Scale Dependent Critical External Pressure for Buckling of Spherical Shell Based on Nonlocal Strain Gradient Theory

被引:17
作者
Alam, Manjur [1 ]
Mishra, Sudib Kumar [1 ]
Kant, Tarun [2 ]
机构
[1] Indian Inst Technol, Dept Civil Engn, Kanpur, Uttar Pradesh, India
[2] Indian Inst Technol, Dept Civil Engn, Bombay, Maharashtra, India
关键词
Pressurized spherical shell; nonlocal; small length; buckling; modes; NONLINEAR FREE-VIBRATION; ELASTICITY; BEAMS; MODEL; MICROTUBULES; PLASTICITY; PLATES;
D O I
10.1142/S0219455421500036
中图分类号
TU [建筑科学];
学科分类号
0813 ;
摘要
Instabilities in nanosized, externally pressurized spherical shells are important for their applications in nano and biotechnology. Mechanics at such length scale is described by nonlocal and Strain Gradient (SG) field theories. However, analysis of shell buckling is involved and becomes even more complicated in presence of nonlocal and SG interactions. This paper demonstrates that such analysis can be largely simplified by a shallow segment representation of the shell by assuming short wave lengths for the incipient buckling modes. The governing equations are derived and linearized equations are solved to obtain a closed form solution for the critical external pressure causing buckling for a pressurized nonlocal shell. Nonlocal interactions are shown to reduce, whereas the SG interaction increases the critical pressure. The relative reduction/increase becomes more prominent for higher modes of buckling and for increasingly thinner shell. A constricting relationship between the two set of wave numbers expressing the buckling modes is also shown to be modified by the nonlocal and SG scale parameters. Consequent wave numbers increase/decrease, accompanied by decreasing/increasing number of wavelengths, thereby further justifying the shallow segment representation employed herein.
引用
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页数:22
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共 53 条
[1]   Continuum elastic model of fullerenes and the sphericity of the carbon onion shells [J].
Ahmad, S .
JOURNAL OF CHEMICAL PHYSICS, 2002, 116 (08) :3396-3400
[2]   ON THE ROLE OF GRADIENTS IN THE LOCALIZATION OF DEFORMATION AND FRACTURE [J].
AIFANTIS, EC .
INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE, 1992, 30 (10) :1279-1299
[3]   Exploring the applicability of gradient elasticity to certain micro/nano reliability problems [J].
Aifantis, Elias C. .
MICROSYSTEM TECHNOLOGIES-MICRO-AND NANOSYSTEMS-INFORMATION STORAGE AND PROCESSING SYSTEMS, 2009, 15 (01) :109-115
[4]   On the gradient approach - Relation to Eringen's nonlocal theory [J].
Aifantis, Elias C. .
INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE, 2011, 49 (12) :1367-1377
[5]   Vibration analysis of porous FG nanoshells with even and uneven porosity distributions using nonlocal strain gradient elasticity [J].
Barati, Mohammad Reza .
ACTA MECHANICA, 2018, 229 (03) :1183-1196
[6]   Variational formulation of gradient or/and nonlocal higher-order shear elasticity beams [J].
Challamel, Noel .
COMPOSITE STRUCTURES, 2013, 105 :351-368
[8]   CRACK-TIP PROBLEM IN NONLOCAL ELASTICITY [J].
ERINGEN, AC ;
SPEZIALE, CG ;
KIM, BS .
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS, 1977, 25 (05) :339-355
[9]   NONLOCAL ELASTICITY [J].
ERINGEN, AC ;
EDELEN, DGB .
INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE, 1972, 10 (03) :233-&
[10]   STRAIN GRADIENT PLASTICITY - THEORY AND EXPERIMENT [J].
FLECK, NA ;
MULLER, GM ;
ASHBY, MF ;
HUTCHINSON, JW .
ACTA METALLURGICA ET MATERIALIA, 1994, 42 (02) :475-487