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Yayın A Higher-order Boussinesq equation in locally non-linear theory of one-dimensional non-local elasticity(Oxford Univ Press, 2009-02) Duruk, Nilay; Erkip, Albert; Erbay, Hüsnü AtaIn one space dimension, a non-local elastic model is based on a single integral law, giving the stress when the strain is known at all spatial points. In this study, we first derive a higher-order Boussinesq equation using locally non-linear theory of 1D non-local elasticity and then we are able to show that under certain conditions the Cauchy problem is globally well-posed.Yayın On travelling wave solutions of a generalized Davey-Stewartson system(Oxford Univ Press, 2005-02) Eden, Osman Alp; Erbay, SaadetThe generalized Davey-Stewartson (GDS) equations, as derived by Babaoglu & Erbay (2004, Int. J. Non-Linear Mech., 39, 941-949), is a system of three coupled equations in (2 + 1) dimensions modelling wave propagation in an infinite elastic medium. The physical parameters (gamma, m(1), m(2), lambda and n) of the system allow one to classify the equations as elliptic-elliptic-elliptic (EEE), elliptic-elliptic-hyperbolic (EEH), elliptic-hyperbolic-hyperbolic (EHH), hyperbolic-elliptic-elliptic (HEE), hyperbolic-hyperbolic-hyperbolic (HHH) and hyperbolic-elliptic-hyperbolic (HEH) (Babaoglu et al., 2004, preprint). In this note, we only consider the EEE and HEE cases and seek travelling wave solutions to GDS systems. By deriving Pohozaev-type identities we establish some necessary conditions on the parameters for the existence of travelling waves, when solutions satisfy some integrability conditions. Using the explicit solutions given in Babaoglu & Erbay (2004) we also show that the parameter constraints must be weaker in the absence of such integrability conditions.Yayın Dynamic extension of a compressible nonlinearly elastic membrane tube(Oxford Univ Press, 2005-02) Erbay, Hüsnü Ata; Tüzel, Vasfiye HandeThe dynamic response of an isotropic compressible hyperelastic membrane tube is considered when one end is fixed and the other is subjected to a suddenly applied dynamic extension. The equations governing dynamic axially symmetric deformations of the membrane tube are presented for a general form of compressible isotropic elastic strain-energy function. Numerical results, obtained using a Godunov-type finite volume method and valid up to the time at which reflections occur at the fixed end of the tube, are given for two specific forms of the strain-energy function that characterizes a class of compressible elastomers (the Blatz-Ko model). The question of how the numerical results are related to the exact solution obtained for a limiting case is discussed.Yayın Measurement and assessment of fatigue life of spot-weld joints(Asme-Amer Soc Mechanical Eng, 2009-01) Ertaş, Ahmet Hanifi; Vardar, Öktem; Sönmez, Fazıl Önder; Solim, ZaferSpot-weld joints are commonly used to fasten together metal sheets. Because fatigue fracture is the most critical failure mode for these joints under fluctuating loads, understanding their fatigue failure behavior and assessment of their fatigue lives are crucial from the viewpoint of failure prevention in design. In this study, a series of experiments was conducted to study the fatigue failure of spot-welded modified tensile-shear specimens made of a low carbon steel. Two different types of resistance spot welding were investigated (manual and automated). Tests were repeated under different load ranges, and the corresponding fatigue lives were determined. The specimens were also examined under an optical microscope. In the numerical part of this study, a finite element analysis was carried out using commercial software, ANSYS, to determine the stress and strain states within the specimens. The material nonlinearity, local plastic deformations around the welds during loading, and the residual stresses and strains developed after unloading as a result of plastic deformations were taken into account. Based on the predicted stress and strain states, fatigue analyses were performed using several models for life assessment. Then, the measured and predicted fatigue lives were compared, and the suitability of the models was discussed. Among the strain-based models, Coffin-Manson and Morrow's means stress models yielded the best predictions.
