• Journal of applied mathematics & informatics
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• v.6 no.3
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• pp.873-884
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• 1999

On the basis of the semi-linear material of John invoking the theory of homogenization for heterogeneous media and the theory of invariants for isotropic scalar functions an energy function is built for a transversely-isotropic medium in finite elastic deformation. The ponyting Effect for material in simple shear is reviewed for this case of transversal isotropy. It is shown that this effect is apprehended by the constructed energy function.

• Earthquakes and Structures
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• v.10 no.1
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• pp.91-104
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• 2016

In this paper we investigate the existence of SH-waves in fiber-reinforced layer placed over a heterogeneous elastic half-space. The heterogeneity of the elastic half-space is caused by the exponential variations of density and rigidity. As a special case when both the layers are homogeneous, our derived equation is in agreement with the general equation of Love wave. Numerically, it is observed that the velocity of SH-waves decreases with the increase of heterogeneity and reinforced parameters. The dimensionless phase velocity of SH-waves increases with the decreases of dimensionless wave number and shown through figures.

• Advances in nano research
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• v.7 no.6
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• pp.405-417
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• 2019

This research is devoted to study post-buckling analysis of functionally graded carbon nanotubes reinforced composite (FG-CNTRC) micro plate with cut out subjected to magnetic field and resting on elastic medium. The basic formulation of plate is based on first order shear deformation theory (FSDT) and the material properties of FG-CNTRCs are presumed to be changed through the thickness direction, and are assumed based on rule of mixture; moreover, nonlocal Eringen's theory is applied to consider the size-dependent effect. It is considered that the system is embedded in elastic medium and subjected to longitudinal magnetic field. Energy approach, domain decomposition and Rayleigh-Ritz methods in conjunction with Newton-Raphson iterative technique are employed to trace the post-buckling paths of FG-CNTRC micro cut out plate. The influence of some important parameters such as small scale effect, cut out dimension, different types of FG distributions of CNTs, volume fraction of CNTs, aspect ratio of plate, magnitude of magnetic field, elastic medium and biaxial load on the post-buckling behavior of system are calculated. With respect to results, it is concluded that the aspect ratio and length of square cut out have negative effect on post-buckling response of micro composite plate. Furthermore, existence of CNTs in system causes improvement in the post-buckling behavior of plate and different distributions of CNTs in plate have diverse response. Meanwhile, nonlocal parameter and biaxial compression load on the plate has negative effect on post-buckling response. In addition, imposing magnetic field increases the post-buckling load of the microstructure.

• Advances in nano research
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• v.6 no.4
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• pp.339-356
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• 2018

In this article, the critical buckling of a single-walled carbon nanotube (SWCNT) embedded in Kerr's medium is studied. Based on the nonlocal continuum theory and the Euler-Bernoulli beam model. The governing equilibrium equations are acquired and solved for CNTs subjected to mechanical loads and embedded in Kerr's medium. Kerr-type model is employed to simulate the interaction of the (SWNT) with a surrounding elastic medium. A first time, a comparison with the available results is made, and another comparison between various models Winkler-type, Pasternak-type and Kerr-type is studied. Effects of nonlocal parameter and aspect ratio of length to diameter of nanobeam, as well as the foundation parameters on buckling of CNT are investigated. These results are important in the mechanical design considerations of nanocomposites based on carbon nanotubes.

• Journal of the Korea institute for structural maintenance and inspection
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• v.20 no.5
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• pp.93-101
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• 2016

In this study, the governing equations of motion for multi-cracked nonuniform nanobeam based on nonlocal elasticity theory and embedded in an elastic medium were derived. DTM(differential transformation method) was applied to vibration analysis of multi-cracked nonuniform nanobeam based on nonlocal elasticity theory and embedded in an elastic medium. The non-dimensional natural frequencies of this nanobeam were obtained for eoe, crack stiffness and elastic medium stiffness with various boundary conditions. The results obtained by this method was compared with previous works and showed the close agreement between two methods. The important conclusions obtained by this study are as follows : 1. As the length of nanobeam is shorter, the effect of scale coefficient is greater. 2. The locations of crack change non-dimensional natural frequency, In the case of fixed-fixed ends, the non-dimensional natural frequency is the biggest in the first crack location of 0.6L of nanobeam length, and the smallest in both ends. In the case of fixed-free ends, the closer the location of first crack go tho the free end, the bigger the non-dimensional natural frequency. 3. As the stiffness of crack is greater, the non-dimensional natural frequency is smaller, And the effect of crack stiffness is similar on both fixed-free ends and fixed-fixed ends. 4. The bigger the stiffness of elastic medium, the greater the non - dimensional natural frequency.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.12
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• pp.2328-2339
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• 1992

The propagation of coherent time-harmonic elastic L-and SV-waves is studied in a medium with random distribution of cylindrical inclusions. The purpose of the research is to characterize the dynamic elastic moduli and the attenuation properties of fiber-reinforced composite materials. The cylindes representing the fibers are assumed to be distributed in parallel with each other and the direction of incident waves are normal to the cylinder axes. A multiple scattering formula using the single scattering coefficients in conjunction with the Lax's quasicrystalline approximation is derived from which the dispersion relation for such medium is obtained. In order to formulate the multiple scattering interaction between cylinders, the pair correlation functions are generated by the Monte Carlo simulation technique. From the numerically evaluated complex wavenumbers, the propagation speed of the average wave, the coherent attenuation and the effective elastic moduli are presented as functions of frequency and fiber volume fraction.

• Advances in nano research
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• v.11 no.6
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• pp.581-593
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• 2021

This model is proposed to describe the buckling behavior of Carbon Nanotubes (CNTs) embedded in an elastic medium taking into account the combined effects of the magnetic field, the temperature, the nonlocal parameter, the number of walls. Using Eringen's nonlocal elasticity theory, thin cylindrical shell theory and Van der Waal force (VdW) interactions, we develop a system of partial differential equations governing the buckling response of CNTs embedded on Winkler, Pasternak, and Kerr foundations in a thermal-magnetic environment. The pre-buckling stresses are obtained by applying airy's stress function and an adjacent equilibrium criterion. To estimate the nonlocal critical buckling load of CNTs under the simultaneous effects of the magnetic field, the temperature change, and the number of walls, an optimization technique is proposed. Furthermore, analytical formulas are developed to obtain the buckling behavior of SWCNTs embedded in an elastic medium without taking into account the effects of the nonlocal parameter. These formulas take into account VdW interactions between adjacent tubes and the effect of terms involving differences in tube radii generally neglected in the derived expressions of the critical buckling load published in the literature. Most scientific research on modeling the effects of magnetic fields is based on beam theories, this motivation pushes me to develop a cylindrical shell model for studying the effect of the magnetic field on the static behavior of CNTs. The results show that the magnetic field has significant effects on the static behavior of CNTs and can lead to slow buckling. On the other hand, thermal effects reduce the critical buckling load. The findings in this work can help us design of CNTs for various applications (e.g. structural, electrical, mechanical and biological applications) in a thermal and magnetic environment.

• Advances in concrete construction
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• v.9 no.5
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• pp.491-501
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• 2020

Microtubules buckle under bending and torsion and this property has been studied for free microtubules before using orthotropic elastic shell model. But as microtubules are embedded in other elastic filaments and it is experimentally showed that these elastic filaments affect the critical buckling moment and critical buckling torque of the microtubules. To prove that, we developed orthotropic Winkler like model and demonstrated that the critical buckling moment and critical buckling torque of the microtubules are orders of higher magnitude than those found for free microtubules. Our results show that Critical buckling moment is about 6.04 nNnm for which the corresponding curvature is about θ = 1.33 rad /㎛ for embedded MTs, and critical buckling torque is 0.9 nNnm for the angle of 1.33 rad/㎛. Our results well proved the experimental findings.

• Structural Engineering and Mechanics
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• v.53 no.1
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• pp.17-26
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• 2015

The cross sections of hollow cylindrical tubes ovalise under a pure bending condition, and this reduces their flexural stiffness as their curvatures increase. It is important to accurately evaluate this phenomenon, known as the 'Brazier effect', to understand the bending behaviour of the systems considered. However, if the tubes are supported by an elastic medium or foundation, the ovalisation displacements of their cross sections may decrease. From this point of view, the purpose of this research is to analytically investigate the bending characteristics of single- and double-walled elastic tubes contacted by an elastic material by considering the Brazier effect. The Brazier moment, which is the maximum moment-carrying capacity of the ovalised cross section, can be calculated by introducing the strain energy per unit length of the tube in terms of the degree of ovalisation for the tube and the curvature. The total strain energy of the double-walled system is the sum of the strain energies of the outer and inner tubes and that of the compliant core. Results are comparatively presented to show the variation in the degree of ovalisation and the Brazier moment for single- and double-walled tubes.

• Journal of applied mathematics & informatics
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• v.8 no.3
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• pp.919-934
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• 2001

The concepts of material frame-indifference and material symmetry group with respect to isotropic scalar functions, as represented by energy functions, are discussed. An energy function for a structured heterogeneous (transversal isotropic) medium in large elastic deformations, which is known to satisfy the Ponyting’s effect [1], is highlighted. It is shown that the constitutive relation due to this energt function is material frame-indifferent.