Nonlocal strain gradient beam model for postbuckling and associated vibrational response of lipid supramolecular protein micro/nano-tubules.

As a supramolecular construction, lipid protein micro/nano-tubules can be utilized in a variety of sustained biological delivery system. The high slenderness ratio of lipid tubules makes their hierarchical assembly into a desired architecture difficult. Therefore, an accurate prediction of mechanical behavior of lipid tubular is essential. The objective of this study is to capture size dependency in the postbuckling and vibrational response of the postbuckled lipid micro/nano-tubules more comprehensively. To this purpose, the nonlocal strain gradient elasticity theory is incorporated to the third-order shear deformation beam theory to develop an unconventional beam model. Hamilton's principle is put to use to establish the size-dependent governing differential equations of motion. After that, an improved perturbation technique in conjunction with Galerkin method is employed to obtain the nonlocal strain gradient load-frequency response and postbuckling stability curves of lipid micro/nano-tubules. It is revealed that by taking the nonlocal size effect into consideration, the influence of the type (geometrical parameters) of an axially compressed lipid micro/nano-tubule on its natural frequency in order decreases and increases within the prebuckling and postbuckling regimes. While the strain gradient size dependency plays an opposite role which causes that the influence of the type of lipid micro/nano-tubule on its natural frequency corresponding to the prebuckling and postbuckling domains increases and decreases, respectively.

[1]  Yong Zhou,et al.  Lipid Nanotubes: A Unique Template To Create Diverse One-Dimensional Nanostructures† , 2008 .

[2]  Chenlin Li,et al.  Buckling of nanobeams under nonuniform temperature based on nonlocal thermoelasticity , 2016 .

[3]  Hui-Shen Shen,et al.  Nonlinear bending and thermal postbuckling of functionally graded fiber reinforced composite laminated beams with piezoelectric fiber reinforced composite actuators , 2016 .

[4]  Mohammad Mohammadi Aghdam,et al.  A nonlocal strain gradient hyperbolic shear deformable shell model for radial postbuckling analysis of functionally graded multilayer GPLRC nanoshells , 2017 .

[5]  M. Bahrami,et al.  An efficient size-dependent shear deformable shell model and molecular dynamics simulation for axial instability analysis of silicon nanoshells. , 2017, Journal of molecular graphics & modelling.

[6]  R. Luciano,et al.  Free vibrations of Bernoulli-Euler nano-beams by the stress-driven nonlocal integral model , 2017 .

[7]  Yiming Fu,et al.  Linear free vibration in pre/post-buckled states and nonlinear dynamic stability of lipid tubules based on nonlocal beam model , 2016 .

[8]  Mesut Şimşek,et al.  Nonlinear free vibration of a functionally graded nanobeam using nonlocal strain gradient theory and a novel Hamiltonian approach , 2016 .

[9]  Ömer Civalek,et al.  Application of strain gradient elasticity theory for buckling analysis of protein microtubules , 2011 .

[10]  Yiming Fu,et al.  Modeling and analysis of microtubules based on a modified couple stress theory , 2010 .

[11]  N. Kameta,et al.  Controllable biomolecule release from self-assembled organic nanotubes with asymmetric surfaces: pH and temperature dependence. , 2008, Soft matter.

[12]  Y. Beni,et al.  Electro-mechanical free vibration of single-walled piezoelectric/flexoelectric nano cones using consistent couple stress theory , 2017 .

[13]  S. Sahmani,et al.  Imperfection sensitivity of the size-dependent postbuckling response of pressurized FGM nanoshells in thermal environments , 2017 .

[14]  S. Sahmani,et al.  Size-dependent axial instability of microtubules surrounded by cytoplasm of a living cell based on nonlocal strain gradient elasticity theory. , 2017, Journal of theoretical biology.

[15]  Y. Liu,et al.  Wave dispersion in viscoelastic single walled carbon nanotubes based on the nonlocal strain gradient Timoshenko beam model , 2017 .

[16]  E. Virga,et al.  Exact Statics and Approximate Dynamics of Adhering Lipid Tubules , 1998 .

[17]  M. Bahrami,et al.  Surface stress effects on the postbuckling behavior of geometrically imperfect cylindrical nanoshells subjected to combined axial and radial compressions , 2015 .

[18]  J. Reddy,et al.  A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation , 2015 .

[19]  R. Barretta,et al.  Stress-driven versus strain-driven nonlocal integral model for elastic nano-beams , 2017 .

[20]  Hui-Shen Shen,et al.  Nonlinear vibration of functionally graded fiber reinforced composite laminated beams with piezoelectric fiber reinforced composite actuators in thermal environments , 2015 .

[21]  M. Bahrami,et al.  Size-dependent axial buckling and postbuckling characteristics of cylindrical nanoshells in different temperatures , 2016 .

[22]  M. Bahrami,et al.  Nonlinear buckling and postbuckling behavior of cylindrical shear deformable nanoshells subjected to radial compression including surface free energy effects , 2017 .

[23]  Mohammad Mohammadi Aghdam,et al.  Nonlocal strain gradient shell model for axial buckling and postbuckling analysis of magneto-electro-elastic composite nanoshells , 2018 .

[24]  Fan Yang,et al.  Experiments and theory in strain gradient elasticity , 2003 .

[25]  I. Elishakoff,et al.  Buckling and vibrations of microstructured rectangular plates considering phenomenological and lattice-based nonlocal continuum models , 2016 .

[26]  S. Sahmani,et al.  Development an efficient calibrated nonlocal plate model for nonlinear axial instability of zirconia nanosheets using molecular dynamics simulation. , 2017, Journal of molecular graphics & modelling.

[27]  B. Zhang,et al.  A size-dependent FG micro-plate model incorporating higher-order shear and normal deformation effects based on a modified couple stress theory , 2015 .

[28]  Mohammad Mohammadi Aghdam,et al.  Nonlocal strain gradient beam model for nonlinear vibration of prebuckled and postbuckled multilayer functionally graded GPLRC nanobeams , 2017 .

[29]  M. Bahrami,et al.  Surface free energy effects on the postbuckling behavior of cylindrical shear deformable nanoshells under combined axial and radial compressions , 2017 .

[30]  Marco Amabili,et al.  A higher-order mathematical modeling for dynamic behavior of protein microtubule shell structures including shear deformation and small-scale effects. , 2014, Mathematical biosciences.

[31]  M. Azhari,et al.  Buckling and free vibration of the FGM thin micro-plate based on the modified strain gradient theory and the spline finite strip method , 2017 .

[32]  Lu Lu,et al.  Size-dependent vibration analysis of nanobeams based on the nonlocal strain gradient theory , 2017 .

[33]  R. Barretta,et al.  On nonlocal integral models for elastic nano-beams , 2017 .

[34]  Wanji Chen,et al.  A size-dependent composite laminated skew plate model based on a new modified couple stress theory , 2017 .

[35]  A. Farajpour,et al.  A higher-order nonlocal strain gradient plate model for buckling of orthotropic nanoplates in thermal environment , 2016 .

[36]  Li Li,et al.  Buckling analysis of size-dependent nonlinear beams based on a nonlocal strain gradient theory , 2015 .

[37]  XiaoBai Li,et al.  Bending, buckling and vibration of axially functionally graded beams based on nonlocal strain gradient theory , 2017 .

[38]  Hai Wang,et al.  Nonlinear bending of FGM cylindrical panels resting on elastic foundations in thermal environments , 2015 .

[40]  Y. Beni,et al.  Buckling analysis of orthotropic protein microtubules under axial and radial compression based on couple stress theory. , 2017, Mathematical biosciences.

[41]  Hui‐Shen Shen Nonlinear analysis of lipid tubules by nonlocal beam model. , 2011, Journal of theoretical biology.

[42]  M. Abdollahian,et al.  Vibration of bioliquid-filled microtubules embedded in cytoplasm including surface effects using modified couple stress theory. , 2015, Journal of theoretical biology.

[43]  Raffaele Barretta,et al.  Constitutive boundary conditions and paradoxes in nonlocal elastic nanobeams , 2017 .

[44]  K. M. Liew,et al.  Nonlocal shell model for elastic wave propagation in single- and double-walled carbon nanotubes , 2008 .

[45]  Mohammad Mohammadi Aghdam,et al.  Nonlinear instability of axially loaded functionally graded multilayer graphene platelet-reinforced nanoshells based on nonlocal strain gradient elasticity theory , 2017 .

[46]  W. Yang,et al.  Coupling influences of nonlocal stress and strain gradients on dynamic pull-in of functionally graded nanotubes reinforced nano-actuator with damping effects , 2016 .

[47]  Morton E. Gurtin,et al.  Surface stress in solids , 1978 .

[48]  Toshimi Shimizu,et al.  Aligning a single-lipid nanotube with moderate stiffness. , 2003, Angewandte Chemie.

[49]  Raffaele Barretta,et al.  Nonlocal elasticity in nanobeams: the stress-driven integral model , 2017 .

[50]  R. Bellamkonda,et al.  Sustained release of plasmid DNA using lipid microtubules and agarose hydrogel. , 2003, Journal of controlled release : official journal of the Controlled Release Society.

[51]  Li Li,et al.  Wave propagation in fluid-conveying viscoelastic carbon nanotubes based on nonlocal strain gradient theory , 2016 .

[52]  A. Eringen On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves , 1983 .