Here 0 < ρ ∈ C(Ω) denotes the density, S is the Piola-Kirchhoff stress tensor which obeys the relation SF T = FS where F = I + ∇u is the deformation gradient. Divergence and transpose are taken with respect to the Euclidean metric | · |. The elasticity tensor C maps infinitesimal strain tensors E = (∇u+∇u )/2 to symmetric stress tensors CE. C represents the material properties on the elastic me...

K.M. Davoudi, M.Yu. Gutkin and H.M. Shodja* Department of Civil Engineering, Center of Excellence in Structures and Earthquake Engineering, Sharif University of Technology, 11155-9313 Tehran, Iran Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, Bolshoj 61, Vasil. Ostrov, St. Petersburg 199178, Russia Department of Physics of Materials Strength and Plasticity, St. P...

The forced vibration behaviors are examined for nonlocal strain gradient nanobeams with surface effects subjected to a moving harmonic load travelling with a constant velocity in terms of three beam models namely, the Euler-Bernoulli, Timoshenko and modified Timoshenko beam models. The modification for nonlocal strain gradient Timoshenko nanobeams is exerted to the constitutive equations by exc...

Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive o...

Abstract In this paper, we analyze some properties of a sixth-order elliptic operator arising in the framework strain gradient linear elasticity theory for nanoplates flexural deformation. We first rigorously deduce weak formulation underlying Neumann problem as well its posedness. Under suitable smoothness assumptions on coefficients and geometry, derive interior boundary regularity estimates ...