• Advances in nano research
• /
• v.17 no.2
• /
• pp.181-195
• /
• 2024

This study introduces a novel functionally graded material model, termed the "Coated Functionally Graded Graphene-Reinforced Composite (FG GRC)" model, for investigating the free vibration response of plates, highlighting its potential to advance the understanding and application of material property variations in structural engineering. Two types of coated FG GRC plates are examined: Hardcore and Softcore, and five distribution patterns are proposed, namely FG-A, FG-B, FG-C, FG-D, and FG-E. A modified displacement field is proposed based on the higher-order shear deformation theory, effectively reducing the number of variables from five to four while accurately accounting for shear deformation effects. To solve the equations of motion, an analytical solution based on the Galerkin approach was developed for FG GRC plates resting on a viscoelastic Winkler/Pasternak foundation, applicable to various boundary conditions. A comprehensive parametric analysis elucidates the impact of multiple factors on the fundamental frequencies. These factors encompass the types and distribution patterns of the coated FG GRC plates, gradient material distribution, porosities, nonlocal length scale parameter, gradient material scale parameter, nanoplate geometry, and variations in the elastic foundation. Our theoretical research aims to overcome the inherent challenges in modeling structures, providing a robust alternative to experimental analyses of the mechanical behavior of complex structures.

• Structural Engineering and Mechanics
• /
• v.58 no.6
• /
• pp.1045-1075
• /
• 2016

Shallow footings are one of the most common types of foundations used to support mid-rise buildings in high risk seismic zones. Recent findings have revealed that the dynamic interaction between the soil, foundation, and the superstructure can influence the seismic response of the building during earthquakes. Accordingly, the properties of a foundation can alter the dynamic characteristics (natural frequency and damping) of the soil-foundation-structure system. In this paper the influence that shallow foundations have on the seismic response of a mid-rise moment resisting building is investigated. For this purpose, a fifteen storey moment resisting frame sitting on shallow footings with different sizes was simulated numerically using ABAQUS software. By adopting a direct calculation method, the numerical model can perform a fully nonlinear time history dynamic analysis to realistically simulate the dynamic behaviour of soil, foundation, and structure under seismic excitations. This three-dimensional numerical model accounts for the nonlinear behaviour of the soil medium and structural elements. Infinite boundary conditions were assigned to the numerical model to simulate free field boundaries, and appropriate contact elements capable of modelling sliding and separation between the foundation and soil elements are also considered. The influence of foundation size on the natural frequency of the system and structural response spectrum was also studied. The numerical results for cases of soil-foundation-structure systems with different sized foundations and fixed base conditions (excluding soil-foundation-structure interaction) in terms of lateral deformations, inter-storey drifts, rocking, and shear force distribution of the structure were then compared. Due to natural period lengthening, there was a significant reduction in the base shears when the size of the foundation was reduced. It was concluded that the size of a shallow foundation influences the dynamic characteristics and the seismic response of the building due to interaction between the soil, foundation, and structure, and therefore design engineer should carefully consider these parameters in order to ensure a safe and cost effective seismic design.

• Advances in aircraft and spacecraft science
• /
• v.3 no.2
• /
• pp.113-148
• /
• 2016

In a whole variety of higher order plate theories existing in the literature no consideration is given to the transverse normal strain / deformation effects on flexural response when these higher order theories are applied to shear flexible composite plates in view of minimizing the number of unknown variables. The objective of this study is to carry out cylindrical bending of simply supported laminated composite and sandwich plates using sinusoidal shear and normal deformation plate theory. The most important feature of the present theory is that it includes the effects of transverse normal strain/deformation. The displacement field of the presented theory is built upon classical plate theory and uses sine and cosine functions in terms of thickness coordinate to include the effects of shear deformation and transverse normal strain. The theory accounts for realistic variation of the transverse shear stress through the thickness and satisfies the shear stress free conditions at the top and bottom surfaces of the plate without using the problem dependent shear correction factor. Governing equations and boundary conditions of the theory are obtained using the principle of minimum potential energy. The accuracy of the proposed theory is examined for several configurations of laminates under various static loadings. Some problems are presented for the first time in this paper which can become the base for future research. For the comparison purpose, the numerical results are also generated by using higher order shear deformation theory of Reddy, first-order shear deformation plate theory of Mindlin and classical plate theory. The numerical results show that the present theory provides displacements and stresses very accurately as compared to those obtained by using other theories.

• Steel and Composite Structures
• /
• v.18 no.2
• /
• pp.443-465
• /
• 2015

In this paper, an efficient and simple trigonometric shear deformation theory is presented for thermal buckling analysis of functionally graded plates. It is assumed that the plate is in contact with elastic foundation during deformation. The theory accounts for sinusoidal distribution of transverse shear stress, and satisfies the free transverse shear stress conditions on the top and bottom surfaces of the plate without using shear correction factor. Unlike the conventional trigonometric shear deformation theory, the proposed sinusoidal shear deformation theory contains only four unknowns. It is assumed that the mechanical and thermal non-homogeneous properties of functionally graded plate vary smoothly by distribution of power law across the plate thickness. Using the non-linear strain-displacement relations, the equilibrium and stability equations of plates made of functionally graded materials are derived. The boundary conditions for the plate are assumed to be simply supported on all edges. The elastic foundation is modelled by two-parameters Pasternak model, which is obtained by adding a shear layer to the Winkler model. The effects of thermal loading types and variations of power of functionally graded material, aspect ratio, and thickness ratio on the critical buckling temperature of functionally graded plates are investigated and discussed.

• Steel and Composite Structures
• /
• v.42 no.6
• /
• pp.805-826
• /
• 2022

The free and live load-forced vibration behaviour of porous functionally graded (PFG) higher order nanobeams in the thermal and magnetic fields is investigated comprehensively through this work in the framework of nonlocal strain gradient theory (NLSGT). The porosity effects on the dynamic behaviour of FG nanobeams is investigated using four different porosity distribution models. These models are exploited; uniform, symmetrical, condensed upward, and condensed downward distributions. The material characteristics gradation in the thickness direction is estimated using the power-law. The magnetic field effect is incorporated using Maxwell's equations. The third order shear deformation beam theory is adopted to incorporate the shear deformation effect. The Hamilton principle is adopted to derive the coupled thermomagnetic dynamic equations of motion of the whole system and the associated boundary conditions. Navier method is used to derive the analytical solution of the governing equations. The developed methodology is verified and compared with the available results in the literature and good agreement is observed. Parametric studies are conducted to show effects of porosity parameter; porosity distribution, temperature rise, magnetic field intensity, material gradation index, non-classical parameters, and the applied moving load velocity on the vibration behavior of nanobeams. It has been showed that all the analyzed conditions have significant effects on the dynamic behavior of the nanobeams. Additionally, it has been observed that the negative effects of moving load, porosity and thermal load on the nanobeam dynamics can be reduced by the effect of the force induced from the directed magnetic field or can be kept within certain desired design limits by controlling the intensity of the magnetic field.

• Journal of the Korea institute for structural maintenance and inspection
• /
• v.20 no.5
• /
• pp.93-101
• /
• 2016

In this study, the governing equations of motion for multi-cracked nonuniform nanobeam based on nonlocal elasticity theory and embedded in an elastic medium were derived. DTM(differential transformation method) was applied to vibration analysis of multi-cracked nonuniform nanobeam based on nonlocal elasticity theory and embedded in an elastic medium. The non-dimensional natural frequencies of this nanobeam were obtained for eoe, crack stiffness and elastic medium stiffness with various boundary conditions. The results obtained by this method was compared with previous works and showed the close agreement between two methods. The important conclusions obtained by this study are as follows : 1. As the length of nanobeam is shorter, the effect of scale coefficient is greater. 2. The locations of crack change non-dimensional natural frequency, In the case of fixed-fixed ends, the non-dimensional natural frequency is the biggest in the first crack location of 0.6L of nanobeam length, and the smallest in both ends. In the case of fixed-free ends, the closer the location of first crack go tho the free end, the bigger the non-dimensional natural frequency. 3. As the stiffness of crack is greater, the non-dimensional natural frequency is smaller, And the effect of crack stiffness is similar on both fixed-free ends and fixed-fixed ends. 4. The bigger the stiffness of elastic medium, the greater the non - dimensional natural frequency.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.29 no.6
• /
• pp.529-538
• /
• 2016

The simplified plate theory is presented for static and free vibration analysis of power-law(P) and sigmoid(S) Functionally Graded Materials(FGM) plates. This theory considers the parabolic distribution of the transverse shear stress, and satisfies the condition that requires the transverse shear stress to be zero on the upper and lower surfaces of the plate, without the shear correction factor. The simplified plate theory uses only four unknown variables and shares strong similarities with classical plate theory(CPT) in many aspects such as stress-resultant expressions, equation of motion and boundary conditions. The material properties of the plate are assumed to vary according to the power-law and sigmoid distributions of the volume fractions of the constituents. The Hamilton's principle is used to derive the equations of motion and Winkler-Pasternak elastic foundation model is employed. The results of static and dynamic responses for a simply supported FGM plate are calculated and a comparative analysis is carried out. The results of the comparative analysis with the solutions of references show relevant and accurate results for static and free vibration problems of FGM plates. Analytical solutions for the static and free vibration problems are presented so as to reveal the effects of the power law index, elastic foundation parameter, and side-to-thickness ratio.

• Investigative Magnetic Resonance Imaging
• /
• v.23 no.4
• /
• pp.328-340
• /
• 2019

Purpose: To generate phase images with free of motion-induced artifact and susceptibility-induced distortion using 3D radial ultrashort TE (UTE) MRI. Materials and Methods: The field map was theoretically derived by solving Laplace's equation with appropriate boundary conditions, and used to simulate the image distortion in conventional spin-warp MRI. Manufacturer's 3D radial imaging sequence was modified to acquire maximum number of radial spokes in a given time, by removing the spoiler gradient and sampling during both rampup and rampdown gradient. Spoke direction randomly jumps so that a readout gradient acts as a spoiling gradient for the previous spoke. The custom raw data was reconstructed using a homemade image reconstruction software, which is programmed using Python language. The method was applied to a phantom and in-vivo human brain and abdomen. The performance of UTE was compared with 3D GRE for phase mapping. Local phase mapping was compared with T₂* mapping using UTE. Results: The phase map using UTE mimics true field-map, which was theoretically calculated, while that using 3D GRE revealed both motion-induced artifact and geometric distortion. Motion-free imaging is particularly crucial for application of phase mapping for abdomen MRI, which typically requires multiple breathold acquisitions. The air pockets, which are caught within the digestive pathway, induce spatially varying and large background field. T₂* map, that was calculated using UTE data, suffers from non-uniform T₂* value due to this background field, while does not appear in the local phase map of UTE data. Conclusion: Phase map generated using UTE mimicked the true field map even when non-zero susceptibility objects were present. Phase map generated by 3D GRE did not accurately mimic the true field map when non-zero susceptibility objects were present due to the significant field distortion as theoretically calculated. Nonetheless, UTE allows for phase maps to be free of susceptibility-induced distortion without the use of any post-processing protocols.

• Journal of the Korean Geotechnical Society
• /
• v.27 no.12
• /
• pp.107-116
• /
• 2011

Rigid soil containers (or rigid boxes) are often used for 1g shaking table tests. The rigid boxes, however, do not accurately simulate the amplification of ground acceleration and phase difference of seismic motion in the model ground due to the confinement of shear deformation and the reflection of seismic wave at the box walls. Laminar soil containers (or laminar shear boxes) can simulate the free field motion at convincingly superior accuracy than the rigid ones. In this study, the soft ground is modeled for both types of boxes and is subjected to seismic loading using a 1g shaking table. The comparison of the results using the two types of soil containers illustrates that, in case of the rigid box, the ground acceleration shows non uniform distribution and the phase synchronization of input motion. Whereas, the dynamic behavior of the laminar shear box shows good agreement with the free field behaviors such as the amplification of ground acceleration and the occurrence of phase difference.

• Journal of the Earthquake Engineering Society of Korea
• /
• v.20 no.4
• /
• pp.223-234
• /
• 2016

To investigate earthquake responses of structures with basements affected by soil deposits, centrifuge tests were performed using an in-flight earthquake simulator. The test specimen was composed of a single-degree-of-freedom structure model, a basement and sub-soil deposits in a centrifuge container. The test parameters were the dynamic period of the structure model, boundary conditions of the basement, existence of soil deposits, centrifugal acceleration level, and type and level of input earthquake accelerations. When soil deposits did not exist, the earthquake responses of the structures with fixed basement were significantly greater than those of the structure without basement. Also, the earthquake responses of the structures with the fixed basement surrounded by soil deposits were amplified, but the amplifications were smaller than those of the structures without basement. The earthquake responses of the structures with the half-embedded basement in the soil deposits were greater than those estimated by the fixed base model using the measured free-field ground motion. The test showed that the basement and the soil deposit should be simultaneously considered in the numerical analysis model, and the stiffness of the half-embedded was not effective.