Nonlocal strain gradient torsion of elastic beams: variational formulation and constitutive boundary conditions

被引:58
作者
Barretta, R. [1 ]
Faghidian, S. Ali [1 ]
de Sciarra, Francesco [1 ]
Vaccaro, M. S. [1 ]
机构
[1] Univ Naples Federico II, Dept Struct Engn & Architecture, Via Claudio 21, I-80125 Naples, Italy
关键词
Torsion; Nano-beams; Nonlocal strain gradient model; Strain gradient elasticity; Integral elasticity; Size effects; Analytical modeling; NEMS; 2-PHASE INTEGRAL ELASTICITY; NANO-BEAMS; FREE-VIBRATIONS; BUCKLING ANALYSIS; STRESS; CONTINUUM; MODEL; NANOBEAMS; MECHANICS; STATICS;
D O I
10.1007/s00419-019-01634-w
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
Nonlocal strain gradient continuum mechanics is a methodology widely employed in the literature to assess size effects in nano-structures. Notwithstanding this, improper higher-order boundary conditions (HOBC) are prescribed to close the corresponding elastostatic problems. In the present study, it is proven that HOBC have to be replaced with univocally determined boundary conditions of constitutive type, established by a consistent variational formulation. The treatment, developed in the framework of torsion of elastic beams, provides an effective approach to evaluate scale phenomena in smaller and smaller devices of engineering interest. Both elastostatic torsional responses and torsional-free vibrations of nano-beams are investigated by applying a simple analytical method. It is also underlined that the nonlocal strain gradient model, if equipped with the inappropriate HOBC, can lead to torsional structural responses which unacceptably do not exhibit nonlocality. The presented variational strategy is instead able to characterize significantly peculiar softening and stiffening behaviors of structures involved in modern nano-electro-mechanical systems.
引用
收藏
页码:691 / 706
页数:16
相关论文
共 72 条
[1]   Update on a class of gradient theories [J].
Aifantis, EC .
MECHANICS OF MATERIALS, 2003, 35 (3-6) :259-280
[2]   On the gradient approach - Relation to Eringen's nonlocal theory [J].
Aifantis, Elias C. .
INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE, 2011, 49 (12) :1367-1377
[3]   Buckling Analysis of Cantilever Carbon Nanotubes Using the Strain Gradient Elasticity and Modified Couple Stress Theories [J].
Akgoz, B. ;
Civalek, O. .
JOURNAL OF COMPUTATIONAL AND THEORETICAL NANOSCIENCE, 2011, 8 (09) :1821-1827
[4]   Effects of thermal and shear deformation on vibration response of functionally graded thick composite microbeams [J].
Akgoz, Bekir ;
Civalek, Omer .
COMPOSITES PART B-ENGINEERING, 2017, 129 :77-87
[5]   Size-dependent bending, buckling and free vibration of functionally graded Timoshenko microbeams based on the most general strain gradient theory [J].
Ansari, R. ;
Gholami, R. ;
Shojaei, M. Faghih ;
Mohammadi, V. ;
Sahmani, S. .
COMPOSITE STRUCTURES, 2013, 100 :385-397
[6]   Nonlocal strain gradient exact solutions for functionally graded inflected nano-beams [J].
Apuzzo, A. ;
Barretta, R. ;
Faghidian, S. A. ;
Luciano, R. ;
de Sciarra, F. Marotti .
COMPOSITES PART B-ENGINEERING, 2019, 164 :667-674
[7]   Axial and Torsional Free Vibrations of Elastic Nano-Beams by Stress-Driven Two-Phase Elasticity [J].
Apuzzo, A. ;
Barretta, R. ;
Fabbrocino, F. ;
Faghidian, S. Ali ;
Luciano, R. ;
de Sciarra, F. Marotti .
JOURNAL OF APPLIED AND COMPUTATIONAL MECHANICS, 2019, 5 (02) :402-413
[8]   Free vibrations of elastic beams by modified nonlocal strain gradient theory [J].
Apuzzo, A. ;
Barretta, R. ;
Faghidian, S. A. ;
Luciano, R. ;
de Sciarra, F. Marotti .
INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE, 2018, 133 :99-108
[9]   Free vibrations of Bernoulli-Euler nano-beams by the stress-driven nonlocal integral model [J].
Apuzzo, Andrea ;
Barretta, Raffaele ;
Luciano, Raimondo ;
de Sciarra, Francesco Marotti ;
Penna, Rosa .
COMPOSITES PART B-ENGINEERING, 2017, 123 :105-111
[10]   Buckling loads of nano-beams in stress-driven nonlocal elasticity [J].
Barretta, R. ;
Fabbrocino, F. ;
Luciano, R. ;
de Sciarra, F. Marotti ;
Ruta, G. .
MECHANICS OF ADVANCED MATERIALS AND STRUCTURES, 2020, 27 (11) :869-875