A mechanically based approach to non-local beam theories

被引：20

作者：

Di Paola, Mario ^{[1
]}

Failla, Giuseppe ^{[2
]}

Sofi, Alba ^{[3
]}

Zingales, Massimiliano ^{[1
]}

机构：

[1] Univ Palermo, DISAG, I-90128 Palermo, Italy

[2] Univ Mediterranea Reggio Calabria, Dipartimento Meccan & Mat MECMAT, I-89124 Reggio Di Calabria, Italy

[3] Univ Mediterranea Reggio Calabria, Dipartimento Patrimonio Architetton & Urbanist PA, I-89124 Reggio Di Calabria, Italy

来源：

INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES | 2011年 / 53卷 / 09期

关键词：

Non-local elasticity; Long-range interactions; Timoshenko beam theory; Total elastic potential energy functional; CARBON NANOTUBES; DISCRETE MICROSTRUCTURE; SCREW DISLOCATION; ELASTICITY THEORY; CONTINUUM MODELS; VIBRATION; NANO; DEFORMATION; MICRO; SHEAR;

D O I：

10.1016/j.ijmecsci.2011.04.005

中图分类号：

TH [机械、仪表工业];

学科分类号：

0802 ;

摘要：

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. (C) 2011 Elsevier Ltd. All rights reserved.

引用

页码：676 / 687

页数：12

共 63 条

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