• Structural Engineering and Mechanics
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• v.56 no.2
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• pp.241-256
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• 2015

Channel girder bridges that consist of a deck slab and two side beams are good choices for railway bridges and urban rail transit bridges when the vertical clearance beneath the bridge is restricted. In this study, the behavior of simply supported channel girder bridges was theoretical studied based on the theory of elasticity. The accuracy of the theoretical solutions was verified by the finite element analysis. The global bending of the channel girder and the local bending of the deck slab are two contributors to the deformations and stresses of the channel girder. Because of the shear lag effect, the maximum deflection due to the global bending could be amplified by 1.0 to 1.2 times, and the effective width of the deck slab for determining the global bending stresses can be as small as 0.7 of the actual width depending on the width-to-span ratio of the channel girder. The maximum deflection and transversal stress due to the local bending are obtained at the girder ends. For the channel girders with open section side beams, the side beam twist has a negligible effect on the deflections and stresses of the channel girder. Simplified equations were also developed for calculating the maximum deformations and stresses.

• Structural Engineering and Mechanics
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• v.40 no.2
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• pp.257-277
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• 2011

In this paper the geometrically nonlinear continuum plate finite element model, hitherto not reported in the literature, is developed using the total Lagrange formulation. With the layerwise displacement field of Reddy, nonlinear Green-Lagrange small strain large displacements relations (in the von Karman sense) and linear elastic orthotropic material properties for each lamina, the 3D elasticity equations are reduced to 2D problem and the nonlinear equilibrium integral form is obtained. By performing the linearization on nonlinear integral form and then the discretization on linearized integral form, tangent stiffness matrix is obtained with less manipulation and in more consistent form, compared to the one obtained using laminated element approach. Symmetric tangent stiffness matrixes, together with internal force vector are then utilized in Newton Raphson's method for the numerical solution of nonlinear incremental finite element equilibrium equations. Despite of its complex layer dependent numerical nature, the present model has no shear locking problems, compared to ESL (Equivalent Single Layer) models, or aspect ratio problems, as the 3D finite element may have when analyzing thin plate behavior. The originally coded MATLAB computer program for the finite element solution is used to verify the accuracy of the numerical model, by calculating nonlinear response of plates with different mechanical properties, which are isotropic, orthotropic and anisotropic (cross ply and angle ply), different plate thickness, different boundary conditions and different load direction (unloading/loading). The obtained results are compared with available results from the literature and the linear solutions from the author's previous papers.

• Wind and Structures
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• v.28 no.1
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• pp.49-62
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• 2019

In this paper, an analytical analysis for the study of vibratory behavior and wave propagation of functionally graded plates (FGM) is presented based on a high order shear deformation theory. The manufacture of these plates' defects can appear in the form of porosity. This latter can question and modify the global behavior of such plates. A new shape of the distribution of porosity according to the thickness of the plate was used. The field of displacement of this theory is present of indeterminate integral variables. The modulus of elasticity and the mass density of these plates are assumed to vary according to the thickness of the plate. Equations of motion are derived by the principle of minimization of energies. Analytical solutions of free vibration and wave propagation are obtained for FGM plates simply supported by integrating the analytic dispersion relation. Illustrative examples are given also to show the effects of variation of various parameters such as(porosity parameter, material graduation, thickness-length ratio, porosity distribution) on vibration and wave propagation of FGM plates.

• Structural Engineering and Mechanics
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• v.83 no.5
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• pp.617-625
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• 2022

A novel three variable refined plate theory (TVRPT) is developed in this article for laminated composite plates for the first time. The theory takes into account the nonlinear variation of transverse shear deformations, and satisfies the boundary conditions of zero traction on the plate surfaces without considering the "shear correction factor". The important characteristic of this new kinematic is that the unknowns numbers is only 3 as is employed in "classical plate theory" (CPT). The numerical results of the current theory are compared with 3D-elasticity solutions and the calculations of "first order theories" and other higher order models found in the literature.

• Current Optics and Photonics
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• v.6 no.1
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• pp.69-78
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• 2022

A high-resolution camera is a precise optical system. Its vibrations during transportation and launch, together with changes in temperature and gravity field in orbit, lead to different degrees of defocus of the camera. Thermal refocusing is one of the solutions to the problems related to in-orbit defocusing, but there are few relevant thermal refocusing mathematical models for systematic analysis and research. Therefore, to further research thermal refocusing systems by using the development of a high-resolution micro-nano satellite (CX6-02) super-resolution camera as an example, we established a thermal refocusing mathematical model based on the thermal elasticity theory on the basis of the secondary mirror position. The detailed design of the thermal refocusing system was carried out under the guidance of the mathematical model. Through optical-mechanical-thermal integration analysis and Zernike polynomial calculation, we found that the data error obtained was about 1%, and deformation in the secondary mirror surface conformed to the optical index, indicating the accuracy and reliability of the thermal refocusing mathematical model. In the final ground test, the thermal vacuum experimental verification data and in-orbit imaging results showed that the thermal refocusing system is consistent with the experimental data, and the performance is stable, which provides theoretical and technical support for the future development of a thermal refocusing space camera.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.36 no.1
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• pp.67-74
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• 2023

A meshless technique using the geometric conservation least-squares method (GC-LSM) was devised to discretize the governing equation of linear elasticity. Although the finite-element method is widely used for structural analysis, a meshless method was developed because of its advantages in a moving grid system. This work is the preliminary phase for developing a fully meshless-based fluid-structure interaction solver. In this study, Cauchy's momentum equation was discretized in strong form using GC-LSM for the structural domain, and the Newmark beta method was used for time integration. The solver was validated in 1D, 2D, and 3D benchmarking problems. Static and dynamic results were obtained. The results are more accurate than those of analytic solutions.

• International Journal of Highway Engineering
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• v.12 no.2
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• pp.107-113
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• 2010

In this study, the relative effects of low-chloride deicier(LCD) and two other deicing agents on the scaling of concrete were conducted in a series of tests at laboratory accordance with the ASTM C 672. The solutions concentration of deicers tested included 1, 4, 10%. Tap water was used as control. The amount of scaling was evaluated gravimetrically. As test result of deicer solution types, when applied to 4% solutions, surface scaling of concrete after 56 freeze-thaw cycles was produced significantly as about 9 times on LCD solution, as about 18 times on $CaCl_2$ solution, and as about 33 times on NaCl solution comparing with tap water. As test result of deicer solution concentrations, relatively low concentrations (of the 4% by weight) of deicer were produced more surface scaling than higher concentrations (of the 10% by weight) or lower concentrations (of the 1% by weight) of deicer. It show that the damaging concentration is of the order of 3~4% for previous research result. It appears that the mechanism of surface scaling is primarily physical rather than chemical. Also, the effect of chloride deicier types, freeze-thaw cycling, and air contents on the performance of concrete was experimentally investigated. The results show that the concrete specimens subjected to freeze-thaw cycling scaled more severely in exposure to deicing salt than those in non-exposure to deicing salt, weight losses of the specimens tested in exposure to deicing salt were twice as much as those tested in non-exposure to deicing salt. Relative dynamic modulus of elasticity of concrete specimens decreased more quickly in exposure to deicing salt than in non-exposure to deicing salt. Also, relative dynamic modulus of elasticity of concrete specimens in exposure to sodium chloride deicing salt was decreased more quickly comparing with exposure to LCD salt. It is also shown that the chloride contents according to concrete specimen depths was more largely in exposure to LCD salt. When concrete specimen is exposed to chloride deicing salts and freeze-thaw cycling, performance degradation in the entrained air concrete(AE concrete) retarded more considerably comparing with non-entrained air concrete(Non-AE concrete).

• Korea-Australia Rheology Journal
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• v.17 no.3
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• pp.131-140
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• 2005

In this work we show the results of our most recent Direct Numerical Simulations (DNS) of turbulent viscoelastic channel flow using spectral spatial approximations and a stabilizing artificial diffusion in the viscoelastic constitutive model. The Finite-Elasticity Non-Linear Elastic Dumbbell model with the Peterlin approximation (FENE-P) is used to represent the effect of polymer molecules in solution, The corresponding rheological parameters are chosen so that to get closer to the conditions corresponding to maximum drag reduction: A high extensibility parameter (60) and a moderate solvent viscosity ratio (0.8) are used with two different friction Weissenberg numbers (50 and 100). We then first find that the corresponding achieved drag reduction, in the range of friction Reynolds numbers used in this work (180-590), is insensitive to the Reynolds number (in accordance to previous work). The obtained drag reduction is at the level of $49\%\;and\;63\%$, for the friction Weissenberg numbers 50 and 100, respectively. The largest value is substantially higher than any of our previous simulations, performed at more moderate levels of viscoelasticity (i.e. higher viscosity ratio and smaller extensibility parameter values). Therefore, the maximum extensional viscosity exhibited by the modeled system and the friction Weissenberg number can still be considered as the dominant factors determining the levels of drag reduction. These can reach high values, even for of dilute polymer solution (the system modeled by the FENE-P model), provided the flow viscoelasticity is high, corresponding to a high polymer molecular weight (which translates to a high extensibility parameter) and a high friction Weissenberg number. Based on that and the changes observed in the turbulent structure and in the most prevalent statistics, as presented in this work, we can still rationalize for an increasing extensional resistance-based drag reduction mechanism as the most prevalent mechanism for drag reduction, the same one evidenced in our previous work: As the polymer elasticity increases, so does the resistance offered to extensional deformation. That, in turn, changes the structure of the most energy-containing turbulent eddies (they become wider, more well correlated, and weaker in intensity) so that they become less efficient in transferring momentum, thus leading to drag reduction. Such a continuum, rheology-based, mechanism has first been proposed in the early 70s independently by Metzner and Lamley and is to be contrasted against any molecularly based explanations.

• Steel and Composite Structures
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• v.18 no.4
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• pp.1063-1081
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• 2015

In this paper, a new nonlocal hyperbolic refined plate model is presented for free vibration properties of functionally graded (FG) plates. This nonlocal nano-plate model incorporates the length scale parameter which can capture the small scale effect. The displacement field of the present theory is chosen based on a hyperbolic variation in the in-plane displacements through the thickness of the nano-plate. By dividing the transverse displacement into the bending and shear parts, the number of unknowns and equations of motion of the present theory is reduced, significantly facilitating structural analysis. The material properties are assumed to vary only in the thickness direction and the effective properties for the FG nano-plate are computed using Mori-Tanaka homogenization scheme. The governing equations of motion are derived based on the nonlocal differential constitutive relations of Eringen in conjunction with the refined four variable plate theory via Hamilton's principle. Analytical solution for the simply supported FG nano-plates is obtained to verify the theory by comparing its results with other available solutions in the open literature. The effects of nonlocal parameter, the plate thickness, the plate aspect ratio, and various material compositions on the dynamic response of the FG nano-plate are discussed.

• Steel and Composite Structures
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• v.26 no.2
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• pp.125-137
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• 2018

In this work, the bending and free vibration analysis of multilayered plates and shells is presented by utilizing a new higher order shear deformation theory (HSDT). The proposed involves only four unknowns, which is even less than the first shear deformation theory (FSDT) and without requiring the shear correction coefficient. Unlike the conventional HSDTs, the present one presents a novel displacement field which incorporates undetermined integral variables. The equations of motion are derived by using the Hamilton's principle. These equations are then solved via Navier-type, closed form solutions. Bending and vibration results are found for cylindrical and spherical shells and plates for simply supported boundary conditions. Bending and vibration problems are treated as individual cases. Panels are subjected to sinusoidal, distributed and point loads. Results are presented for thick to thin as well as shallow and deep shells. The computed results are compared with the exact 3D elasticity theory and with several other conventional HSDTs. The proposed HSDT is found to be precise compared to other several existing ones for investigating the static and dynamic response of isotropic and multilayered composite shell and plate structures.