• Steel and Composite Structures
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• v.39 no.1
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• pp.95-107
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• 2021

In this work, the dynamic response of functionally graded beams on variable elastic foundations is studied using a novel higher-order shear deformation theory (HSDT). Unlike the conventional HSDT, the present one has a new displacement field which introduces undetermined integral variables. The FG beams were assumed to be supported on Winkler-Pasternak type foundations in which the Winkler modulus is supposed to be variable in the length of the beam. The variable rigidity of the elastic foundation is assumed to be linear, parabolic and sinusoidal along the length of the beam. The material properties of the FG porous beam vary according to a power law distribution in terms of the volume fraction of the constituents. The equations of motion are determined using the virtual working principle. For the analytical solution, Navier method is used to solve the governing equations for simply supported porous FG beams. Numerical results of the present theory for the free vibration of FG beams resting on elastic foundations are presented and compared to existing solutions in the literature. A parametric study will be detailed to investigate the effects of several parameters such as gradient index, thickness ratio, porosity factor and foundation parameters on the frequency response of porous FG beams.

• Advances in nano research
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• v.14 no.3
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• pp.211-224
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• 2023

This work presents a modified analytical model for the bending behavior of axially functionally graded (AFG) carbon nanotubes reinforced composite (CNTRC) nanobeams. New higher order shear deformation beam theory is exploited to satisfy parabolic variation of shear through thickness direction and zero shears at the bottom and top surfaces.A Modified continuum nonlocal strain gradient theoryis employed to include the microstructure and the geometrical nano-size length scales. The extended rule of the mixture and the molecular dynamics simulations are exploited to evaluate the equivalent mechanical properties of FG-CNTRC beams. Carbon nanotubes reinforcements are distributed axially through the beam length direction with a new power graded function with two parameters. The equilibrium equations are derived with associated nonclassical boundary conditions, and Navier's procedure are used to solve the obtained differential equation and get the response of nanobeam under uniform, linear, or sinusoidal mechanical loadings. Numerical results are carried out to investigate the impact of inhomogeneity parameters, geometrical parameters, loadings type, nonlocal and length scale parameters on deflections and stresses of the AFG CNTRC nanobeams. The proposed model can be used in the design and analysis of MEMS and NEMS systems fabricated from carbon nanotubes reinforced composite nanobeam.

• Structural Engineering and Mechanics
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• v.86 no.1
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• pp.1-16
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• 2023

The free vibration of temperature-dependent functionally graded plates (FGPs) resting on a viscoelastic foundation is investigated in this paper using a newly developed simple first-order shear deformation theory (FSDT). Unlike other first order shear deformation (FSDT) theories, the proposed model contains only four variables' unknowns in which the transverse shear stress and strain follow a parabolic distribution along the plates' thickness, and they vanish at the top and bottom surfaces of the plate by considering a new shape function. For this reason, the present theory requires no shear correction factor. Linear steady-state thermal loads and power-law material properties are supposed to be graded across the plate's thickness. Uniform, linear, non-linear, and sinusoidal thermal rises are applied at the two surfaces for simply supported FGP. Hamilton's principle and Navier's approach are utilized to develop motion equations and analytical solutions. The developed theory shows progress in predicting the frequencies of temperature-dependent FGP. Numerical research is conducted to explain the effect of the power law index, temperature fields, and damping coefficient on the dynamic behavior of temperature-dependent FGPs. It can be concluded that the equation and transformation of the proposed model are as simple as the FSDT.

• Steel and Composite Structures
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• v.49 no.3
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• pp.307-323
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• 2023

In this research, the study of the thermoelastic flexural analysis of silicon carbide/Aluminum graded (FG) sandwich 2D uniform structure (plate) under harmonic sinusoidal temperature load over time is presented. The plate is modeled using a simple two dimensional integral shear deformation plate theory. The current formulation contains an integral terms whose aim is to reduce a number of variables compared to others similar solutions and therefore minimize the computation time. The transverse shear stresses vary according to parabolic distribution and vanish at the free surfaces of the structure without any use of correction factors. The external load is applied on the upper face and varying in the thickness of the plates. The structure is supposed to be composed of "three layers" and resting on nonlinear visco-Pasternak's-foundations. The governing equations of the system are deduced and solved via Hamilton's principle and general solution. The computed results are compared with those existing in the literature to validate the current formulation. The impacts of the parameters (material index, temperature exponent, geometry ratio, time, top/bottom temperature ratio, elastic foundation type, and damping coefficient) on the dynamic flexural response are studied.

• Earthquakes and Structures
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• v.26 no.2
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• pp.131-147
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• 2024

Damage caused by an earthquake depends on not just the intensity of an earthquake but also the region-specific construction practices. Past earthquakes in Asian countries have highlighted inadequate construction practices, which caused huge life and property losses, indicating the severe need to strengthen existing structures. Strengthening activities shall be proposed as per the proposed weighting factors, first at the higher weighted members to increase the capacity of the building immediately and thereafter, the other members. Through this study on gravity load-designed (GLD) buildings, relative weights are assigned to each storey and exterior and interior columns within a storey based on their contribution to the energy dissipation capacity of the building. The numerical study is conducted on mid-rise archetype GLD buildings, i.e., 4, 6, 8, and 10 stories with variable storey heights, in the high seismic zones. Non-linear static analysis is performed to compute weights based on energy dissipation capacities. The results obtained are verified with the non-linear time history analysis of 4 GLD buildings. It was observed that exterior columns have higher weightage in the energy dissipation capacity of the building than interior columns up to a certain building height. The damage in stories is distributed in a convex to concave parabolic shape from bottom to top as building height increases, and the maxima location of the parabola shifts from bottom to middle stories. Relative weighting factors are assigned as per the damage contribution. And the sequence for strengthening activities is proposed as per the computed weighting factors in descending order for regular RCC buildings. Therefore, proposals made in the study would increase the efficacy of strengthening activities.

• Computers and Concrete
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• v.33 no.1
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• pp.27-39
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• 2024

In this study, the authors investigate the free vibration behavior of three-phases functionally graded sandwich plates using a novel nth-order shear deformation theory. These plates are composed of a homogeneous core and two face-sheet layers made of different functionally graded materials. This is the novel type of the sandwich structures that can be applied in many fields of mechanical engineering and industrial. The proposed theory only requires four unknown displacement functions, and the transverse displacement does not need to be separated into bending and shear parts, simplifying the theory. One noteworthy feature of the proposed theory is its ability to capture the parabolic distribution of transverse shear strains and stresses throughout the plate's thickness while ensuring zero values on the two free surfaces. By eliminating the need for shear correction factors, the theory further enhances computational efficiency. Equations of motion are established using Hamilton's principle and solved via Navier's solution. The accuracy and efficiency of the proposed theory are verified by comparing results with available solutions. The authors then use the proposed theory to investigate the free vibration characteristics of three-phases functionally graded sandwich plates, considering the effects of parameters such as aspect ratio, side-to-thickness ratio, skin-core-skin thicknesses, and power-law indexes. Through careful analysis of the free vibration behavior of three-phases functionally graded sandwich plates, the work highlighted the significant roles played by individual material ingredients in influencing their frequencies.

• Journal of the Korea Concrete Institute
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• v.16 no.6 s.84
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• pp.841-850
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• 2004

The modeling of uplift pressure within dam, on the foundation on which it was constructed, and on the interface between the dam and foundation is a critical aspect in the analysis of concrete gravity dams, i.e. crack stability in concrete dam can correctly be predicted when uplift pressures are accurately modelled. Current models consider a uniform uplift distribution, but recent experimental results show that it varies along the crack faces and the procedures for modeling uplift pressures are well established for the traditional hand-calculation methods, but this is not the case for finite element (FE) analysis. In large structures, such as dams, because of smaller size of the fracture process zone with respect to the structure size, limited errors should occur under the assumptions of linear elastic fracture mechanics (LEFM). In this paper, the fracture behaviour of concrete gravity dams mainly subjected to uplift Pressure at the crack face was studied. Triangular type, trapezoidal type and parabolic type distribution of the uplift pressure including uniform type were considered in case of evaluating stress intensity factor by surface integral method. The effects of body forces, overtopping pressures are also considered and a parametric study of gravity dams under the assumption of LEFM is performed.

• Journal of the Korean Geotechnical Society
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• v.31 no.9
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• pp.69-78
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• 2015

If an active displacement occurs on a wall with finite size, the ground behind the wall forms shapes of 3-dimensional wedges and 3-dimensional active earth pressure are applied on the wall. In the previous studies, shapes of 3-dimensional wedges were measured and the resultant of 3-dimensional active earth pressure has been calculated. In this study, the magnitude and the distribution of 3-dimensional active earth pressure depending on the size of a rectangular wall, which was defined by the aspect ratio (h/w), that is, the ratio between the height and the width of wall, were measured and compared with previous 3-dimensional models. The result shows that, the horizontal displacement (S) of the wall is approx 0.12% of the height of wall (h). The resultant 3-dimensional active earth pressure is similar to that of Karstedt (1982). The distributions of earth pressures on the wall are parabolic shape. The peak earth pressure was measured at the 0.5~0.55 depth from the ground surface. The reduction factor of 3-dimensional active earth pressure against the 2-dimensional earth pressure (${\alpha}$) depending the aspect ratio (h/w) is presented by the diagram.

• Computers and Concrete
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• v.31 no.3
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• pp.267-276
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• 2023

The main purpose of the current research is to develop an efficient two variables trigonometric shear deformation beam theory to investigate the buckling behavior of symmetric and non-symmetric functionally graded carbon nanotubes reinforced composite (FG-CNTRC) beam resting on an elastic foundation with various boundary conditions. The proposed theory obviates the use to shear correction factors as it satisfies the parabolic variation of through-thickness shear stress distribution. The composite beam is made of a polymeric matrix reinforced by aligned and distributed single-walled carbon nanotubes (SWCNTs) with different patterns of reinforcement. The material properties of the FG-CNTRC beam are estimated by using the rule of mixture. The governing equilibrium equations are solved by using new analytical solutions based on the Galerkin method. The robustness and accuracy of the proposed analytical model are demonstrated by comparing its results with those available by other researchers in the existing literature. Moreover, a comprehensive parametric study is presented and discussed in detail to show the effects of CNTs volume fraction, distribution patterns of CNTs, boundary conditions, length-to-thickness ratio, and spring constant factors on the buckling response of FG-CNTRC beam. Some new referential results are reported for the first time, which will serve as a benchmark for future research.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.25 no.6
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• pp.505-512
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• 2012

In this paper, an efficient yet accurate method for the thermal stress analysis using a first order shear deformation theory(FSDT) is presented. The main objective herein is to systematically modify transverse shear strain energy through the mixed variational theorem(MVT). In the mixed formulation, independent transverse shear stresses are taken from the efficient higher-order zigzag plate theory, and the in-plane displacements are assumed to be those of the FSDT. Moreover, a smooth parabolic distribution through the thickness is assumed in the transverse normal displacement field in order to consider a transverse normal deformation. The resulting strain energy expression is referred to as an enhanced first order shear deformation theory, which is obtained via the mixed variational theorem with transverse normal deformation effect(EFSDTM_TN). The EFSDTM_TN has the same computational advantage as the FSDT_TN(FSDT with transverse normal deformation effect) does, which allows us to improve the through-the-thickness distributions of displacements and stresses via the recovery procedure. The thermal stresses obtained by the present theory are compared with those of the FSDT_TN and three-dimensional elasticity.