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Öğe Airy's functions in nonlocal elasticity(2011) Altan B.S.Nanostructured devices and materials, such as carbon nanotubes, Atomic Force Microscope, MEMS, etc. attract increasing attention in the scientific world. It has been realized that the classical elasticity is not capable to capture the mechanical behavior of them precisely. There is a wide consensus among the scientists that nonlocal elasticity is more capable than the classical counterpart to model the mechanical behavior of nanostructured materials and devices. In this paper a method which is useful for solving problems in nonlocal is introduced. Airy's stress functions for plane stress problems in nonlocal elasticity are studied. The nonlocal constitutive equations in integral form are discussed and a method is suggested to invert the constitutive equation which allows expressing strains in terms of stresses. A qualitative discussion is given on this inversion process. For the nonlocality kernel of exponential form, the differential equation for Airy's functions in nonlocal elasticity is obtained by introducing the strains into the compatibility condition. Appropriate polynomial forms for the Airy's function are considered and are applied to solve beam bending problems. The solutions are compared with their classical counterparts. The results are given in a series of figures and tables and are discussed in detail. This paper is concluded by indicating the implications of the presented study in nanomechanics and nanotechnology. Copyright © 2011 American Scientific Publishers.Öğe A Novel approach for modeling mechanical behavior of porous media(2011) Altan B.S.; Mollamahmutoglu M.A multi-scale novel homogenization technique is introduced to model mechanical behavior of open-cell porous media. The proposed method consists of primarily four components. The first component is based on two assumptions. First, a random porous structure can be approximated by superimposing regular grids that are interacting with each other at "junction" points. The second component consists of replacing each grid by an equivalent continuum. The forces at the junction points are also replaced by interacting body forces. The third component is to represent the equivalent media by single medium by expressing the "average stresses" in the elastic mixture in terms of the "average displacement" It is discussed how to extract the information about the geometrical and mechanical properties of the grids by comparing the analytical and experimental data for the dispersion of waves propagating in porous medium.Öğe Reflection and refraction of a harmonic SH wave at the interface of two dissimilar media with microheterogeneity(2012) Altan B.S.Reflection and refraction of harmonic SH-waves from the interface of two dissimilar media with microheterogeneity is studied. The effect of the microheterogeneity on the overall behavior of the media is taken into account by adding higher order displacement gradients in the stress-strain relationship. It is found that a harmonic wave reflects back with the same angle of the incident wave, like in a classical case. However, it is found that the direction of propagation of the refracted wave is dependent on the wave number. It is also shown that the critical angle for which the incident wave cannot be transmitted to the other half plane is dependent on the wave number. © 2012 American Society of Mechanical Engineers.
