• Steel and Composite Structures
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• v.44 no.2
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• pp.155-169
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• 2022

In the present paper an analytical model was developed to study the non-linear vibrations of Functionally Graded Carbon Nanotube (FG-CNT) reinforced doubly-curved shallow shells using the Multiple Scales Method (MSM). The nonlinear partial differential equations of motion are based on the FGM shallow shell hypothesis, the non-linear geometric Von-Karman relationships, and the Galerkin method to reduce the partial differential equations associated with simply supported boundary conditions. The novelty of the present model is the simultaneous prediction of the natural frequencies and their mode shapes versus different curvatures (cylindrical, spherical, conical, and plate) and the different types of FG-CNTs. In addition to combining the vibration analysis with optimization algorithms based on the genetic algorithm, a design optimization methode was developed to maximize the natural frequencies. By considering the expression of the non-dimensional frequency as an objective optimization function, a genetic algorithm program was developed by valuing the mechanical properties, the geometric properties and the FG-CNT configuration of shallow double curvature shells. The results obtained show that the curvature, the volume fraction and the types of NTC distribution have considerable effects on the variation of the Dimensionless Fundamental Linear Frequency (DFLF). The frequency response of the shallow shells of the FG-CNTRC showed two types of nonlinear hardening and softening which are strongly influenced by the change in the fundamental vibration mode. In GA optimization, the mechanical properties and geometric properties in the transverse direction, the volume fraction, and types of distribution of CNTs have a considerable effect on the fundamental frequencies of shallow double-curvature shells. Where the difference between optimized and not optimized DFLF can reach 13.26%.

• Steel and Composite Structures
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• v.46 no.3
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• pp.367-383
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• 2023

In this investigation, an improved integral trigonometric shear deformation theory is employed to examine the vibrational behavior of the functionally graded (FG) sandwich plates resting on visco-Pasternak foundations. The studied structure is modelled with only four unknowns' variables displacements functions. The simplicity of the developed model being in the reduced number of variables which was made with the help of the use of the indeterminate integral in the formulation. The current kinematic takes into consideration the shear deformation effect and does not require any shear correction factors as used in the first shear deformation theory. The equations of motion are determined from Hamilton's principle with including the effect of the reaction of the visco-Pasternak's foundation. A Galerkin technique is proposed to solve the differentials governing equations, which enables one to obtain the semi-analytical solutions of natural frequencies for various clamped and simply supported FG sandwich plates resting on visco-Pasternak foundations. The validity of proposed model is checked with others solutions found in the literature. Parametric studies are performed to illustrate the impact of various parameters as plate dimension, layer thickness ratio, inhomogeneity index, damping coefficient, vibrational mode and elastic foundation on the vibrational behavior of the FG sandwich plates.

• Structural Engineering and Mechanics
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• v.84 no.3
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• pp.295-310
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• 2022

This paper proposes a modified bar simulation method for analyzing the shear lag effect of variable sectional box girder with multiple cells. This theoretical method formulates the equivalent area of stiffening bars and the allocation proportion of shear flows in webs, and re-derives the governing differential equations of bar simulation method. The feasibility of the proposed method is verified by the model test and finite element (FE) analysis of a simply supported multi-cell box girder with constant depth. Subsequently, parametric analysis is conducted to explore the mechanism of shear lag effect of varied sectional cantilever box girder with multiple cells. Results show that the shear lag behavior of variable box-section cantilever box girder is weaker than that of box girder with constant section. It is recommended to make the gradient of shear flow in the web with respect to span length vary as smoothly as possible for eliminating the shear lag effect of box girder. An effective countermeasure for diminishing shear lag effect is to increase the number of box chambers or change the variation manner of bridge depth. The shear lag effect of varied sectional cantilever box girder will get more server when the length of central flanges is shorter than 0.26 or longer than 0.36 times of total width of top flange, as well as the cantilever length exceeds 0.29 times of total length of box's flange. Therefore, the distance between central webs can adjust the shear lag effect of box girder. Especially, the width ratio of cantilever plate with respect to total length of top flange is proposed to be no more 1/3.

• Steel and Composite Structures
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• v.48 no.1
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• pp.27-41
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• 2023

Under the long-term effect of corrosive environment, many cold-formed steel (CFS) structures have serious corrosion problems. Corrosion leads to the change of surface morphology and the loss of section thickness, which results in the change of instability mode and failure mechanism of CFS structure. This paper mainly investigates the elastic local buckling behavior of corroded CFS columns. The surface morphology scanning test was carried out for eight CFS columns accelerated corrosion by the outdoor periodic spray test. The thin shell finite element (FE) eigen-buckling analysis was also carried out to reveal the influence of corrosion surface characteristics, corrosion depth, corrosion location and corrosion area on the elastic local buckling behaviour of the plates with four simply supported edges. The accuracy of the proposed formulas for calculating the elastic local buckling stress of the corroded plates and columns was assessed through extensive parameter studies. The results indicated that for the plates considering corrosion surface characteristics, the maximum deformation area of local buckling was located at the plates with the minimum average section area. For the plates with localized corrosion, the main buckling shape of the plates changed from one half-wave to two half-wave with the increase in corrosion area length. The elastic local buckling stress decreased gradually with the increase in corrosion area width and length. In addition, the elastic local buckling stress decreased slowly when corrosion area thickness was relatively large, and then tends to accelerate with the reduction in corrosion area thickness. The distance from the corrosion area to the transverse and longitudinal centerline of the plate had little effect on the elastic local buckling stress. Finally, the calculation formula of the elastic local buckling stress of the corroded plates and CFS columns was proposed.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.18 no.9
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• pp.52-60
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• 2017

This study examined the structural stability of nonlocal magneto-electro-elastic nano plates on elastic foundations using first-order shear deformation theory. Navier's method has been used to solve the buckling loads for all edges simply supported boundary conditions. On the other hand, biaxial buckling analysis of nano-plates has beenrarely studied. According to the Maxwell equation and the magneto-electro boundary condition, the change inthe magnetic and electric potential along the thickness direction of the magneto-electro-elastic nano plate wasdetermined. To reformulate the elasticity theory of the magneto- electro-elastic nano plate, the differential constitutive equation of Eringen was used and the governing equation of the nonlocal elasticity theory was studied using variational theory. The effects of the elastic foundation arebased on Pasternak's assumption. The relationship between nonlocal theory and local theory was analyzed through calculation results. In addition, structural stability problems were investigated according to the electric and magnetic potentials, nonlocal parameters, elastic foundation parameters, and side-to-thickness ratio. The results of the analysis revealedthe effects of the magnetic and electric potential. These calculations can be used to compare future research on new material structures made of magneto-electro-elastic materials.

• Journal of the Korean Society for Advanced Composite Structures
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• v.3 no.1
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• pp.29-34
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• 2012

Even though the longitudinally stiffened laminated composite plates with closed section ribs should be an effective system for axially compressed members, the existing researches on the applications of closed-section ribs, especially for the laminated composite plates, are not sufficient. This study is aimed to examine the influence of the sectional stiffness of U-shaped ribs on the buckling modes and strengths of laminated composite plates. Applying the orthotropic plates with eight layers of the layup $[(0^{\circ})_4]_s$ and $[(0^{\circ}/90^{\circ})_2]_s$, 3-dimensional finite element models for the U-rib stiffened plates were setup by using ABAQUS and then a series of eigenvalue analyses were conducted. From the parametric studies, the minimum required ply thicknesses as well as the buckling strengths were presented for the analysis models. The buckling strengths were compared with the theoretical critical stress equation for simply supported plates based on the Classical laminated plate theory. This study will contribute to the future study for evaluating the minimum required stiffness and optimum design of U-rib stiffened plates.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.28 no.3A
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• pp.305-313
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• 2008

A reliability based calibration of dynamic load allowance (DLA) of highway bridge is performed by numerical dynamic analysis of various types of bridges taking into account of the road surface roughness and bridge-vehicle interaction. A total of 10 simply supported bridges with three girder types in the form of prestressed concrete girder, steel plate girder, and steel box girder is analyzed. The cross sections recommended in "The Standardized Design of Highway Bridge Superstructure" by the Korean Ministry of Construction are used for the prestressed concrete girder bridges and steel plate girder bridges while the box girder bridges are designed by the LRFD method. Ten sets of road surface roughness for each bridge are generated from power spectral density (PSD) function by assuming the roadway as "Average Road". A three dimensionally modeled 5-axle tractor-trailer with its gross weight the same as that of DB-24 design truck is used in the dynamic analysis. For the finite element modeling of superstructure, beam elements for the main girder, shell elements for concrete deck, and rigid links between main girder and concrete deck are used. The statistical mean and coefficient of variation of DLA are obtained from a total of 100 DLA results for 10 different bridges with each having 10 sets of road surface roughness. Applying the DLA statistics obtained, the DLA is finally calibrated in a reliability based LRFD format by using the formula developed in the calibration of OHBDC code.

• Journal of Navigation and Port Research
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• v.31 no.3 s.119
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• pp.235-245
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• 2007

Stiffened steel plates are basic structural members on the deck and bottom structure in ship, offshore. It has a number of one sided stiffeners in either one or both directions, the latter structure was called grillage structure. At the ship structural desgn stage, one of the major consideration is evaluation for ultimate strength of the hull girder. In general, it is accepted that hull girder strength can be represented by the local strength of the longitudinal stiffened panel. In case of considering hogging condition in a stormy sea, stiffened panel was acting on the bottom structure under axial compressive load induced hull girder bending moment, also simultaneously arising local bending moment induced lateral pressure load. In this paper, results of the structural analysis have been compared with another detailed FEA program and prediction from design guideline and a series analysis was conducted consideration of changing parameters for instance, analysis range, cross-section of stiffener, web height and amplitude of lateral pressure load subjected to combined load (axial compression and lateral pressure load). It has been found that finite element modeling is capable of predicting the behaviour and ultimate load capacity of a simply supported stiffened plate subjected to combined load of axial compression and lateral pressure load It is expected that these results will be used to examine the effect of interaction between lateral pressure and axial loads for the ultimate load-carrying capacity based on the Ultimate Limit State design guideline.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.13 no.11
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• pp.5542-5550
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• 2012

Third-order shear deformation theory is reformulated using the nonlocal elasticity of Eringen. The equation of equilibrium of the nonlocal elasticity are derived. This theory has ability to capture the both small scale effects and quadratic variation of shear strain through the plate thickness. Navier's method has been used to solve the governing equations for all edges simply supported boundary conditions. Analytical solutions of buckling of nano-scale plates are presented using this theory to illustrate the effect of nonlocal theory on buckling load of the nano-scale plates. The relations between nonlocal third-order and local theories are discussed by numerical results. Further, effects of (i) length (ii) nonlocal parameter, (iii) aspect ratio and (iv) mode number on nondimensional buckling load are studied. In order to validate the present solutions, the reference solutions are used and discussed. The present results of nano-scale plates using the nonlocal theory can provide a useful benchmark to check the accuracy of related numerical solutions.

• Journal of Korean Society of Steel Construction
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• v.9 no.4 s.33
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• pp.543-555
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• 1997

Generally, in a steel-concrete composite gilder, the shear connector which was constructed between concrete deck and steel girder should have enough stiffness to behave as one body, because the conformity between plate and concrete deck is influences by the stiffness and spacing of the shear connectors. If the stiffness of shear connectors are insufficient, slip would happen at the contact surface. Partial interaction is the case that takes account of slips. In this paper, an easy method is presented to evaluate the stiffness or spacing of the shear connector according to the degree of imperfection without difficult calculations for a composite gilder with partial interaction. Also, the horizontal shearing force applied to the shear connector and the longitudinal axial force, which is occurs at contact surface between concrete deck and steel girder, have been presented in a simple influence line that is various to the parameters of sectional properties, degree of imperfection and applied load points. Furthermore, through the case study, it determined the relationships between the degree of imperfection and the follows 1) spring constants 2) axial force and horizontal shearing force 3) stress and neutral axis by using the partial differential equation based on Newmark's Partial Interaction Theory.