TY - JOUR
T1 - A mechanically based approach to non-local beam theories
AU - Di Paola, Mario
AU - Zingales, Massimiliano
AU - Sofi, Alba
AU - Failla, Giuseppe
PY - 2011
Y1 - 2011
N2 - A mechanically based non-local beam theory is proposed. The key idea is that the equilibrium of each beam volume element is attained due to contact forces and long-range body forces exerted, respectively, by adjacent and non-adjacent volume elements. The contact forces result in the classical Cauchy stress tensor while the long-range forces are modeled as depending on the product of the interacting volume elements, their relative displacement and a material-dependent distance-decaying function. To derive the beam equilibrium equations and the pertinent mechanical boundary conditions, the total elastic potential energy functional is used based on the Timoshenko beam theory. In this manner, the mechanical boundary conditions are found coincident with the corresponding mechanical boundary conditions of classical elasticity theory. Numerical applications are also reported. © 2011 Elsevier Ltd. All rights reserved.
AB - A mechanically based non-local beam theory is proposed. The key idea is that the equilibrium of each beam volume element is attained due to contact forces and long-range body forces exerted, respectively, by adjacent and non-adjacent volume elements. The contact forces result in the classical Cauchy stress tensor while the long-range forces are modeled as depending on the product of the interacting volume elements, their relative displacement and a material-dependent distance-decaying function. To derive the beam equilibrium equations and the pertinent mechanical boundary conditions, the total elastic potential energy functional is used based on the Timoshenko beam theory. In this manner, the mechanical boundary conditions are found coincident with the corresponding mechanical boundary conditions of classical elasticity theory. Numerical applications are also reported. © 2011 Elsevier Ltd. All rights reserved.
KW - Civil and Structural Engineering
KW - Condensed Matter Physics
KW - Long-range interactions
KW - Materials Science (all)
KW - Mechanical Engineering
KW - Mechanics of Materials
KW - Non-local elasticity
KW - Timoshenko beam theory
KW - Total elastic potential energy functional
KW - Civil and Structural Engineering
KW - Condensed Matter Physics
KW - Long-range interactions
KW - Materials Science (all)
KW - Mechanical Engineering
KW - Mechanics of Materials
KW - Non-local elasticity
KW - Timoshenko beam theory
KW - Total elastic potential energy functional
UR - http://hdl.handle.net/10447/112713
M3 - Article
VL - 53
SP - 676
EP - 687
JO - International Journal of Mechanical Sciences
JF - International Journal of Mechanical Sciences
SN - 0020-7403
ER -