Precritical equilibrium of a thin shallow shell of revolution and its stability

Srubshchik, L.S.

doi:10.1016/0021-8928(80)90152-5

Cited by 5 publications

(2 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is observed that, as the imperfection increases the buckling load is increased to a specific value and then decreased from a positive value (compressive force) to a negative one (tensile force). This phenomenon is consistent with the shell structure theories, Srubshchik [72]. It is found that the critical buckling load nearly doubles as the normalized imperfection reaches 3 for all CNTs.…”

Section: Parametric Studies A) Effect Of Imperfection On the Critical...supporting

confidence: 91%

Postbuckling of Curved Carbon Nanotubes Using Energy Equivalent Model

Eltaher

Mohamed

et al. 2019

JNanoR

View full text Add to dashboard Cite

This paper presents a novel numerical procedure to predict nonlinear buckling and postbuckling stability of imperfect clamped–clamped single walled carbon nanotube (SWCNT) surrounded by nonlinear elastic foundation. Nanoscale effect of CNTs is included by using energy-equivalent model (EEM) which transferring the chemical energy between carbon atoms to mechanical strain energy. Young’s modulus and Poisson’s ratio for zigzag (n, 0), and armchair (n, n) carbon nanotubes (CNTs) are presented as functions of orientation and force constants by using energy-equivalent model (EEM). Nonlinear Euler-Bernoulli assumptions are proposed considering mid-plane stretching to exhibit a large deformation and a small strain. To simulate the interaction of CNTs with the surrounding elastic medium, nonlinear elastic foundation with cubic nonlinearity and shearing layer are employed. The governing nonlinear integro-partial-differential equations are derived in terms of only the lateral displacement. The modified differential quadrature method (DQM) is exploited to obtain numerical results of the nonlinear governing equations. The static problem is solved for critical buckling loads and the postbuckling deformation as a function of applied axial load, curved amplitude, CNT length, and orientations. Numerical results show that the effects of chirality angle and curved amplitude on static response of armchair and zigzag CNTs are significant. This model is helpful especially in mechanical design of NEMS manufactured from CNTs.

show abstract

Section: Parametric Studies A) Effect Of Imperfection On the Critical...supporting

confidence: 91%

Postbuckling of Curved Carbon Nanotubes Using Energy Equivalent Model

Eltaher

Mohamed

et al. 2019

JNanoR

View full text Add to dashboard Cite

show abstract

“…The buckling load increases from 39.48 to 78.86 as the initial curvature increases from 0 to 3 before the buckling loads drops with the increase of initial curvature. At a certain beam curvature, the buckling load may change its sense (i.e., from compression to tension), which is consistent with the shell structure theories [71]. The loads at which the buckling load changes sense are dubbed 'null-loads'.…”

Section: Buckling Load Of Imperfect Multilayer Nanobeamssupporting

confidence: 76%

Postbuckling and Free Vibration of Multilayer Imperfect Nanobeams under a Pre-Stress Load

et al. 2018

View full text Add to dashboard Cite

This paper investigates the postbuckling and free vibration response of geometrically imperfect multilayer nanobeams. The beam is assumed to be subjected to a pre-stress compressive load due to the manufacturing and its ends are kept at a fixed distance in space. The small-size effect is modeled according to the nonlocal elasticity differential model of Eringen within the nonlinear Bernoulli-Euler beam theory. The constitutive equations relating the stress resultants to the cross-section stiffness constants for a nonlocal multilayer beam are developed. The governing nonlinear equation of motion is derived and then manipulated to be given in terms of only the lateral displacement. The static problem is solved for the buckling load and the postbuckling deflection in terms of three parameters: Imperfection amplitude, size, and lamination. A closed-form solution for the buckling load in terms of all of the beam parameters is developed. With the presence of imperfection and size effects, it has been shown that the buckling load can be either less or greater than the Euler buckling load. Moreover, the free vibration in the pre and postbuckling domains are investigated for the first five modes. Numerical results show that the effects of imperfection, the nonlocal parameter, and layup on buckling loads and natural frequencies of the nanobeams are significant.

show abstract

Secondary edge effect in the bending of thin elastic shells

Srubshchik¹

1981

Journal of Applied Mathematics and Mechanics

View full text Add to dashboard Cite

Precritical equilibrium of a thin shallow shell of revolution and its stability

Cited by 5 publications

References 9 publications

Postbuckling of Curved Carbon Nanotubes Using Energy Equivalent Model

Postbuckling of Curved Carbon Nanotubes Using Energy Equivalent Model

Postbuckling and Free Vibration of Multilayer Imperfect Nanobeams under a Pre-Stress Load

Secondary edge effect in the bending of thin elastic shells

Contact Info

Product

Resources

About