Bending of small-scale Timoshenko beams based on the integral/differential nonlocal-micropolar elasticity theory: a finite element approach  

作　　者：M. FARAJI-OSKOUIE A. NOROUZZADEH R. ANSARI H. ROUHI 

机构地区：[1]Department of Mechanical Engineering,University of Guilan,Rasht 3756,Iran [2]Department of Engineering Science,Faculty of Technology and Engineering,University of Guilan,Rudsar-Vajargah 44891-63157,Iran

出　　处：《Applied Mathematics and Mechanics(English Edition)》2019年第6期767-782,共16页应用数学和力学（英文版）

摘　　要：A novel size-dependent model is developed herein to study the bending behavior of beam-type micro/nano-structures considering combined effects of nonlocality and micro-rotational degrees of freedom. To accomplish this aim, the micropolar theory is combined with the nonlocal elasticity. To consider the nonlocality, both integral (original) and differential formulations of Eringen’s nonlocal theory are considered. The beams are considered to be Timoshenko-type, and the governing equations are derived in the variational form through Hamilton’s principle. The relations are written in an appropriate matrix-vector representation that can be readily utilized in numerical approaches. A finite element (FE) approach is also proposed for the solution procedure. Parametric studies are conducted to show the simultaneous nonlocal and micropolar effects on the bending response of small-scale beams under different boundary conditions.A novel size-dependent model is developed herein to study the bending behavior of beam-type micro/nano-structures considering combined effects of nonlocality and micro-rotational degrees of freedom. To accomplish this aim, the micropolar theory is combined with the nonlocal elasticity. To consider the nonlocality, both integral(original)and differential formulations of Eringen’s nonlocal theory are considered. The beams are considered to be Timoshenko-type, and the governing equations are derived in the variational form through Hamilton’s principle. The relations are written in an appropriate matrix-vector representation that can be readily utilized in numerical approaches. A finite element(FE) approach is also proposed for the solution procedure. Parametric studies are conducted to show the simultaneous nonlocal and micropolar effects on the bending response of small-scale beams under different boundary conditions.

关 键 词：INTEGRAL MODEL of NONLOCAL ELASTICITY DIFFERENTIAL MODEL of NONLOCAL ELASTICITY MICROPOLAR theory finite element (FE) analysis Timoshenko nano-beam 

分 类 号：O346[理学—固体力学] O242.21[理学—力学]