• Structural Engineering and Mechanics
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• 제28권5호
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• pp.603-633
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• 2008

A four-node plate finite element for the analysis of laminated composites which is developed using strain gradient notation is presented. The element is based on a first-order shear deformation theory and on the equivalent lamina assumption. Strains and stresses can be calculated at different points through the thickness of the plate. They are averaged values due to the equivalent lamina assumption. A shear correction factor is used as the transverse shear strain is taken to be constant over the plate thickness while its actual variation is parabolic. Strain gradient notation, which is physically interpretable, allows for the detailed a-priori analysis of the finite element model. The polynomial expansions are inspected and spurious terms responsible for modeling errors are identified in the shear strains polynomial expansions. The element is corrected by simply removing the spurious terms from the shear strains expansions. The element is implemented into a FORTRAN finite element code in two versions; namely, with and without spurious terms. Results are compared to show the effects of the spurious terms on the solutions. It is also shown that a refined mesh composed of corrected elements provides solutions which approximate very well the analytical solutions, validating the procedure.

• 한국지반신소재학회논문집
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• 제4권3호
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• pp.3-10
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• 2005

본 연구는 연직 배수재의 통수능력 저감 요인인 측방토압, 동수경사, 배수재의 변형에 의한 통수능력의 저감을 밝히기 위하여 현장조건에 가장 부합되는 고무 멤부레인 안에 하모니카형, 성곽형, 파이버형 드레인을 설치한 후 드레인 주변에 슬러리 상태의 점토를 넣고 통수능 특성에 관한 실험을 실시하였다. 그 결과 배수재의 종류에 따른 통수능력은 하모니카형, 성곽형, 파이버형 순으로 통수능력이 컸으며, 또한 측압 보다 동수경사에 대한 통수능력 감소가 높게 나타났다.

• Structural Engineering and Mechanics
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• 제76권4호
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• pp.551-559
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• 2020

On the basis of nonlocal strain gradient theory, considering the material properties of porous FGM changing with thickness and the influence of moment of inertia, the wave equation of FG nano circular plate is derived by using the first-order shear deformation plate theory, by introducing dimensionless parameters, we transform the equations into dimensionless wave equations, and the dispersion relations of bending wave, shear wave and longitudinal wave are obtained by Laplace and Hankel integral transformation method. The influence of nonlocal parameter, porosity volume fraction, strain gradient parameters and power law index on the propagation characteristics of bending wave, shear wave and longitudinal wave in FG nano circular plate.

• 한국전산유체공학회지
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• 제6권4호
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• pp.15-25
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• 2001

Numerical prediction of the diffusion controlled transition in a turbine gas pass is important because it can change the local heat transfer rate over a turbine blade as much as three times. In this study, the gas flow over turbine blade is simplified to the flat plate boundary layer, and an adaptive grid scheme redistributing grid points within the computation domain is proposed with a great emphasis on the construction of the grid control function. The function is sensitized to the second invariant of the mean strain tensor, its spatial gradient, and the interaction of pressure gradient and flow deformation. The transition process is assumed to be described with a κ-ε turbulence model. An elliptic solver is employed to integrate governing equations. Numerical results show that the proposed adaptive grid scheme is very effective in obtaining grid independent numerical solution with a very low grid number. It is expected that present scheme is helpful in predicting actual flow within a turbine to improve computation efficiency.

• 대한전기학회논문지:전기물성ㆍ응용부문C
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• 제50권2호
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• pp.86-95
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• 2001

Mechanical properties of electroplated gold microstructures were determined from the micromachined beam structures. Cantilever and bridge beam structures of different length were fabricated by electroplating-surface micromachining technique, which is specially designed to realize an anchor structure close to an ideal fixed-boundary condition. Fabricated beams were electrostatically excited and their resonance frequencies were measured by optical system composed of laser displacement meter with dynamic signal analyzer. Young's modulus and mean residual stress were calculated from the measured frequencies of microbeams. In addtion, stress gradient was measured using deformation of released cantilever beam structure.

• 대한기계학회논문집A
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• 제27권6호
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• pp.914-922
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• 2003

In this paper, the strain localization of voided ductile material has been analyzed by nonlocal plasticity formulation in which the yield strength not only depends on an equivalent plastic strain measure (hardening parameter), but also on the Laplacian thereof. The gradient terms in yield criterion show an important role on modeling strain-softening phenomena of material. The influence of the mesh size on the elastic -plastic deformation behavior and the effect of the characteristic length parameter for localization prediction are also investigated. The proposed nonlocal plasticity shows that the load -strain curves converge to one curve. Results using nonlocal plasticity also exhibit the dependence of mesh size is much less sensitivity than that for a corresponding local plasticity formulation.

• Steel and Composite Structures
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• 제25권5호
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• pp.581-591
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• 2017

The dynamic instability of truncated conical shells subjected to dynamic axial load within first order shear deformation theory (FSDT) is examined. The conical shell is made from functionally graded (FG) orthotropic material. In the formulation of problem a dynamic version of Donnell's shell theory is used. The equations are converted to a Mathieu-Hill type differential equation employing Galerkin's method. The boundaries of main instability zones are found applying the method proposed by Bolotin. To verify these results, the results of other studies in the literature were compared. The influences of material gradient, orthotropy, as well as changing the geometric dimensions on the borders of the main areas of the instability are investigated.

• Advances in nano research
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• 제12권4호
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• pp.427-440
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• 2022

In the present study, the nonlocal strain gradient theory is used to predict the size-dependent buckling and post-buckling behavior of geometrically imperfect nano-scale piezo-flexomagnetic plate strips in two modes of direct and converse flexomagnetic effects. The first-order shear deformation plate theory is used to analyze analytically nano-strips with simply supported boundary conditions. The nonlinear governing equations of equilibrium and associated boundary conditions are derived using the principle of minimum total potential energy with consideration of the von Kármán-type of geometric nonlinearity. A closed-form solution of governing differential equation is obtained, which is easily usable for engineers and designers. To validate the presented formulations, whenever possible, a comparison with the results found in the open literature is reported for buckling loads. A parametric study is presented to examine the effect of scaling parameters, plate slenderness ratio, temperature, the mid-plane initial rise, flexomagnetic coefficient, different temperature distributions, and magnetic potential, in case of the converse flexomagnetic effect, on buckling and post-buckling loads in detail.

• Computers and Concrete
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• 제30권4호
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• pp.243-256
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• 2022

The static analysis of spinning functionally graded (FG) nanotube on the basis of the nonlocal strain gradient theory (NSGT) is presented. The high-order beam theory is employed for mathematical modeling of the tube structures according to the Sinusoidal shear deformation beam theory. The energy conservation principle is operated to generate the equations. The centrifugal force is assumed along the tube length due to the rotating of the tube, moreover, the nanotube is made of functionally graded material (FGM) composed of ceramic and metal phases along the tube radius direction. The generalized differential quadratic method (GDQM) is utilized to solve the formulations. Finally, the numerical results are discussed in detail to examine the impact of different relevant parameters on the bending the buckling behavior of the rotating nanotube.

• Advances in concrete construction
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• 제15권2호
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• pp.97-114
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• 2023

The nonlocal strain gradient theory for the static bending analysis of graphene nanoplatelets (GPLs) reinforced the nanoplate is developed in this paper. The nanoplatelet is exposed to thermo-mechanical loads and is also supposed to stand on an elastic foundation. For computing impressive composite material characteristics, the Halpin-Tsai model is selected for various sectors. The various distributions are propounded including UD, FG-O, and FG-X. The represented equations are acquired based on the virtual work and sinusoidal shear and normal deformation theory (SSNDT). Navier's solution as the analytical method is applied to solve these equations. Furthermore, the effects of GPL weight fraction, temperature parameters, distribution pattern and parameters of the foundation are presented and discussed.