• Geomechanics and Engineering
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• v.34 no.3
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• pp.233-250
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• 2023

This paper investigates the flexural analysis of isotropic, transversely isotropic, and laminated composite plates using a new higher-order normal and shear deformation theory. In the present theory, only five unknown functions are involved compared to six or more unknowns used in the other similar theories. The developed theory does not need a shear correction factor. It can satisfy the zero traction boundary conditions on the top and the bottom surfaces of the plate as well as account for sufficient distribution of the transverse shear strains. The thickness stretching effect is considered in the computation. A simply supported was considered on all edges of the plate. The plate is subjected to uniform and sinusoidal distributed load in the static analysis. Laminated composite, isotropic, and transversely isotropic plates are considered. The governing equations are obtained utilizing the virtual work principle. The differential equations are solved via Navier's procedure. The results obtained from the developed theory are compared with other higher-order theories considered in the previous studies and 3D elasticity solutions. The results showed that the proposed theory accurately and effectively predicts the bidirectional bending responses of laminated composite plates. Several parametric studies are presented to illustrate the various parameters influencing the static response of the laminated composite plates.

• Steel and Composite Structures
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• v.44 no.4
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• pp.451-471
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• 2022

In the present paper, the static bending and buckling responses of functionally graded carbon nanotubes-reinforced composite (FG-CNTRC) beam under various boundary conditions are investigated within the framework of higher shear deformation theory. The significant feature of the proposed theory is that it provides an accurate parabolic distribution of transverse shear stress through the thickness satisfying the traction-free boundary conditions needless of any shear correction factor. Uniform (UD) and four graded distributions of CNTs which are FG-O, FG-X, FG- and FG-V are selected here for the analysis. The effective material properties of FG-CNTRC beams are estimated according to the rule of mixture. To model the FG-CNTRC beam realistically, an efficient Hermite-Lagrangian finite element formulation is successfully developed. The accuracy and efficiency of the present model are demonstrated by comparison with published benchmark results. Moreover, comprehensive numerical results are presented and discussed in detail to investigate the effects of CNTs volume fraction, distribution patterns of CNTs, boundary conditions, and length-to-thickness ratio on the bending and buckling responses of FG-CNTRC beam. Several new referential results are also reported for the first time which will serve as a benchmark for future studies in a similar direction. It is concluded that the FG-X-CNTRC beam is the strongest beam that carries the lowest central deflection and is followed by the UD, V, Λ, and FG-O-CNTRC beam. Besides, the critical buckling load belonging to the FG-X-CNTRC beam is the highest, followed by UD and FG-O.

• Structural Engineering and Mechanics
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• v.90 no.3
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• pp.233-252
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• 2024

This research explores a new finite element model for the free vibration analysis of bi-directional functionally graded (BDFG) beams. The model is based on an efficient higher-order shear deformation beam theory that incorporates a trigonometric warping function for both transverse shear deformation and stress to guarantee traction-free boundary conditions without the necessity of shear correction factors. The proposed two-node beam element has three degrees of freedom per node, and the inter-element continuity is retained using both C1 and C0 continuities for kinematics variables. In addition, the mechanical properties of the (BDFG) beam vary gradually and smoothly in both the in-plane and out-of-plane beam's directions according to an exponential power-law distribution. The highly elevated performance of the developed model is shown by comparing it to conceptual frameworks and solution procedures. Detailed numerical investigations are also conducted to examine the impact of boundary conditions, the bi-directional gradient indices, and the slenderness ratio on the free vibration response of BDFG beams. The suggested finite element beam model is an excellent potential tool for the design and the mechanical behavior estimation of BDFG structures.

• Structural Engineering and Mechanics
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• v.90 no.3
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• pp.253-261
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• 2024

This research explores a new finite element model for the free vibration analysis of bi-directional functionally graded (BDFG) beams. The model is based on an efficient higher-order shear deformation beam theory that incorporates a trigonometric warping function for both transverse shear deformation and stress to guarantee traction-free boundary conditions without the necessity of shear correction factors. The proposed two-node beam element has three degrees of freedom per node, and the inter-element continuity is retained using both C1 and C0 continuities for kinematics variables. In addition, the mechanical properties of the (BDFG) beam vary gradually and smoothly in both the in-plane and out-of-plane beam's directions according to an exponential power-law distribution. The highly elevated performance of the developed model is shown by comparing it to conceptual frameworks and solution procedures. Detailed numerical investigations are also conducted to examine the impact of boundary conditions, the bi-directional gradient indices, and the slenderness ratio on the free vibration response of BDFG beams. The suggested finite element beam model is an excellent potential tool for the design and the mechanical behavior estimation of BDFG structures.

• Advances in nano research
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• v.16 no.5
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• pp.509-519
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• 2024

In this study, the static analysis of carbon nanotube-reinforced composites (CNTRC) beams resting on a Winkler-Pasternak elastic foundation is presented. The developed theories account for higher-order variation of transverse shear strain through the depth of the beam and satisfy the stress-free boundary conditions on the top and bottom surfaces of the beam. To study the effect of carbon nanotubes distribution in functionally graded (FG-CNT), we introduce in the equation of CNT volume fraction a new exponent equation. The SWCNTs are assumed to be aligned and distributed in the polymeric matrix with different patterns of reinforcement. The rule of mixture is used to describe the material properties of the CNTRC beams. The governing equations were derived by employing Hamilton's principle. The models presented in this work are numerically provided to verify the accuracy of the present theory. The analytical solutions are presented, and the obtained results are compared with the existing solutions to verify the validity of the developed theories. Many parameters are investigated, such as the Pasternak shear modulus parameter, the Winkler modulus parameter, the volume fraction, and the order of the exponent in the volume fraction equation. New results obtained from bending and stresses are presented and discussed in detail. From the obtained results, it became clear the influence of the exponential CNTs distribution and Winkler-Pasternak model improved the mechanical properties of the CNTRC beams.

• Structural Engineering and Mechanics
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• v.91 no.1
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• pp.1-23
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• 2024

This paper formulates a new integral shear deformation shell theory to investigate the free vibration response of carbon nanotube (CNT) reinforced structures with only four independent variables, unlike existing shell theories, which invariably and implicitly induce a host of unknowns. This approach guarantees traction-free boundary conditions without shear correction factors, using a non-polynomial hyperbolic warping function for transverse shear deformation and stress. By introducing undetermined integral terms, it will be possible to derive the motion equations with a low order of differentiation, which can facilitate a closed-form solution in conjunction with Navier's procedure. The mechanical properties of the CNT reinforcements are modeled to vary smoothly and gradually through the thickness coordinate, exhibiting different distribution patterns. A comparison study is performed to prove the efficacy of the formulated shell theory via obtained results from existing literature. Further numerical investigations are current and comprehensive in detailing the effects of CNT distribution patterns, volume fractions, and geometrical configurations on the fundamental frequencies of CNT-reinforced nanocomposite shells present here. The current shell theory is assumed to serve as a potent conceptual framework for designing reinforced structures and assessing their mechanical behavior.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.6 no.1
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• pp.1-11
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• 1986

Welded connectors of the cover plates, the transverse stiffeners of the plate girders, and the gusset plates of the plates girders or box girders, were selected as studying objects. A simplified method of drawing the S-N curves in these welded joints by a computer program without the direct fatigue tests was established. The plots on the S-N curve using the values from the practical fatigue tests were compared with the results from the method of the computer programming. The results of these studies are as follows. It appeared that the fatigue life by calculation method was a little less than the practical fatigue life from the actual tests. The latter values included both life $N_c$ of occurrence of initial crack $a_i$ and the life $N_p$ of propagation of critical crack. On the other hand, the former values included only the life $N_p$. Therefore, these results should be considered as justifiable ones. Since the difference between the two results was not significant, the results by calculation method should be in the conservation side when the safety of the structures was considered. Consequently, the results by calculation method should be applicable to the fracture fatigue design of structure. For reference, the same fatigue tests were performed with the specimens of 3 pieces in each case made of the low-strength steel, SS 41. The results went unexpected showing that the fatigue strength was lower in the case of low-strength steel. That is, in the case of the cover plate, the fatigue strength became slowly higher than the case of high-strength steel, SWS 50. That was observed when the maximum testing stress was higher than $14kg/mm^2$. In addition, in the case of the transverse stiffener, the fatique strength became rapidly higher than the case of SWS 50. That was observed when the maximum testing stress was lower than $31kg/mm^2$. It was thought that more such fatigue tests should be performed for more reliable results.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.33 no.6
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• pp.2267-2275
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• 2013

Existing conventional model for analysis of shallow water flow just assumed the internal boundary condition as free-slip, which resulted in the wrong prediction about the velocity, vorticity, water level, shear stress distribution, and time variation of drag and lift force around a structure. In this study, a finite element model that can predict flow characteristics around the structure accurately was developed and internal boundary conditions were generalized as partial slip condition using slip length concept. Laminar flow characteristics behind circular cylinder were analyzed by varying the internal boundary conditions. The simulation results of (1) time variations of longitudinal and transverse velocities, and vorticity; (2) wake length; (3) vortex shedding phenomena by slip length; (4) and mass conservation showed that the vortex shedding had never observed and laminar flow like creeping motion was occurred under free-slip condition. Assignment of partial slip condition changed the velocity distribution on the cylinder surface and influenced the magnitude of the shear stress and the occurrence of vorticity so that the period of vortex shedding was reduced compared with the case of no slip condition. The maximum mass conservation error occurred in the case of no slip condition, which had the value of 0.73%, and there was 0.21 % reduction in the maximum mass conservation error by changing the internal boundary condition from no slip to partial slip condition.

• Journal of the Korean Arthroscopy Society
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• v.5 no.1
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• pp.7-12
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• 2001

Purpose : We observed usability of allograft by evaluating the clinical results, second look arthroscopic and histologic findings at last follow up after anterior cruciate ligament(ACL) reconstruction using by fresh frozen Achilles allograft. Materials and Methods : We analyzed in 58 patients(59 cases) by subjective and objective parameters, Telos stress arthrometer and Modified Feagin Scoring System. The average age and follow up period was 25 years(ranging from 18 to 49 years), and 15 months(ranging from 12 to 19 months). Among them we studied second look arthroscopic and histologic findings in 16 patients. Results : The mean Lysholm Score wits improved from 60 to 88.2 as well the anterior translation was improved from 7.1 min to 2.3mm at last follow up. The second look arthroscopic findings were close to normal in ligament thickness, tension and showed revasculization at the holly attachment site. Light microscope(LM) findings showed dense cellularity like a normal ligament. In electron microscope(EM) collagen fibrils showed parallel arrangement longitudinally and unimodal pattern diameter close to normal tissue in the transverse section. Conclusion : We think that the fresh frozen Achilles allograft is a good substitution of autograft in cruciate ligament reconstruction.

• Journal of the Korean earth science society
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• v.21 no.3
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• pp.315-322
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• 2000

In this study, the data used for the models were a set of 56 geologic estimates of long-term fault slip rates. The hest models were those in which mantle drag was convergent on the Transverse Ranges in the San Andreas fault system, and faults had a low friction (${\mu}$= 0.3). It is clearly important to decide whether these cases of low strength are local anomalies or whether they are representative. Furthermore, it would be helpful to determine fault strength in as many tectonic settings as possible. Analysis of data was considered by unsuspected sources of pore pressure, or even to question the relevance of the friction law. To contribute to the solution of this problem, three attempts were tried to apply finite element method that would permit computational experiments with different hypothesized fault rheologies. The computed model has an assumed rheology and plate tectonic boundary conditions, and produces predictions of present surface velocity, strain rate, and stress. The results of model will be acceptably close to reality in its predictions of mean fault slip rates, stress directions and geodetic data. This study suggests some implications of the thermoelastic characteristics to interpret the relationship with very low strength of San Andreas fault system.