Buckling analysis of nano composite sandwich Euler-Bernoulli beam considering porosity distribution on elastic foundation using DQM

Nejadi, Mohammad Mehdi,Mohammadimehr, Mehdi Techno-Press 2020 Advances in nano research Vol.8 No.1

In the present study, buckling analysis of sandwich composite (carbon nanotube reinforced composite and fiber reinforced composite) Euler-Bernoulli beam in two configurations (core and layers material), three laminates (combination of different angles) and two models (relative thickness of core according to peripheral layers) using differential quadrature method (DQM) is studied. Also, the effects of porosity coefficient and different types of porosity distribution on critical buckling load are discussed. Using sandwich beam, it shows a considerable enhancement in the critical buckling load when compared to ordinary composite. Actually, resistance against buckling in sandwich beam is between two to four times more. It is also showed the critical buckling loads of laminate 1 and 3 are significantly larger than the results of laminate 2. When Configuration 2 is used, the critical buckling load rises about 3 percent in laminate 1 and 3 compared to the results of configuration 1. The amount of enhancement for laminate 3 is about 17 percent. It is also demonstrated that the influence of the core height (thickness) in the case of lower carbon volume fractions is ignorable. Even though, when volume fraction of fiber increases, differences grow smoothly. It should be noticed the amount of decline has inverse relationship with the beam aspect ratio. Among three porosity patterns investigated, beam with the distribution of porosity Type 2 (downward parabolic) has the maximum critical buckling load. At the end, the first three modes of buckling will be demonstrated to investigate the effect of spring constants.

Buckling influence of intermediate filaments with and without surface effects

Taj, Muhammad,Khadimallah, Mohamed A.,Ayed, Hamdi,Hussain, Muzamal,Mahmood, Shaid,Ahmad, Imtiaz Techno-Press 2022 Advances in nano research Vol.12 No.4

Intermediate filaments are the mechanical ropes for both cytoskeleton and nucleoskeleton of the cell which provide tensile force to these skeletons. In providing the mechanical support to the cell, they are likely to buckle. We used conventional Euler buckling model to find the critical buckling force under different boundary conditions which they assume during different functions. However, there are many experimental and theoretical studies about other cytoskeleton components which demonstrate that due to mechanical coupling with the surrounding surface, the critical buckling force increases considerably. Motivated with these results, we also investigated the influence of surface effects on the critical buckling force of intermediate filaments. The surface effects become profound because of increasing ratio of surface area of intermediate filaments to bulk at nano-scale. The model has been solved analytically to obtain relations for the critical forces for the buckling of intermediate filaments without and with surface effects. We found that critical buckling force with surface effects increases to a large extent due to mechanical coupling of intermediate filaments with the surrounding surface. Our study may be useful to develop a unified experimental protocol to characterize the physical properties of Intermediate filaments and may be helpful in understanding many biological phenomenon involving intermediate filaments.

Axial buckling scrutiny of doubly orthogonal slender nanotubes via nonlocal continuum theory

Keivan Kiani 대한기계학회 2015 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.29 No.10

Using nonlocal Euler-Bernoulli beam theory, buckling behavior of elastically embedded Doubly orthogonal single-walled carbonnanotubes (DOSWCNTs) is studied. The nonlocal governing equations are obtained. In fact, these are coupled fourth-order integroordinarydifferential equations which are very difficult to be solved explicitly. As an alternative solution, Galerkin approach in conjunctionwith assumed mode method is employed, and the axial compressive buckling load of the nanosystem is evaluated. For DOSWCNTswith simply supported tubes, the influences of the slenderness ratio, aspect ratio, intertube free space, small-scale parameter, and propertiesof the surrounding elastic matrix on the axial buckling load of the nanosystem are addressed. The proposed model could be consideredas a pivotal step towards better understanding the buckling behavior of more complex nanosystems such as doubly orthogonalmembranes or even jungles of carbon nanotubes.

Frequency, bending and buckling loads of nanobeams with different cross sections

Civalek, Omer,Uzun, Busra,Yayli, M. Ozgur Techno-Press 2020 Advances in nano research Vol.9 No.2

The bending, stability (buckling) and vibration response of nano sized beams is presented in this study based on the Eringen's nonlocal elasticity theory in conjunction with the Euler-Bernoulli beam theory. For this purpose, the bending, buckling and vibration problem of Euler-Bernoulli nanobeams are developed and solved on the basis of nonlocal elasticity theory. The effects of various parameters such as nonlocal parameter e₀a, length of beam L, mode number n, distributed load q and cross-section on the bending, buckling and vibration behaviors of carbon nanotubes idealized as Euler-Bernoulli nanobeam is investigated. The transverse deflections, maximum transverse deflections, vibrational frequency and buckling load values of carbon nanotubes are given in tables and graphs.

Buckling analysis of FGM Euler-Bernoulli nano-beams with 3D-varying properties based on consistent couple-stress theory

Amin Hadi,Mohammad Zamani Nejad,Abbas Rastgoo,Mohammad Hosseini 국제구조공학회 2018 Steel and Composite Structures, An International J Vol.26 No.6

This paper contains a consistent couple-stress theory to capture size effects in Euler-Bernoulli nano-beams made of three-directional functionally graded materials (TDFGMs). These models can degenerate into the classical models if the material length scale parameter is taken to be zero. In this theory, the couple-stress tensor is skew-symmetric and energy conjugate to the skew-symmetric part of the rotation gradients as the curvature tensor. The material properties except Poisson's ratio are assumed to be graded in all three axial, thickness and width directions, which it can vary according to an arbitrary function. The governing equations are obtained using the concept of minimum potential energy. Generalized differential quadrature method (GDQM) is used to solve the governing equations for various boundary conditions to obtain the natural frequencies of TDFG nano-beam. At the end, some numerical results are performed to investigate some effective parameter on buckling load. In this theory the couple-stress tensor is skew-symmetric and energy conjugate to the skew-symmetric part of the rotation gradients as the curvature tensor.

Critical buckling loads of carbon nanotube embedded in Kerr's medium

Bensattalah, Tayeb,Bouakkaz, Khaled,Zidour, Mohamed,Daouadji, Tahar Hassaine Techno-Press 2018 Advances in nano research Vol.6 No.4

In this article, the critical buckling of a single-walled carbon nanotube (SWCNT) embedded in Kerr's medium is studied. Based on the nonlocal continuum theory and the Euler-Bernoulli beam model. The governing equilibrium equations are acquired and solved for CNTs subjected to mechanical loads and embedded in Kerr's medium. Kerr-type model is employed to simulate the interaction of the (SWNT) with a surrounding elastic medium. A first time, a comparison with the available results is made, and another comparison between various models Winkler-type, Pasternak-type and Kerr-type is studied. Effects of nonlocal parameter and aspect ratio of length to diameter of nanobeam, as well as the foundation parameters on buckling of CNT are investigated. These results are important in the mechanical design considerations of nanocomposites based on carbon nanotubes.

Influence of porosity on thermal buckling behavior of functionally graded beams

Hichem Bellifa,Mahmoud M. Selim,Abdelbaki Chikh,Abdelmoumen Anis Bousahla,Fouad Bourada,Abdeldjebbar Tounsi,Kouider Halim Benrahou,Mesfer Mohammad Al-Zahrani,Abdelouahed Tounsi 국제구조공학회 2021 Smart Structures and Systems, An International Jou Vol.27 No.4

The interest of this work is the analysis of the effect of porosity on the nonlinear thermal stability response of power law functionally graded beam with various boundary conditions. The modelling was done according to the Euler-Bernoulli beam model where the distribution of material properties is imitated polynomial function. The thermal loads are assumed to be not only uniform but linear as well non-linear and the temperature rises through the thickness direction. The effects of the porosity parameter, slenderness ratio and power law index on the thermal buckling of P-FG beam are discussed.

Application of strain gradient elasticity theory for buckling analysis of protein microtubules

Bekir Akgöz,Ömer Civalek 한국물리학회 2011 Current Applied Physics Vol.11 No.5

In this paper, size effect of microtubules (MTs) is studied via modified strain gradient elasticity theory for buckling. MTs are modeled by Bernoulli―Euler beam theory. By using the variational principle, the governing equations for buckling and related boundary conditions are obtained in conjunctions with the strain gradient elasticity. The size effect for buckling analysis of MTs is investigated and results are presented in graph form. The results obtained by strain gradient elasticity theory are discussed through the numerical simulations. The results based on the modified couple stress theory, nonlocal elasticity theory and classical elasticity theories have been also presented for comparison purposes.

On the static and dynamic stability of beams with an axial piezoelectric actuation

C. Zehetner,H. Irschik 국제구조공학회 2008 Smart Structures and Systems, An International Jou Vol.4 No.1

The present contribution is concerned with the static and dynamic stability of a piezo-laminated Bernoulli-Euler beam subjected to an axial compressive force. Recently, an inconsistent derivation of the equations of motions of such a smart structural system has been presented in the literature, where it has been claimed, that an axial piezoelectric actuation can be used to control its stability. The main scope of the present paper is to show that this unfortunately is impossible. We present a consistent theory for composite beams in plane bending. Using an exact description of the kinematics of the beam axis, together with the Bernoulli-Euler assumptions, we obtain a single-layer theory capable of taking into account the effects of piezoelectric actuation and buckling. The assumption of an inextensible beam axis, which is frequently used in the literature, is discussed afterwards. We show that the cited inconsistent beam model is due to inadmissible mixing of the assumptions of an inextensible beam axis and a vanishing axial displacement, leading to the erroneous result that the stability might be enhanced by an axial piezoelectric actuation. Our analytical formulations for simply supported Bernoulli-Euler type beams are verified by means of three-dimensional finite element computations performed with ABAQUS.

On the static and dynamic stability of beams with an axial piezoelectric actuation

Zehetner, C.,Irschik, H. Techno-Press 2008 Smart Structures and Systems, An International Jou Vol.4 No.1

The present contribution is concerned with the static and dynamic stability of a piezo-laminated Bernoulli-Euler beam subjected to an axial compressive force. Recently, an inconsistent derivation of the equations of motions of such a smart structural system has been presented in the literature, where it has been claimed, that an axial piezoelectric actuation can be used to control its stability. The main scope of the present paper is to show that this unfortunately is impossible. We present a consistent theory for composite beams in plane bending. Using an exact description of the kinematics of the beam axis, together with the Bernoulli-Euler assumptions, we obtain a single-layer theory capable of taking into account the effects of piezoelectric actuation and buckling. The assumption of an inextensible beam axis, which is frequently used in the literature, is discussed afterwards. We show that the cited inconsistent beam model is due to inadmissible mixing of the assumptions of an inextensible beam axis and a vanishing axial displacement, leading to the erroneous result that the stability might be enhanced by an axial piezoelectric actuation. Our analytical formulations for simply supported Bernoulli-Euler type beams are verified by means of three-dimensional finite element computations performed with ABAQUS.