Thermal Post-Buckling Analysis of Nanoscale Films Based on a Non-Classical Finite Element Approach

REFERENCES

• X. B. Lu , L. H. Cui , and M. Y. Ren , Young's Modulus of Nano Polycrystalline Silicon Film , Proc. Eng. , vol. 29 , pp. 4025 – 4029 , 2012 .
   Google Scholar
• S. I. Sadovnikov , N. S. Kozhevnikova , A. A. Rempel , and A. Magerl , Thermal Expansion of a Lead Sulfide Nanofilm , Thin Solid Films , vol. 548 , pp. 23 – 234 , 2013 .
   Web of Science ®Google Scholar
• Y. Jing , L. Guo , Y. Sun , J. Shen , and N. R. Aluru , Mechanical Properties of a Silicon Nanofilm Covered With Defective Graphene , Surf. Sci. , vol. 611 , pp. 80 – 85 , 2013 .
   Web of Science ®Google Scholar
• X. Liu , X. Lu , R. Chuai , C. Shi , and C. Suo , Polysilicon Nanofilm Pressure Sensor , Sens. Actuat. A: Phys. , vol. 154 , pp. 42 – 45 , 2009 .
   Web of Science ®Google Scholar
• S. Taccola , S. Palagi , A. Menciassi , E. Sinibaldi , V. Mattoli , V. Pensabene , and P. Dario , Magnetic Nanofilms for Biomedical Applications , J. Nanotechnol. Eng. Med. , vol. 1 , p. 021008 , 2010 .
   Google Scholar
• M. Nolte and M. Knoll , Nanofilm Processors Controlled by Electrolyte Flows of Femtoliter Volume , Langmuir , vol. 29 , pp. 8179 – 8186 , 2013 .
   PubMed Web of Science ®Google Scholar
• P. Hojati-Talemi , C. Bächler , M. Fabretto , P. Murphy , and D. Evans , Ultrathin Polymer Films for Transparent Electrode Applications Prepared by Controlled Nucleation , ACS Appl. Mater. Interfaces , vol. 5 , pp. 11654 – 11660 , 2013 .
   PubMed Web of Science ®Google Scholar
• A. C. Eringen , On Differential Equations of Nonlocal Elasticity and Solutions of Screw Dislocation and Surface Waves , J. Appl. Phys. , vol. 54 , pp. 4703 – 4710 , 1983 .
   Web of Science ®Google Scholar
• A. C. Eringen , Nonlocal Continuum Field Theories , Springer , New York , 2002 .
   Google Scholar
• J. Peddieson , G. R. Buchanan , and R. P. McNitt , Application of Nonlocal Continuum Models to Nanotechnology , Int. J. Eng. Sci. , vol. 41 , pp. 305 – 312 , 2003 .
   Web of Science ®Google Scholar
• L. J. Sudak , Column Buckling of Multiwalled Carbon Nanotubes Using Nonlocal Continuum Mechanics , J. Appl. Phys. , vol. 94 , pp. 7281 – 7287 , 2003 .
   Web of Science ®Google Scholar
• R. Li and G. A. Kardomateas , Thermal Buckling of Multi-Walled Carbon Nanotubes by Nonlocal Elasticity , ASME J. Appl. Mech. , vol. 74 , pp. 399 – 405 , 2007 .
   Web of Science ®Google Scholar
• Y. G. Hu , K. M. Liew , Q. Wang , X. Q. He , and B. I. Yakobson , Nonlocal Shell Model for Elastic Wave Propagation in Single- and Double-Walled Carbon Nanotubes , J. Mech. Phys. Solids , vol. 56 , pp. 3475 – 3485 , 2008 .
   Web of Science ®Google Scholar
• H. S. Shen and C. L. Zhang , Nonlocal Shear Deformable Shell Model for Post-Buckling of Axially Compressed Double-Walled Carbon Nanotubes Embedded in an Elastic Matrix , ASME J. Appl. Mech. , vol. 77 , p. 041006 , 2010 .
   Web of Science ®Google Scholar
• R. Ansari and H. Rouhi , Nonlocal Flugge Shell Model for Thermal Buckling of Multi-Walled Carbon Nanotubes with Layerwise Boundary Conditions , J. Therm. Stresses , vol. 35 , pp. 326 – 341 , 2012 .
   Web of Science ®Google Scholar
• R. E. Miller and V. B. Shenoy , Size-Dependent Elastic Properties of Nanosized Structural Elements , Nanotechnology , vol. 11 , pp. 139 – 147 , 2002 .
   Web of Science ®Google Scholar
• V. B. Shenoy , Size-Dependent Rigidities of Nanosized Torsional Elements , Int. J. Solids Struct. , vol. 39 , pp. 4039 – 4052 , 2002 .
   Web of Science ®Google Scholar
• Y. Sapsathiarn and R. K. N. D. Rajapakse , A Model for Large Deflections of Nanobeams and Experimental Comparison, IEEE Trans. Nanotechnology , vol. 11, pp. 247–254, 2012.
   Web of Science ®Google Scholar
• M. E. Gurtin and A. I. Murdoch , A Continuum Theory of Elastic Material Surface , Arch. Rat. Mech. Anal. , vol. 57 , pp. 291 – 323 , 1975 .
   Web of Science ®Google Scholar
• M. E. Gurtin and A. I. Murdoch , Surface Stress in Solids , Int. J. Solids Struct. , vol. 14 , pp. 431 – 440 , 1978 .
   Web of Science ®Google Scholar
• C. F. Lü , W. Q. Chen , and C. W. Lim , Elastic Mechanical Behavior of Nano-Scaled FGM Films Incorporating Surface Energies , Compos. Sci. Technol. , vol. 69 , pp. 1124 – 1130 , 2009 .
   Web of Science ®Google Scholar
• A. Assadi and B. Farshi , Size Dependent Stability Analysis of Circular Ultrathin Films in Elastic Medium with Consideration of Surface Energies , Physica E , vol. 43 , pp. 1111 – 1117 , 2011 .
   Google Scholar
• J. Zhang , C. Wang , and S. Adhikari , Surface Effect on the Buckling of Piezoelectric Nanofilms , J. Phys. D: Appl. Phys. , vol. 45 , p. 285301 , 2012 .
   Web of Science ®Google Scholar
• C. Zhang , C. Zhang , and W. Chen , Modeling of Piezoelectric Bimorph Nano-Actuators with Surface Effects , ASME J. Appl. Mech. , vol. 80 , p. 061015 , 2013 .
   Web of Science ®Google Scholar
• Y. Zhang , L. J. Zhuo , and H. S. Zhao , Determining the Effects of Surface Elasticity and Surface Stress by Measuring the Shifts of Resonant Frequencies , Proc. R. Soc. A , vol. 469 , p. 20130449 , 2013 .
   Google Scholar
• M. Shaat , F. F. Mahmoud , A. E. Alshorbagy , and S. S. Alieldin , Bending Analysis of Ultra-Thin Functionally Graded Mindlin Plates Incorporating Surface Energy Effect , Int. J. Mech. Sci. , vol. 75 , pp. 223 – 232 , 2013 .
   Web of Science ®Google Scholar
• R. D. Cook , D. S. Malkus , M. E. Plesha , and R. J. Witt , Concepts and Applications of Finite Element Analysis, , 4th Edition , John Wiley & Sons , New York , 2002 .
   Google Scholar
• O. C. Zienkiewicz and R. L. Taylor , The Finite Element Method for Solid and Structural Mechanics, , 6th Edition , Elsevier , Barcelona , Spain , 2005 .
   Google Scholar
• H. B. Keller , Numerical Solution of Bifurcation and Nonlinear Eigenvalue Problems , in P. Rabinowitz (ed.), Applications of Bifurcation Theory , Academic Press , New York , 1977 .
   Google Scholar
• Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/uths.
   Google Scholar