Sung-Cheon Han

Analysis of Sigmoid Functionally Graded Material (S-FGM) Nanoscale Plates Using the Nonlocal Elasticity Theory

Based on a nonlocal elasticity theory, a model for sigmoid functionally graded material (S-FGM) nanoscale plate with first-order shear deformation is studied. The material properties of S-FGM nanoscale plate are assumed to vary according to sigmoid function (two power law distribution) of the volume fraction of the constituents. Elastic theory of the sigmoid FGM (S-FGM) nanoscale plate is reformulated using the nonlocal differential constitutive relations of Eringen and first-order shear deformation theory. The equations of motion of the nonlocal theories are derived using Hamilton’s principle. The nonlocal elasticity of Eringen has the ability to capture the small scale effect. The solutions of S-FGM nanoscale plate are presented to illustrate the effect of nonlocal theory on bending and vibration response of the S-FGM nanoscale plates. The effects of nonlocal parameters, power law index, aspect ratio, elastic modulus ratio, side-to-thickness ratio, and loading type on bending and vibration response are investigated. Results of the present theory show a good agreement with the reference solutions. These results can be used for evaluating the reliability of size-dependent S-FGM nanoscale plate models developed in the future.

Nonlocal elasticity theory for transient analysis of higher-order shear deformable nanoscale plates

The small scale effect on the transient analysis of nanoscale plates is studied. The elastic theory of the nano-scale plate is reformulated using Eringens nonlocal differential constitutive relations and higher-order shear deformation theory (HSDT). The equations of motion of the nonlocal theories are derived for the nano-scale plates. The Eringens nonlocal elasticity of Eringen has ability to capture the small scale effects and the higher-order shear deformation theory has ability to capture the quadratic variation of shear strain and consequently shear stress through the plate thickness. The solutions of transient dynamic analysis of nano-scale plate are presented using these theories to illustrate the effect of nonlocal theory on dynamic response of the nano-scale plates. On the basis of those numerical results, the relations between nonlocal and local theory are investigated and discussed, as are the nonlocal parameter, aspect ratio, side-to-thickness ratio, nano-scale plate size, and time step effects on the dynamic response. In order to validate the present solutions, the reference solutions are employed and examined. The results of nano-scale plates using the nonlocal theory can be used as a benchmark test for the transient analysis.

A refined element-based Lagrangian shell element for geometrically nonlinear analysis of shell structures

For the solution of geometrically nonlinear analysis of plates and shells, the formulation of a nonlinear nine-node refined first-order shear deformable element-based Lagrangian shell element is presented. Natural co-ordinate-based higher order transverse shear strains are used in present shell element. Using the assumed natural strain method with proper interpolation functions, the present shell element generates neither membrane nor shear locking behavior even when full integration is used in the formulation. Furthermore, a refined first-order shear deformation theory for thin and thick shells, which results in parabolic through-thickness distribution of the transverse shear strains from the formulation based on the third-order shear deformation theory, is proposed. This formulation eliminates the need for shear correction factors in the first-order theory. To avoid difficulties resulting from large increments of the rotations, a scheme of attached reference system is used for the expression of rotations of shell normal. Numerical examples demonstrate that the present element behaves reasonably satisfactorily either for the linear or for geometrically nonlinear analysis of thin and thick plates and shells with large displacement but small strain. Especially, the nonlinear results of slit annular plates with various loads provided the benchmark to test the accuracy of related numerical solutions.

An 8-Node Shell Element for Nonlinear Analysis of Shells Using the Refined Combination of Membrane and Shear Interpolation Functions

An improved 8-node shell finite element applicable for the geometrically linear and nonlinear analyses of plates and shells is presented. Based on previous first-order shear deformation theory, the finite element model is further improved by the combined use of assumed natural strains and different sets of collocation points for the interpolation of the different strain components. The influence of the shell element with various conditions such as locations, number of enhanced membranes, and shear interpolation is also identified. By using assumed natural strain method with proper interpolation functions, the present shell element generates neither membrane nor shear locking behavior even when full integration is used in the formulation. Furthermore, to characterize the efficiency of these modifications of the 8-node shell finite elements, numerical studies are carried out for the geometrically linear and non-linear analysis of plates and shells. In comparison to some other shell elements, numerical examples for the methodology indicate that the modified element described locking-free behavior and better performance. More specifically, the numerical examples of annular plate presented herein show good validity, efficiency, and accuracy to the developed nonlinear shell element.

An improved treatment of mixed interpolation functions in eight-node assumed natural strain shell element for vibration analysis

In this article, we investigate the vibration analysis of plates and shells, using an eight-node shell element that allows for the effects of transverse shear deformation and rotary inertia. The natural frequencies of plates and shells are presented, and the forced vibration analysis of plates and shells subjected to arbitrary loading is carried out. In order to overcome membrane and shear locking phenomena, the assumed natural strain method is used. To improve the eight-node shell element for free and forced vibration analysis, a new combination of sampling points for assumed natural strain method was applied. The refined first-order shear deformation theory based on Reissner–Mindlin theory, which directly addresses the transverse shear deformation without a shear correction factor, is adopted for the development of a new eight-node assumed strain shell element with rotary inertia effect. In order to validate the finite element numerical solutions, the reference solutions of plates based on the first-order shear deformation theory are presented. Results of the present theory show good agreement with the reference solutions. In addition, the effect of damping is investigated on the forced vibration analysis of plates and shells.

Fatigue life evaluation of continuous welded rails on concrete slab track in Korea high-speed railway:

There is a rapidly increasing demand for continuous welded rails. Continuous welded rails provide a more suitable installation on concrete slab tracks and more rapid and smooth movement and reduce overall maintenance cost. During the relatively short period in which concrete slab tracks have been used in Korea, there has been no documented case of rail fracture caused by repeated loading. This makes the evaluation of rail fatigue life using field data more difficult. In this study, the rail bending stress developed during high-speed train operation is obtained through analysis of vehicle–track interaction, and the correlation is analyzed by performing multiple regression analysis on train speed and rail surface irregularities. Equations for predicting the rail bending stress with regard to train speed and rail surface irregularity were derived. The effects of vehicle speed, track support stiffness, and fracture probability on the fatigue life of continuous welded rails on a concrete slab track in Korea high-speed railway were analyzed.

Experimental study of effects of track systems on static and dynamic behavior of railway bridges

The characteristic exposure of railway bridges to periodic live loads makes an understanding of their dynamic behavior important to their design and construction. This, together with the fact that the behavior of a railway bridge is affected by its track system, has prompted our study of the static and dynamic properties of such bridges. The deflection and stress due to the bending moment were measured, and the location of the neutral axis of each section, the natural frequency, and the damping ratio were analyzed for three systems: girder only, ballast track, and concrete track with various stiffnesses of resilience pad of rail fastening system. Compared to the ballast track, the concrete track extended the location of the neutral axis of the structure by about 6% in the upward direction. Moreover, the dynamic responses of the structure linearly increased with the maximum load and dramatically increased with the load amplitude during resonance. However, the damping ratio was the same with and without a track system. These results confirm the importance of a track system on the essential behavior of railway bridges, especially when a concrete track system is used.

Buckling analysis of nano-scale magneto-electro-elastic plates using the nonlocal elasticity theory

Buckling analysis of nonlocal magneto-electro-elastic nano-plate is investigated based on the higher-order shear deformation theory. The in-plane magnetic and electric fields can be ignored for magneto-electro-elastic nano-plates. According to magneto-electric boundary condition and Maxwell equation, the variation of magnetic and electric potentials along the thickness direction of the magneto-electro-elastic plate is determined. To reformulate the elastic theory of magneto-electro-elastic nano-plate, the nonlocal differential constitutive relations of Eringen is applied. Using the variational principle, the governing equations of the nonlocal theory are derived. The relations between local and nonlocal theories are studied by numerical results. Also, the effects of nonlocal parameters, in-plane load directions, and aspect ratio on buckling response are investigated. Numerical results show the effects of the electric and magnetic potentials. These numerical results can be useful in the design and analysis of advanced structures constructed from magneto-electro-elastic materials.