• Structural Engineering and Mechanics
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• v.65 no.5
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• pp.573-585
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• 2018

This article presents strain gradient elasticity-based procedures for static bending, free vibration and buckling analyses of functionally graded rectangular micro-plates. The developed method allows consideration of smooth spatial variations of length scale parameters of strain gradient elasticity. Governing partial differential equations and boundary conditions are derived by following the variational approach and applying Hamilton's principle. Displacement field is expressed in a unified way to produce numerical results in accordance with Kirchhoff, Mindlin, and third order shear deformation theories. All material properties, including the length scale parameters, are assumed to be functions of the plate thickness coordinate in the derivations. Developed equations are solved numerically by means of differential quadrature method. Proposed procedures are verified through comparisons made to the results available in the literature for certain limiting cases. Further numerical results are provided to illustrate the effects of material and geometric parameters on bending, free vibrations, and buckling. The results generated by Kirchhoff and third order shear deformation theories are in very good agreement, whereas Mindlin plate theory slightly overestimates static deflection and underestimates natural frequency. A rise in the length scale parameter ratio, which identifies the degree of spatial variations, leads to a drop in dimensionless maximum deflection, and increases in dimensionless vibration frequency and buckling load. Size effect is shown to play a more significant role as the plate thickness becomes smaller compared to the length scale parameter. Numerical results indicate that consideration of length scale parameter variation is required for accurate modelling of graded rectangular micro-plates.

• Journal of the Society of Naval Architects of Korea
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• v.36 no.3
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• pp.83-92
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• 1999

In this paper, the fluid-structure interaction of large floating structures has been rigorously analyzed and the shear effect on the structural deformation has been investigated in oblique waves. A constant panel method(CPM) based on the Green function method is implemented for computing the hydrodynamic pressure, while a finite element method(FEM) is applied for the structural response based on the Mindlin plate theory with including shear deformation. In order to validate the method, we compared numerical results with experimental ones of Mega Float carried out by Yago & Endo in head waves. General behavior shows good agreement but the local displacement at the ends is slightly different. The numerical results show that the radiation pressure due to the fluid-structure interaction is locally larger than that of wave excitation and mooring devices greatly reduce the response. It is observed that the shear effects among the total deformation constitutes about 4% in the case of Mega Float in oblique waves.

• Wind and Structures
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• v.27 no.4
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• pp.235-245
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• 2018

In this study the stress analysis of orthotropic thin plate with arbitrary shapes for different boundary conditionsis investigated. Meshfreemethod is applied to static analysis of thin plates with various geometries based on the Kirchhoff classical plate theory. According to the meshfree method the domain of the plates are expressed through a set of nodes without using mesh. In this method, a set of nodes are defined in a standard rectangular domain, then via a third order map, these nodes are transferred to the main domain of the original geometry; therefore the analysis of the plates can be done. Herein, Meshless local Petrov-Galerkin (MLPG) as a meshfree numerical method is utilized. The MLS function in MLPG does not satisfy essential boundary conditions using Delta Kronecker. In the MLPG method, direct interpolation of the boundary conditions can be applied due to constructing node by node of the system equations. The detailed parametric study is conducted, focusing on the arbitrary geometries of the thin plates. Results show that the meshfree method provides better accuracy rather than finite element method. Also, it is found that trend of the figures have good agreement with relevant published papers.

• Structural Engineering and Mechanics
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• v.53 no.3
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• pp.497-517
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• 2015

In this study, nonlocal nonlinear buckling analysis of embedded polymeric temperature-dependent microplates resting on an elastic matrix as orthotropic temperature-dependent elastomeric medium is investigated. The microplate is reinforced by single-walled carbon nanotubes (SWCNTs) in which the equivalent material properties nanocomposite are estimated based on the rule of mixture. For the carbon-nanotube reinforced composite (CNTRC) plate, both cases of uniform distribution (UD) and functionally graded (FG) distribution patterns of SWCNT reinforcements are considered. The small size effects of microplate are considered based on Eringen's nonlocal theory. Based on orthotropic Mindlin plate theory along with von K$\acute{a}$rm$\acute{a}$n geometric nonlinearity and Hamilton's principle, the governing equations are derived. Generalized differential quadrature method (GDQM) is applied for obtaining the buckling load of system. The effects of different parameters such as nonlocal parameters, volume fractions of SWCNTs, distribution type of SWCNTs in polymer, elastomeric medium, aspect ratio, boundary condition, orientation of foundation orthtotropy direction and temperature are considered on the nonlinear buckling of the microplate. Results indicate that CNT distribution close to top and bottom are more efficient than those distributed nearby the mid-plane for increasing the buckling load.

• Computers and Concrete
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• v.19 no.6
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• pp.677-687
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• 2017

The nonlinear buckling response of nano composite anti-symmetric functionally graded polymeric microplate reinforced by single-walled carbon nanotubes (SWCNTs) rested on orthotropic elastomeric foundation with temperature dependent properties is investigated. For the carbon-nanotube reinforced composite (CNTRC) microplate, a uniform distribution (UD) and four types of functionally graded (FG) distribution are considered. Based on orthotropic Mindlin plate theory, von Karman geometric nonlinearity and Hamilton's principle, the governing equations are derived. Generalized differential quadrature method (GDQM) is employed to calculate the non-linear buckling response of the plate. Effects of FG distribution type, elastomeric foundation, aspect ratio (thickness to width ratio), boundary condition, orientation of foundation orthotropy and temperature are considered. The results are validated. It is found that the critical buckling load without elastic medium is significantly lower than considering Winkler and Pasternak medium.

• Ocean Systems Engineering
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• v.2 no.1
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• pp.69-81
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• 2012

Presented herein is a study on reducing the hydroelastic response of very large floating structures (VLFS) by altering their plan shapes. Two different categories of VLFS geometries are considered. The first category comprises longish VLFSs with different fore/aft end shapes but keeping their aspect ratios constant. The second category comprises various polygonal VLFS plan shapes that are confined within a square boundary or a circle. For the hydroelastic analysis, the water is modeled as an ideal fluid and its motion is assumed to be irrotational so that a velocity potential exists. The VLFS is modeled as a plate by adopting the Mindlin plate theory. The VLFS is assumed to be placed in a channel or river so that only the head sea condition is considered. The results show that the hydroleastic response of the VLFS could be significantly reduced by altering its plan shape.

• Structural Engineering and Mechanics
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• v.62 no.6
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• pp.675-693
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• 2017

In this paper, based on the first-order shear deformation plate theory, buckling analysis of piezoelectric coupled transversely isotropic rectangular plates is investigated. By assuming the transverse distribution of electric potential to be a combination of a parabolic and a linear function of thickness coordinate, the equilibrium equations for buckling analysis of plate with surface bonded piezoelectric layers are established. The Maxwell's equation and all boundary conditions including the conditions on the top and bottom surfaces of the plate for closed and open circuited are satisfied. The analytical solution is obtained for Levy type of boundary conditions. The accurate buckling load of laminated plate is presented for both open and closed circuit conditions. From the numerical results it is found that, the critical buckling load for open circuit is more than that of closed circuit in all boundary and loading conditions. Furthermore, the critical buckling loads and the buckling mode number increase by increasing the thickness of piezoelectric layers for both open and closed circuit conditions.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1992.04a
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• pp.7-12
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• 1992

The variable node plate bending element, ie, the element with one or two additional mid-side nodes is used in the analysis of mat foundation to generate the nearly ideal grid model in which more nodes are defined near the column location. The plate bending element used in this study is the one based on Mindlin/Reissner plate theory with substitute shear strain field and the nodal stresses of that element are obtained by the local smoothing technique. The interaction of the soil material with the mat foundation is modeled with Winkler springs connected to the nodal points in the mat model. The vertical stiffness of the soil material are represented in terms of a modulus of subgrade reaction and are computed in the same way as to the computation of consistent nodal force of uniform surface loading. Several mesh schemes were proposed and tested to find the most suitable scheme for mat foundation analysis.

• Structural Engineering and Mechanics
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• v.4 no.2
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• pp.149-162
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• 1996

A postbuckling analysis is presented for a simply supported, moderately thick rectangular plate subjected to combined axial compression and uniform temperature loading and resting on a two-parameter elastic foundation. The two cases of thermal postbuckling of initially compressed plates and of compressive postbuckling of initially heated plates are considered. The initial geometrical imperfection of the plate is taken into account. The formulations are based on the Reissner-Mindlin plate theory considering the first order shear deformation effect, and including the plate-foundation interaction and thermal effect. The analysis uses a deflection-type perturbation technique to determine the buckling loads and postbuckling equilibrium paths. Numerical examples cover the performances of perfect and imperfect, moderately thick plates resting on Winkler or Pasternak-type elastic foundations. Typical results are presented in dimensionless graphical form.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.9 no.1
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• pp.25-32
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• 1989

A finite element program for material nonlinear fracture analysis of reinforced concrete shell was developed. This method can be used to trace the load-displacement response and crack propagation through the elastic and inelastic ranges. A layered isoparametric flat finite element considering the coupling effect between the in-plane and the bending action was developed. Mindlin plate theory taking account of transverse shear deformation was used. The validity of the present program was proved by comparing the numerical results with Hedgren's experimental data.