• 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.

• Advances in nano research
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• v.7 no.6
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• pp.443-457
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• 2019

In this investigation, dynamic and bending behaviors of isolated protein microtubules are analyzed. Microtubules (MTs) can be considered as bio-composite structures that are elements of the cytoskeleton in eukaryotic cells and posses considerable roles in cellular activities. They have higher mechanical characteristics such as superior flexibility and stiffness. In the modeling purpose of microtubules according to a hollow beam element, a novel single variable sinusoidal beam model is proposed with the conjunction of modified strain gradient theory. The advantage of this model is found in its new displacement field involving only one unknown as the Euler-Bernoulli beam theory, which is even less than the Timoshenko beam theory. The equations of motion are constructed by considering Hamilton's principle. The obtained results are validated by comparing them with those given based on higher shear deformation beam theory containing a higher number of variables. A parametric investigation is established to examine the impacts of shear deformation, length scale coefficient, aspect ratio and shear modulus ratio on dynamic and bending behaviors of microtubules. It is remarked that when length scale coefficients are almost identical of the outer diameter of MTs, microstructure-dependent behavior becomes more important.

• Journal of the Microelectronics and Packaging Society
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• v.26 no.4
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• pp.39-46
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• 2019

A stiffness-gradient soft PDMS/hard PDMS/FPCB stretchable package of the island-bridge structure was processed using the polydimethylsiloxane (PDMS) as the base substrate and the more stiff flexible printed circuit board (FPCB) as the island substrate, and its effective elastic modulus and stretchable deformation characteristics were analyzed. With the elastic moduli of the soft PDMS, hard PDMS, and FPCB to be 0.28 MPa, 1.74 MPa, and 1.85 GPa, respectively, the effective elastic modulus of the soft PDMS/hard PDMS/FPCB package was analyzed as 0.58 MPa. When the soft PDMS of the soft PDMS/hard PDMS/FPCB package was stretched to a tensile strain of 0.3, the strains occurring at hard PDMS and FPCB were found to be 0.1 and 0.003, respectively.

• Design & Manufacturing
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• v.7 no.1
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• pp.11-18
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• 2013

This paper presents the plastic inhomogeneous deformation behavior of bimetal composite rods during the axisymmetric and steady-state extrusion process through a conical die. The rigid-plastic FE model considering frictional contact problem was used to analyze the co-extrusion process with material combinations of Cu/Al. Different cases of initial geometry shape for composite material were simulated under different conditions of co-extrusion process, which includes the interference and frictional conditions. The main design parameters influencing on deformation pattern are diameter ratio of the composite components and semi-die angle. Efforts are focused on the deformation patterns, velocity gradient, predicted forming load and the end distance through the various simulations. Simulation results indicate that there is an obvious difference of forming pattern with various diameter ratio and semi-die angle. The analysis in this paper is concentrated on the evaluation of the design parameters on the deformation pattern of composite rod.

• Structural Engineering and Mechanics
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• v.61 no.6
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• pp.721-736
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• 2017

In this paper, free vibration characteristics of functionally graded (FG) nanobeams embedded on elastic medium are investigated based on third order shear deformation (Reddy) beam theory by presenting a Navier type solution for the first time. The material properties of FG nanobeam are assumed to vary gradually along the thickness and are estimated through the power-law and Mori-Tanaka models. A two parameters elastic foundation including the linear Winkler springs along with the Pasternak shear layer is in contact with beam. The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen. The nonlocal equations of motion are derived based on third order shear deformation beam theory through Hamilton's principle and they are solved applying analytical solution. According to the numerical results, it is revealed that the proposed modeling can provide accurate frequency results of the FG nanobeams as compared to some cases in the literature. The obtained results are presented for the vibration analysis of the FG nanobeams such as the influences of foundation parameters, gradient index, nonlocal parameter and slenderness ratio in detail.

• Steel and Composite Structures
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• v.32 no.3
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• pp.389-410
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• 2019

In this article, a simple quasi-3D shear deformation theory is employed for thermo-mechanical bending analysis of functionally graded material (FGM) sandwich plates. The displacement field is defined using only 5 variables as the first order shear deformation theory (FSDT). Unlike the other high order shear deformation theories (HSDTs), the present formulation considers a new kinematic which includes undetermined integral variables. The governing equations are determined based on the principle of virtual work and then they are solved via Navier method. Analytical solutions are proposed to provide the deflections and stresses of simply supported FGM sandwich structures. Comparative examples are presented to demonstrate the accuracy of the present theory. The effects of gradient index, geometrical parameters and thermal load on thermo-mechanical bending response of the FG sandwich plates are examined.

• Journal of the Korean Society for Railway
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• v.20 no.5
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• pp.637-648
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• 2017

In this paper, the effects of initial built-in deformation and temperature deformation on the stress distribution of discontinuous precast concrete track slab under train load were examined. According to the results, when train load is put on a precast concrete slab with initial built-in deformation and deformation due to temperature gradient, the maximum tensile stresses develop at the upper side of slab in the slab center, edge center and corner of shear pocket; the stress distribution is different from that of the case under train load only. Therefore, to accurately predict the actual weak points and failure modes, one should calculate the stress under train load considering the initial built-in and temperature deformation of the slab.

• Journal of KIISE:Software and Applications
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• v.37 no.1
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• pp.9-18
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• 2010

This paper proposes a deformable registration method using a demon algorithm for aligning the lungs between end-exhale and end-inhale CT scans. The lungs are globally aligned by affine transformation and locally deformed by a demon algorithm. The use of floating gradient force allows a fast convergence in the lung regions with a weak gradient of the reference image. The active-cell-based demon algorithm helps to accelerate the registration process and reduce the probability of deformation folding because it avoids unnecessary computation of the displacement for well-matched lung regions. The performance of the proposed method was evaluated through comparisons of methods that use a reference gradient force or a combined gradient force as well as methods with and without active cells. The results show that the proposed method can accurately register lungs with large deformations and can reduce the processing time considerably.

• Journal of Powder Materials
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• v.29 no.5
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• pp.382-389
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• 2022

A typical trade-off relationship exists between strength and elongation in face-centered cubic metals. Studies have recently been conducted to enhance strength without ductility reduction through surface-treatment-based ultrasonic nanocrystalline surface modification (UNSM), which creates a gradient microstructure in which grains become smaller from the inside to the surface. The transformation-induced plasticity effect in Fe-Mn alloys results in excellent strength and ductility due to their high work-hardening rate. This rate is achieved through strain-induced martensitic transformation when an alloy is plastically deformed. In this study, Fe-6%Mn powders with different sizes were prepared by high-energy ball milling and sintered through spark plasma sintering to produce Fe-6%Mn samples. A gradient microstructure was obtained by stacking the different-sized powders to achieve similar effects as those derived from UNSM. A compressive test was performed to investigate the mechanical properties, including the yielding behavior. The deformed microstructure was observed through electron backscatter diffraction to determine the effects of gradient plastic deformation.

• Structural Engineering and Mechanics
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• v.28 no.5
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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.