• Journal of Korean Society of Steel Construction
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• v.13 no.1
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• pp.53-60
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• 2001

Theories for advanced composite structures are too difficult for such design engineers for construction and some simple but accurate enough methods are necessary. The senior author has reported that some laminate orientations have decreasing values of $D_{16}$, $B_{16}$, $D_{26}$ and $B_{26}$ stiffnesses as the ply number increases. For such plates the fiber orientations given above behave as specially orthotropic plates and simple formulas developed by the senior author. Most of the bidge and building slabs on girders have large aspect ratios For such cases frurther simplification is possible by neglecting the effect of the longitudinal moment terms(Mx) on the relevant partial differential equationsof equilibrium In this paper, the result of the study on the subject problem is presented.

• Structural Engineering and Mechanics
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• v.65 no.4
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• pp.491-504
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• 2018

Because of sandwich structures with low weight and high stiffness have much usage in various industries such as civil and aerospace engineering, in this article, buckling and free vibration analyses of coupled micro composite sandwich plates are investigated based on sinusoidal shear deformation (SSDT) and most general strain gradient theories (MGSGT). It is assumed that the sandwich structure rested on an orthotropic elastic foundation and make of four composite face sheets with temperature-dependent material properties that they reinforced by carbon and boron nitride nanotubes and two flexible transversely orthotropic cores. Mathematical formulation is presented using Hamilton's principle and governing equations of motions are derived based on energy approach and applying variation method for simply supported edges under electro-magneto-thermo-mechanical, axial buckling and pre-stresses loadings. In order to predict the effects of various parameters such as material length scale parameter, length to width ratio, length to thickness ratio, thickness of face sheets to core thickness ratio, nanotubes volume fraction, pre-stress load and orthotropic elastic medium on the natural frequencies and critical buckling load of double-bonded micro composite sandwich plates. It is found that orthotropic elastic medium has a special role on the system stability and increasing Winkler and Pasternak constants lead to enhance the natural frequency and critical buckling load of micro plates, while decrease natural frequency and critical buckling load with increasing temperature changes. Also, it is showed that pre-stresses due to help the axial buckling load causes that delay the buckling phenomenon. Moreover, it is concluded that the sandwich structures with orthotropic cores have high stiffness, but because they are not economical, thus it is necessary the sandwich plates reinforce by carbon or boron nitride nanotubes specially, because these nanotubes have important thermal and mechanical properties in comparison of the other reinforcement.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.14 no.11
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• pp.5930-5938
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• 2013

The sigmoid functionally graded mateiral(S-FGM) theory is reformulated using the nonlocal elatictiry of Erigen. The equation of equilibrium of the nonlocal elasticity are derived. This theory has ability to capture the both small scale effects and sigmoid function in terms of the volume fraction of the constituents for material properties through the plate thickness. Navier's method has been used to solve the governing equations for all edges simply supported boundary conditions. Numerical solutions of biaxial buckling of nano-scale plates are presented using this theory to illustrate the effects of nonlocal theory and power law index of sigmoid function on buckling load. The relations between nonlocal and local theories are discussed by numerical results. Further, effects of (i) power law index, (ii) length, (iii) nonlocal parameter, (iv) aspect ratio and (v) mode number on nondimensional biaxial buckling load are studied. To validate the present solutions, the reference solutions are discussed.

• Smart Structures and Systems
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• v.26 no.3
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• pp.331-343
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• 2020

In this paper, based on the CPT, motion equations for a sandwich plate containing a core and two integrated face-sheets have derived. The structure rests on the Visco-Pasternak foundation, which includes normal and shear modules. The piezo-magnetic core is made of CoFe₂O₄ and also is subjected to 3D magnetic potential. Two face sheets at top and bottom of the core are under electrical fields. Also, in order to obtain more accuracy, the effect of flexoelectricity has took into account at face sheets' relations in this work. Flexoelectricity is a property of all insulators whereby they polarize when subject to an inhomogeneous deformation. This property plays a crucial role in small-scale rather than macro scale. Employing CPT, Hamilton's principle, flexoelectricity considerations, the governing equations are derived and then solved analytically. By present work a detailed numerical study is obtained based on Piezoelectricity, Flexoelectricity and modified couple stress theories to indicate the significant effect of length scale parameter, shear correction factor, aspect and thickness ratios and boundary conditions on natural frequency of sandwich plates. Also, the figures show that there is an excellent agreement between present study and previous researches. These finding can be used for automotive industries, aircrafts, marine vessels and building industries.

• Structural Engineering and Mechanics
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• v.74 no.3
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• pp.365-380
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• 2020

The focus of this paper is to develop an analytical approach based on an efficient shear deformation theory with stretching effect for bending stress analysis of cross-ply laminated composite plates subjected to transverse parabolic load and line load by using a new kinematic model, in which the axial displacements involve an undetermined integral component in order to reduce the number of unknowns and a sinusoidal function in terms of the thickness coordinate to include the effect of transverse shear deformation. The present theory contains only five unknowns and satisfies the zero shear stress conditions on the top and bottom surfaces of the plate without using any shear correction factors. The governing differential equations and its boundary conditions are derived by employing the static version of principle of virtual work. Closed-form solutions for simply supported cross-ply laminated plates are obtained applying Navier's solution technique, and the numerical case studies are compared with the theoretical results to verify the utility of the proposed model. Lastly, it can be seen that the present outlined theory is more accurate and useful than some higher-order shear deformation theories developed previously to study the static flexure of laminated composite plates.

• 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.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.5 no.1
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• pp.43-53
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• 1985

This study proposes a reliability based design criteria for the steel bridge (H-beam, plate-girder and composite-beam), which is most common type of steel bridge, and also proposes the theoretical bases of nominal safety factors as well as load and rasistance factors based on the reliability theory. Major 2nd moment reliability analysis and design theories including both Cornell's MFOSM (Mean First Order 2nd Moment) Methods and Lind-Hasofer's AFOSM(Advanced First Order 2nd Moment) Methods are summarized and compared, and it has been found that Lind-Hasofer's approximate and an approximate Log-normal type reliability formula are well suited for the proposed reliability study. A target reliability index (${\beta}_0=3.5$) is selected as an optimal value considering our practice based on the calibration with the safety pravisions of the current steel bridge design code. Galambo's theory is used for the derivation of the algorithm for the evaluation of uncertainties associated with resistences by LRFD Format and SGST Format, whereas the magnitude of the uncertainties associated with load effects are chosen primarily by considering our level of practice. It may be concluded that the proposed LRFD reliability based design provisions for the steel highway bridge give more rational design than the current standard code for steel highway bridge.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.34 no.1
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• pp.59-69
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• 2021

Recently, large-scale offshore and coastal structures have been constructed owing to the increasing interest in eco-friendly energy development. To achieve this, precise simulations of waves are necessary to ensure the safe operations of marine structures. Several experiments are required in the field to understand the offshore wave; however, in terms of scale, it is difficult to control variables, and the cost is significant. In this study, numerical waves under various wave conditions are produced using a piston-type wavemaker, and the produced wave profiles are verified by comparing with the results from a numerical wave tank (NWT) modeled using the smoothed particle hydrodynamics (SPH) method and theoretical equations. To minimize the effect by the reflected wave, a mass-weighted damping zone is set at the right end of the NWT, and therefore, stable and uniform waves are simulated. The waves are generated using the linear and Stokes wave theories, and it is observed that the numerical wave profiles calculated by the Stokes wave theory yield high accuracy. When the relative depth is smaller than two, the results show good agreement irrespective of the wave steepness. However, when the relative depth and wave steepness are larger than 2 and 0.04, respectively, the errors are negligible if the measurement position is close to the excitation plate. However, the error is 10% or larger if the measurement position is away from the excitation location. Applicable target wave ranges are confirmed through various case studies.