112>, <111> and <001> agreed with the theoretical values of the plastic deformation, following Schmid's Law. Dislocations play a major role in the plastic deformation of this crystal. At the early stages of plastic deformation, all samples exhibited dislocation dipoles and, in the later stages, dislocation interactions occurred by forming nodes, tangles and networks. In this study, three different orientations, [11-2], [111] and [001] were employed to explain the plastic deformation behavior. A microstructural analysis was performed to elucidate the mechanism of the plastic behavior of this crystal.

• Smart Structures and Systems
• /
• 제20권3호
• /
• pp.369-383
• /
• 2017

In this work, the effects of moisture and temperature on free vibration characteristics of functionally graded (FG) nanobeams resting on elastic foundation is studied by proposing a novel simple trigonometric shear deformation theory. The main advantage of this theory is that, in addition to including the shear deformation influence, the displacement field is modeled with only 2 unknowns as the case of the classical beam theory (CBT) and which is even less than the Timoshenko beam theory (TBT). Three types of environmental condition namely uniform, linear, and sinusoidal hygrothermal loading are studied. Material properties of FG beams are assumed to vary according to a power law distribution of the volume fraction of the constituents. Equations of motion are derived from Hamilton's principle. Numerical examples are presented to show the validity and accuracy of present shear deformation theories. The effects of hygro-thermal environments, power law index, nonlocality and elastic foundation on the free vibration responses of FG beams under hygro-thermal effect are investigated.

• Wind and Structures
• /
• 제27권4호
• /
• pp.269-282
• /
• 2018

In this paper, a new displacement field based on quasi-3D hybrid-type higher order shear deformation theory is developed to analyze the static and dynamic response of exponential (E), power-law (P) and sigmoïd (S) functionally graded beams. Novelty of this theory is that involve just three unknowns with including stretching effect, as opposed to four or even greater numbers in other shear and normal deformation theories. It also accounts for a parabolic distribution of the transverse shear stresses across the thickness, and satisfies the zero traction boundary conditions at beams surfaces without introducing a shear correction factor. The beam governing equations and boundary conditions are determined by employing the Hamilton's principle. Navier-type analytical solutions of bending and free vibration analysis are provided for simply supported beams subjected to uniform distribution loads. The effect of the sigmoid, exponent and power-law volume fraction, the thickness stretching and the material length scale parameter on the deflection, stresses and natural frequencies are discussed in tabular and graphical forms. The obtained results are compared with previously published results to verify the performance of this theory. It was clearly shown that this theory is not only accurate and efficient but almost comparable to other higher order shear deformation theories that contain more number of unknowns.

• Structural Engineering and Mechanics
• /
• 제89권3호
• /
• pp.225-238
• /
• 2024

In this paper, a quasi-3D hyperbolic shear deformation theory for the bending responses of a functionally graded (FG) porous micro-beam is based on a modified couple stress theory requiring only one material length scale parameter that can capture the size influence. The model proposed accounts for both shear and normal deformation effects through an illustrative variation of all displacements across the thickness and satisfies the zero traction boundary conditions on the top and bottom surfaces of the micro-beam. The effective material properties of the functionally graded micro-beam are assumed to vary in the thickness direction and are estimated using the homogenization method of power law distribution, which is modified to approximate the porous material properties with even and uneven distributions of porosity phases. The equilibrium equations are obtained using the virtual work principle and solved using Navier's technique. The validity of the derived formulation is established by comparing it with the ones available in the literature. Numerical examples are presented to investigate the influences of the power law index, material length scale parameter, beam thickness, and shear and normal deformation effects on the mechanical characteristics of the FG micro-beam. The results demonstrate that the inclusion of the size effects increases the microbeams stiffness, which consequently leads to a reduction in deflections. In contrast, the shear and normal deformation effects are just the opposite.

• 한국자동차공학회논문집
• /
• 제17권5호
• /
• pp.115-126
• /
• 2009

This paper studied on the application of the crashworthiness regulations of Korean Railway Safety Law and Urban Transit Safety Law to the urban Maglev vehicle of KIMM. The Urban Maglev vehicle has to comply with the crashworthiness regulations for urban transit vehicles. The collision load cases have been simulated by using explicit finite element analysis. From the numerical results, the crashworthiness regulations of the Urban Transit Safety Law were completely satisfied, but maximum crash pulse requirement in 25 km/h crash event and no plastic deformation requirement in 10 km/h crash event in the Korean Railway Safety Law were not. If a commercial urban Maglev vehicle is developed in the near future, it is necessary that some soft buffing and energy absorbing devices are adopted in its front end so as to satisfy the crashworthiness regulations of the Korean Railway Safety Law.

• 한국해양공학회지
• /
• 제20권3호
• /
• pp.103-108
• /
• 2006

It has been well appreciated that reducing weld-induced deformation as law as possible is important during fabrication for a more efficient production of blocks. The weld-induced deformation is more serious in thin plates than in thick plates because heat affect zone of thin plates is wider than that of thick plates and in addition internal and external constraints much more influence upon weld-induced deformation of thin plates. This paper deals with the application of the mechanical tensioning method to butt weld of thin plates to reduce the weld-induced deformation. In order to investigate the quantitative effect of tensioning method upon the reduction of angular deformation and shrinkage in longitudinal and transverse direction of weld line, butt welding test have been carried out for several thin plate specimens with varying plate thickness and magnitude of tensile load. From the present experimental study, it has been found that the tensioning method is very effective on reduction of weld-induced residual stress as well as weld-induced deformation.

• Geomechanics and Engineering
• /
• 제11권2호
• /
• pp.289-307
• /
• 2016

A simple hyperbolic shear deformation theory taking into account transverse shear deformation effects is proposed for the free flexural vibration analysis of thick functionally graded plates resting on elastic foundations. By considering further supposition, the present formulation introduces only four unknowns and its governing equations are therefore reduced. Hamilton's principle is employed to obtain equations of motion and Navier-type analytical solutions for simply-supported plates are compared with the available solutions in literature to check the accuracy of the proposed theory. Numerical results are computed to examine the effects of the power-law index and side-to-thickness ratio on the natural frequencies.