• International Journal of Precision Engineering and Manufacturing
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• v.3 no.2
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• pp.33-44
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• 2002

The problem of eigenvalues and eigenvectors is obtained from a v-notched crack in pseudo-isotropic dissimilar materials by the traction free boundary and the perfect bonded conditions at interface. The complex stress function of the two-term William's type is used. The eigenvalues are solved by a commercial numerical program, MATHEMATICA. Stress singularities for v-notched cracks in pseudo-isotropic dissimilar materials are discussed. The RWCIM(Reciprocal Work Contour Integral Method) is applied to the determination of eigenvector coefficients associated with eigenvalues with egenvalues. The RWCIM algorithm is also coded by the MATHEMATICA.

• Interaction and multiscale mechanics
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• v.5 no.1
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• pp.13-26
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• 2012

In this paper, the wave propagation in a generalized thermo elastic plate embedded in an elastic medium (Winkler model) is studied based on the Lord-Schulman (LS) and Green-Lindsay (GL) generalized two dimensional theory of thermo elasticity. Two displacement potential functions are introduced to uncouple the equations of motion. The frequency equations that include the interaction between the plate and foundation are obtained by the traction free boundary conditions using the Bessel function solutions. The numerical calculations are carried out for the material Zinc and the computed non-dimensional frequency and attenuation coefficient are plotted as the dispersion curves for the plate with thermally insulated and isothermal boundaries. The wave characteristics are found to be more stable and realistic in the presence of thermal relaxation times and the foundation parameter. A comparison of the results for the case with no thermal effects shows well agreement with those by the membrane theory.

• Advances in aircraft and spacecraft science
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• v.4 no.6
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• pp.639-650
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• 2017

The objective of this paper is to obtain three-dimensional (3D) effective properties for layered composites with imperfect interfaces using mechanics of structure genome. The imperfect interface is modeled using linear traction-displacement model that allows small infinitesimal displacement jump across the interface. The predictions obtained from the current analysis are compared with the 3D finite element analysis (FEA). In this study, it is found that the present model shows excellent agreement with the results obtained using 3D FEA by employing periodic boundary conditions. The prediction also reveals that in-plane longitudinal and shear moduli, and all Poisson's ratios are observed to be not affected by the interfacial stiffness while the predictions of transverse longitudinal and shear moduli are significantly influenced by interfacial stiffness.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.4
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• pp.941-949
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• 1995

An efficient method based on analytic solutions is applied to solve anti-plane Mode III crack problems. The analytic technique developed earlier by the present authors for Laplace's equation in a simply-connected region is now extended to general Mode III crack problems. Unlike typical numerical methods which require fine meshing near crack tips, the present method divides the cracked bodies, typically non-convex or multiply-connected, into only a few super elements. In each super element, an element stiffness matrix, relating the series coefficients of the traction and displacement, is first formed. Then an assembly algorithm similar to that used in the finite elements, is first formed. Then an assembly algorithm similar to that used in the finite elements, is developed. A big advantage of the present method is that only the boundary conditions are to be satisfied in the solution procedure due to the use of analytic solutions. Several numerical results demonstrate the efficiency and accuracy of the present method.

• Wind and Structures
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• v.23 no.6
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• pp.543-558
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• 2016

The response of functionally graded ceramic-metal plates is investigated using theoretical formulation, Navier's solutions, and a new displacement based on the high-order shear deformation theory are presented for static analysis of functionally graded plates. 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 plates are assumed to have isotropic, two-constituent material distribution through the thickness, and the modulus of elasticity of the plate is assumed to vary according to a power-law distribution in terms of the volume fractions of the constituents. Numerical results of the new refined plate theory are presented to show the effect of the material distribution on the deflections, stresses and fundamental frequencies. It can be concluded that the proposed theory is accurate and simple in solving the static and free vibration behavior of functionally graded plates.

• Advances in aircraft and spacecraft science
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• v.5 no.6
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• pp.671-689
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• 2018

Bending, buckling and free vibration responses of functionally graded (FG) higher-order beams resting on two parameter (Winkler-Pasternak) elastic foundation are studied using a new inverse hyperbolic beam theory. The material properties of the beam are graded along the thickness direction according to the power-law distribution. In the present theory, the axial displacement accounts for an inverse hyperbolic distribution, and the transverse shear stress satisfies the traction-free boundary conditions on the top and bottom surfaces of the beams. Hamilton's principle is employed to derive the governing equations of motion. Navier type analytical solutions are obtained for the bending, bucking and vibration problems. Numerical results are obtained to investigate the effects of power-law index, length-to-thickness ratio and foundation parameter on the displacements, stresses, critical buckling loads and frequencies. Numerical results by using parabolic beam theory of Reddy and first-order beam theory of Timoshenko are specially generated for comparison of present results and found in excellent agreement with each other.

• Earthquakes and Structures
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• v.19 no.2
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• pp.91-101
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• 2020

This work presents an efficient and original hyperbolic shear deformation theory for the bending and dynamic behavior of functionally graded (FG) beams resting on Winkler - Pasternak foundations. The theory accounts for hyperbolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the beam without using shear correction factors. Based on the present theory, the equations of motion are derived from Hamilton's principle. Navier type analytical solutions are obtained for the bending and vibration problems. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions. It can be concluded that the present theory is not only accurate but also simple in predicting the bending and vibration behavior of functionally graded beams.

• Steel and Composite Structures
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• v.19 no.4
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• pp.829-841
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• 2015

In this paper, a refined exponential shear deformation beam theory is developed for bending analysis of functionally graded beams. The theory account for parabolic variation of transverse shear strain through the depth of the beam and satisfies the zero traction boundary conditions on the surfaces of the beam without using shear correction factors. Contrary to the others refined theories elaborated, where the stretching effect is neglected, in the current investigation this so-called "stretching effect" is taken into consideration. The material properties of the functionally graded beam are assumed to vary according to power law distribution of the volume fraction of the constituents. Based on the present shear deformation beam theory, the equilibrium equations are derived from the principle of virtual displacements. Analytical solutions for static are obtained. Numerical examples are presented to verify the accuracy of the present theory.

• Journal of the Korean Society for Precision Engineering
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• v.20 no.9
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• pp.159-165
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• 2003

Most engineers interested in stress singularities have focused mainly on the research of power stress singularities for v-notched cracks in dissimilar materials. The logarithmic stress singularity was discussed a little in Bogy's paper. The power-logarithmic stress singularity was reported by Dempsey and Sinclair. It was indicated that the logarithmic singularity is only a special case of power-logarithmic stress singularities. Then, Dempsey reported specific cases which have power-logarithmic singularities even fur homogeneous boundary conditions. It was known that logarithmic stress singularities for v-notched cracks in dissimilar materials occurs when the surfaces of a v-notched crack have constant tractions. In this paper, using the complex potential method, the stresses and displacements having logarithmic stress singularities were obtained and the coefficients vectors were calculated by a numerical program code: Mathematica. It was shown that our analysis models don't have logarithmic stress singularities under the constant tractions, although the coefficient vectors are existing.

• Steel and Composite Structures
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• v.16 no.5
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• pp.507-519
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• 2014

In this paper, a higher order shear deformation beam theory is developed for static and free vibration analysis of functionally graded beams. The theory account for higher-order variation of transverse shear strain through the depth of the beam and satisfies the zero traction boundary conditions on the surfaces of the beam without using shear correction factors. The material properties of the functionally graded beam are assumed to vary according to power law distribution of the volume fraction of the constituents. Based on the present higher-order shear deformation beam theory, the equations of motion are derived from Hamilton's principle. Navier type solution method was used to obtain frequencies. Different higher order shear deformation theories and classical beam theories were used in the analysis. A static and free vibration frequency is given for different material properties. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions.