• Geomechanics and Engineering
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• v.16 no.1
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• pp.1-9
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• 2018

In this paper an efficient and simple refined shear deformation theory is presented for the free vibration of Functionally Graded Plates Under Various Boundary Conditions. The theory accounts for a quadratic variation of the transverse shear strains across the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. The number of independent unknowns of present theory is four, as against five in other shear deformation theories. The plates are considered of the type having two opposite sides simply-supported, and the two other sides having combinations of simply-supported, clamped, and free boundary conditions. The mechanical properties of functionally graded material are assumed to vary according to power law distribution of the volume fraction of the constituents. Equations of motion are derived using Hamilton's principle. The results of this theory are compared with those of other shear deformation theories. Various numerical results including the effect of boundary conditions, power-law index, plate aspect ratio, and side-to-thickness ratio on the free vibration of FGM plates are presented.

• Steel and Composite Structures
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• v.23 no.3
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• pp.339-350
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• 2017

In this paper, various nonlocal higher-order shear deformation beam theories that consider the size dependent effects in Functionally Graded Material (FGM) beam are examined. The presented theories fulfill the zero traction boundary conditions on the top and bottom surface of the beam and a shear correction factor is not required. Hamilton's principle is used to derive equation of motion as well as related boundary condition. The Navier solution is applied to solve the simply supported boundary conditions and exact formulas are proposed for the bending and static buckling. A parametric study is also included to investigate the effect of gradient index, length scale parameter and length-to-thickness ratio (aspect ratio) on the bending and the static buckling characteristics of FG nanobeams.

• Journal of Korea Foundry Society
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• v.26 no.3
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• pp.140-145
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• 2006

Sr, added in the hypereutectic Al-Si alloys, is absorbed on the surfaces of primary Si as well as eutectic Si, and can change the growth mode of primary Si from non-faceted to faceted mode, as the amount of Sr increases larger than 0.04 wt.%, even though it cannot affect the grain size of primary Si, significantly. The EBSD analysis shows that the traction of ${\Sigma}3$ boundary(twin boundary) increases as the amount of Sr in the hypereutectic Al-Si alloys increase until the over-modification occurs at 1.6 wt.%Sr and proves that the change in growth mode of primary Si results from the change of TPRE growth to IIT growth.

• The Journal of the Acoustical Society of Korea
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• v.18 no.1E
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• pp.37-43
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• 1999

This paper deals with a hybrid finite element method for wave scattering problems in infinite domains. Scattering of waves involving complex geometries, in conjunction with infinite domains is modeled by introducing a mathematical boundary within which a finite element representation is employed. On the mathematical boundary, the finite element representation is matched with a known analytical solution in the infinite domain in terms of fields and their derivatives. The derivative continuity is implemented by using a slope constraint. Drilling degrees of freedom at each node of the finite element model are introduced to make the numerical model more sensitive to the transverse component of the elastodynamic field. To verify the effects of drilling degrees freedom and slope constraints individually, reflection of normally incident P and SV waves on a traction free half spaces is considered. For the P-wave incidence, the results indicate that the use of slope constraint is more effective because it suppresses artificial reflection at the mathematical boundary. For the SV-wave case, the use of drilling degrees freedom is more effective by reducing numerical error at irregular frequencies.

• Bulletin of the Society of Naval Architects of Korea
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• v.25 no.4
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• pp.39-46
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• 1988

The purpose of this paper is to apply the boundary element method to predict the crack growth path. The quarter point element with traction singularity at the crack tip is applied to compact tension type specimens and two inclined slit problems under compression load. The maximum stress criterion which was originally derived for the crack initiation is extended to the analysis of the crack propagation. The predicted crack paths with 1/4 crack growth increment of initial crack length agree quite well with experimental results. It is found that the computed crack path of the boundary element analysis is not mainly affected by the crack increment length.

• Smart Structures and Systems
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• v.18 no.2
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• pp.267-291
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• 2016

In this research work, an exact analytical solution for thermal buckling analysis of functionally graded material (FGM) sandwich plates with clamped boundary condition subjected to uniform, linear, and non-linear temperature rises across the thickness direction is developed. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The theory accounts for parabolic distribution of the transverse shear strains, and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factor. A power law distribution is used to describe the variation of volume fraction of material compositions. Equilibrium and stability equations are derived based on the present refined theory. The non-linear governing equations are solved for plates subjected to simply supported and clamped boundary conditions. The thermal loads are assumed to be uniform, linear and non-linear distribution through-the-thickness. The effects of aspect and thickness ratios, gradient index, on the critical buckling are all discussed.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.30 no.2A
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• pp.131-136
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• 2010

In this study, most of famous algorithms for the corner problem are listed. By comparing these with implemented codes and theoretical dissections, new algorithms are developed. These algorithms are combined by the existing auxiliary equations. All relating algorithms are numerically tested with 3 problems. Two problems have well-known analytical solutions and the result of another example is compared with the one of the published paper. The conducted research reveals the characteristics of existing algorithms and demonstrates newly developed algorithms can produce a reasonable solution by reflecting various type of boundary conditions.

• Journal of Mechanical Science and Technology
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• v.14 no.2
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• pp.197-206
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• 2000

A boundary integral equation method in the shape design sensitivity analysis is developed for the elasticity problems with axisymmetric non-homogeneous bodies. Functionals involving displacements and tractions at the zonal interface are considered. Sensitivity formula in terms of the interface shape variation is then derived by taking derivative of the boundary integral identity. Adjoint problem is defined such that displacement and traction discontinuity is imposed at the interface. Analytic example for a compound cylinder is taken to show the validity of the derived sensitivity formula. In the numerical implementation, solutions at the interface for the primal and adjoint system are used for the sensitivity. While the BEM is a natural tool for the solution, more generalization should be made since it should handle the jump conditions at the interface. Accuracy of the sensitivity is evaluated numerically by the same compound cylinder problem. The endosseous implant-bone interface problem is considered next as a practical application, in which the stress value is of great importance for successful osseointegration at the interface. As a preliminary step, a simple model with tapered cylinder is considered in this paper. Numerical accuracy is shown to be excellent which promises that the method can be used as an efficient and reliable tool in the optimization procedure for the implant design. Though only the axisymmetric problem is considered here, the method can be applied to general elasticity problems having interface.

• Transactions of the Korean Society of Mechanical Engineers
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• v.10 no.5
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• pp.787-797
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• 1986

An implicit approach is employed to obtain a general boundary integral formulation of axisymmetric elastic problems in terms of a pair of singular integral equations. The corresponding kernel functions from the solutions of Navier's equation are derived by applying a three dimensional integral and a direct axisymmetrical approach. A numerical discretization schem including the evaluation of Cauchy principal values of the singular integral is described. Finally the typical axisymmetric elastic models are analyzed, i.e. the hollow sphere, the constant thickness and the V-notched round bar.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.1
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• pp.66-76
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• 2003

The arbitrary V-notched crack problem is considered. The general expressions for the stress components on this problem are obtained as explicit series forms composed of independent unknown coefficients which are denoted by coefficients of eigenvector. For this results eigenvalue equation is performed first through introducing complex stress functions and applying the traction free boundary conditions. Next solving this equation, eigenvalues and corresponding eigenvectors are obtained respectively, and finally inserting these results into stress components, the general equations are obtained. These results are also shown to be applicable to the symmetric V-notched crack or straight crack. It can be shown that this solutions are composed of the linear combination of Mode I and Mode II solutions which are obtained from different characteristic equations, respectively. Through performing asymptotic analysis for stresses, the stress intensity factor is given as a closed form equipped with the unknown coefficients of eigenvector. In order to calculate the unknown coefficients. based on these general explicit equations, numerical programming using the overdetermined boundary collocation method which is algorithmed originally by Carpenter is also worked out. As this programming requires the input data, the commercial FE analysis for stresses is performed. From this study, for some V-notched problems, unknown coefficients can be calculated numerically and also fracture parameters are determined.