Variational formulations, model comparisons and numerical methods for Euler–Bernoulli micro- and nano-beam models
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Viacheslav Balobanov | Josef Kiendl | Jarkko Niiranen | V. Balobanov | J. Niiranen | J. Kiendl | S. B. Hosseini | SB Hosseini
[1] T. Hughes,et al. Isogeometric analysis : CAD, finite elements, NURBS, exact geometry and mesh refinement , 2005 .
[2] F. F. Mahmoud,et al. A new Bernoulli–Euler beam model incorporating microstructure and surface energy effects , 2014 .
[3] Mohammad Taghi Ahmadian,et al. Vibrational analysis of single-walled carbon nanotubes using beam element , 2009 .
[4] R. Rafiee,et al. On the modeling of carbon nanotubes: A critical review , 2014 .
[5] G. G. Stokes. "J." , 1890, The New Yale Book of Quotations.
[6] Jianbin Xu,et al. Surface effects on elastic properties of silver nanowires: Contact atomic-force microscopy , 2006 .
[7] E. Aifantis,et al. On Some Aspects in the Special Theory of Gradient Elasticity , 1997 .
[8] Yunan Prawoto,et al. Seeing auxetic materials from the mechanics point of view: A structural review on the negative Poisson’s ratio , 2012 .
[9] E. Aifantis,et al. Gradient elasticity in statics and dynamics: An overview of formulations, length scale identification procedures, finite element implementations and new results , 2011 .
[10] M. Pulvirenti,et al. Macroscopic Description of Microscopically Strongly Inhomogenous Systems: A Mathematical Basis for the Synthesis of Higher Gradients Metamaterials , 2015, 1504.08015.
[11] M. Lazar,et al. Nonsingular stress and strain fields of dislocations and disclinations in first strain gradient elasticity , 2005, cond-mat/0502023.
[12] Elias C. Aifantis,et al. Exploring the applicability of gradient elasticity to certain micro/nano reliability problems , 2008 .
[13] R. D. Mindlin. Micro-structure in linear elasticity , 1964 .
[14] Alessandro Reali,et al. Isogeometric analysis for sixth-order boundary value problems of gradient-elastic Kirchhoff plates , 2017 .
[15] Wolfgang H. Müller,et al. Applications of Strain Gradient Theories to the Size Effect in Submicro-Structures incl. Experimental Analysis of Elastic Material Parameters , 2022 .
[16] Alex J. Zelhofer,et al. Auxeticity in truss networks and the role of bending versus stretching deformation , 2016 .
[17] Pierre Seppecher,et al. Linear elastic trusses leading to continua with exotic mechanical interactions , 2011 .
[18] Meral Tuna,et al. Exact solution of Eringen's nonlocal integral model for bending of Euler–Bernoulli and Timoshenko beams , 2016 .
[19] J. N. Reddy,et al. Bending of Euler–Bernoulli beams using Eringen’s integral formulation: A paradox resolved , 2016 .
[20] K. A. Lazopoulos,et al. Bending and buckling of thin strain gradient elastic beams , 2010 .
[21] Jaehong Lee,et al. Modal analysis of carbon nanotubes and nanocones using FEM , 2012 .
[22] Francesco dell’Isola,et al. Dynamics of 1D nonlinear pantographic continua , 2017 .
[23] K. F. Wang,et al. A review on the application of modified continuum models in modeling and simulation of nanostructures , 2016 .
[24] Huu-Tai Thai,et al. A review of continuum mechanics models for size-dependent analysis of beams and plates , 2017 .
[25] Sergey Y. Yurish. Sensors and Biosensors , MEMS Technologies and its Applications , 2013 .
[26] D. E. Beskos,et al. Finite element static and stability analysis of gradient elastic beam structures , 2015 .
[27] Y. S. Zhang,et al. Size dependence of Young's modulus in ZnO nanowires. , 2006, Physical review letters.
[28] Alireza Beheshti. Large deformation analysis of strain-gradient elastic beams , 2016 .
[29] P. Tong,et al. Couple stress based strain gradient theory for elasticity , 2002 .
[30] K. Harris,et al. Flexible electronics under strain: a review of mechanical characterization and durability enhancement strategies , 2016, Journal of Materials Science.
[31] Demosthenes Polyzos,et al. Bending and stability analysis of gradient elastic beams , 2003 .
[32] Gérard A. Maugin,et al. A Historical Perspective of Generalized Continuum Mechanics , 2010 .
[33] Xiangyang Zhang,et al. A Review of Graphene on NEMS. , 2016, Recent patents on nanotechnology.
[34] Fan Yang,et al. Experiments and theory in strain gradient elasticity , 2003 .
[35] Robert Bogue,et al. Recent developments in MEMS sensors: a review of applications, markets and technologies , 2013 .
[36] Morton E. Gurtin,et al. Surface stress in solids , 1978 .
[37] Hwan-Sik Yoon,et al. A Review on Electromechanical Devices Fabricated by Additive Manufacturing , 2017 .
[38] Majid Minary-Jolandan,et al. A Review of Mechanical and Electromechanical Properties of Piezoelectric Nanowires , 2012, Advanced materials.
[39] Alessandro Reali,et al. Isogeometric Analysis of Structural Vibrations , 2006 .
[40] Antti H. Niemi,et al. Variational formulation and isogeometric analysis for fourth-order boundary value problems of gradient-elastic bar and plane strain/stress problems , 2016 .
[41] Viacheslav Balobanov,et al. Variational formulations and isogeometric analysis for the dynamics of anisotropic gradient-elastic Euler-Bernoulli and shear-deformable beams , 2018 .
[42] S. K. Park,et al. Bernoulli–Euler beam model based on a modified couple stress theory , 2006 .
[43] Andrei V. Metrikine,et al. Mechanics of generalized continua : one hundred years after the Cosserats , 2010 .
[44] Pierre Seppecher,et al. Truss Modular Beams with Deformation Energy Depending on Higher Displacement Gradients , 2003 .
[45] Tsuyoshi Murata,et al. {m , 1934, ACML.
[46] S. K. Park,et al. Variational formulation of a simplified strain gradient elasticity theory and its application to a pressurized thick-walled cylinder problem , 2007 .
[47] L. Tjeng,et al. Orbitally driven spin-singlet dimerization in S=1 La4Ru2O10. , 2006, Physical review letters.
[48] Sergei Khakalo,et al. Gradient-elastic stress analysis near cylindrical holes in a plane under bi-axial tension fields , 2017 .
[49] J. Niiranen,et al. Variational formulations and general boundary conditions for sixth-order boundary value problems of gradient-elastic Kirchhoff plates , 2017 .
[50] G. E. Exadaktylos,et al. Gradient elasticity with surface energy: Mode-I crack problem , 1998 .
[51] Shenjie Zhou,et al. Static and dynamic analysis of micro beams based on strain gradient elasticity theory , 2009 .
[52] F. Auricchio,et al. Single-variable formulations and isogeometric discretizations for shear deformable beams , 2015 .
[53] R. D. Mindlin. Second gradient of strain and surface-tension in linear elasticity , 1965 .
[54] B. Akgöz,et al. Analysis of micro-sized beams for various boundary conditions based on the strain gradient elasticity theory , 2012 .
[55] Robert Bogue. Towards the trillion sensors market , 2014 .
[56] Hendrik Speleers,et al. A locking-free model for Reissner-Mindlin plates: Analysis and isogeometric implementation via NURBS and triangular NURPS , 2015 .
[57] Gérard A. Maugin,et al. Generalized Continuum Mechanics: What Do We Mean by That? , 2010 .
[58] A. Eringen. On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves , 1983 .
[59] Andrew W. Mcfarland,et al. Role of material microstructure in plate stiffness with relevance to microcantilever sensors , 2005 .
[60] Gary R. Consolazio,et al. Finite Elements , 2007, Handbook of Dynamic System Modeling.
[61] D. Beskos,et al. Wave dispersion in gradient elastic solids and structures: A unified treatment , 2009 .
[62] C. Polizzotto. A gradient elasticity theory for second-grade materials and higher order inertia , 2012 .
[63] J. Paavola,et al. Size effects on centrosymmetric anisotropic shear deformable beam structures , 2017 .
[64] J. N. Reddy,et al. A microstructure-dependent Timoshenko beam model based on a modified couple stress theory , 2008 .
[65] Quan Wang,et al. A Review on the Application of Nonlocal Elastic Models in Modeling of Carbon Nanotubes and Graphenes , 2012 .
[66] M. Nikkhah-bahrami,et al. A discussion on incorporating the Poisson effect in microbeam models based on modified couple stress theory , 2015 .
[67] I. Vardoulakis,et al. Bifurcation Analysis in Geomechanics , 1995 .
[68] Katja Bachmeier,et al. Finite Elements Theory Fast Solvers And Applications In Solid Mechanics , 2017 .
[69] J. Bleustein. A note on the boundary conditions of toupin's strain-gradient theory , 1967 .
[70] M E Khater,et al. A review on nonlocal elastic models for bending, buckling, vibrations, and wave propagation of nanoscale beams , 2016 .
[71] S. M. Mousavi,et al. Strain and velocity gradient theory for higher-order shear deformable beams , 2015 .
[72] Sergei Khakalo,et al. Isogeometric analysis of higher-order gradient elasticity by user elements of a commercial finite element software , 2017, Comput. Aided Des..
[73] K. Novoselov,et al. The mechanics of graphene nanocomposites: A review , 2012 .
[74] S. Shen,et al. A new Bernoulli-Euler beam model based on a simplified strain gradient elasticity theory and its applications , 2014 .
[75] Leopoldo Greco,et al. B-Spline interpolation of Kirchhoff-Love space rods , 2013 .