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

doi:10.1007/s10483-019-2491-9

摘要/Abstract

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.

关键词: closed orbit, limit cycle, fine focus, Hopf bifurcation, differential model of nonlocal elasticity, Timoshenko nano-beam, integral model of nonlocal elasticity, micropolar theory, finite element (FE) analysis

Abstract: 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.

Key words: integral model of nonlocal elasticity, closed orbit, limit cycle, fine focus, Hopf bifurcation, micropolar theory, finite element (FE) analysis, differential model of nonlocal elasticity, Timoshenko nano-beam

中图分类号:

M. FARAJI-OSKOUIE, A. NOROUZZADEH, R. ANSARI, H. ROUHI. Bending of small-scale Timoshenko beams based on the integral/differential nonlocal-micropolar elasticity theory: a finite element approach[J]. Applied Mathematics and Mechanics (English Edition), 2019, 40(6): 767-782.

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