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Nonlocal strain gradient‑based quasi‑3D nonlinear dynamical stability behavior of agglomerated nanocomposite microbeams

Yue Xiao‑Guang, Sahmani Saeid, Luo Haopin, Safaei Babak

Archives of Civil and Mechanical Engineering

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2023

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Vol. 23, no. 1

art. no. e21, 2023

EN

An efficient numerical quasi-3D beam model is introduced to analyze the effect of carbon nanotube (CNT) agglomeration on the nonlinear dynamical stability characteristics of agglomerated beams at microscale made of agglomerated CNT-reinforced nanocomposites. For this objective, the constructive material properties are estimated based upon a micromechanical homogenization scheme containing only two parameters to capture the associated agglomeration of randomly oriented CNTs, while the nonlocal strain gradient continuum theory of elasticity is enrolled to apprehend various size dependency features. The unconventional nonlinear governing differential equations of motion are solved numerically via the shifted Chebyshev-Gauss-Lobatto discretization pattern together with the pseudo-arc-length continuation strategy. The size-dependent frequency-load-deflection characteristic curves are traced corresponding to different degrees of agglomeration including complete and partial ones. It is revealed that for an agglomerated CNT-reinforced nanocomposite microbeam in which the most CNTs are inside clusters, a higher value of the cluster volume fraction results in to reduce the significance of the softening and stiffing characters associated with the nonlocal and strain gradient small-scale effects, respectively. However, for an agglomerated CNT-reinforced nanocomposite microbeam in which the most CNTs are outside clusters, increasing the value of the cluster volume fraction plays an opposite role in the size dependency features.

2

Description of large deformations of continuum and shellsand their visualisation with Mathematica

Walentyński Ryszard

Computer Assisted Methods in Engineering and Science

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2019

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vol. 26, no. 3-4

191--209

EN

A proper description of large deformation of continuum or shell requires dealing with curved spacesand application of tensor analysis and distinguishing of covariant and contravariant bases. Thanks tosymbolic computations and visualization capabilities of theMathematicasystem, this task can be carriedout in a straightforward manner. This has been already discussed in [9] and [10]. This paper is a furtherextension of these researches. First, it will be shown that the deformation is indeed changing a curvatureof the considered space. Next, there will be shown how the Cartesian basis of the undeformed flat spacesplits into the covariant and contravariant ones and this basis changes in the space. This makes it possibleto explain why we have to introduce covariant derivatives and Christoffel symbols, for example. This isimportant in the case of the optical analysis of large deformations of thin-wall structures. Moreover, itis possible to easily explain that strain tensor is defined with a change of metric tensor. It also helps to showthe idea of material (Lagrangian) and spatial (Eulerian) description of the deformation and the motion,and avoid misunderstandings in this matter. Everything is visualised with 3D graphical capabilities andinteractive manipulation of the plots provided within theMathematicasystem. This paper can also bea useful inspiration both in teaching and learning of continuum mechanics, the theory of shells and thin-wall structures. This work has been presented at the conference “4th Polish Congress of Mechanics, 23rd International Conference on Computer Methods in Mechanics” PCM-CMM-2019 in Kraków.

3

Continuum mechanical considerations for rigid bodies and fluid-structure interaction problems

Hesch C., Betsch P.

Archive of Mechanical Engineering

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2013

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Vol. LX, nr 1

95--108

EN

The present work deals with continuum mechanical considerations for deformable and rigid solids as well as for fluids. A common finite element framework is used to approximate all systems under considerations. In particular, we present a standard displacement based formulation for the deformable solids and make use of this framework for the transition of the solid to a rigid body in the limit of infinite stiffness. At last, we demonstrate how to immerse a discretized solid into a fluid for fluid-structure interaction problems.

PL

Przedstawiona praca dotyczy mechaniki continuum w zastosowaniu do ciał sztywnych i odkształcalnych oraz do płynów. W ramach wspólnego systemu elementów skończonych dokonano aproksymacji całego rozważanego systemu. W szczególności, przedstawiono standardowe, oparte na przemieszczeniach, sformułowanie FEM dla ciał deformowalnych i wykorzystano je przy przejściu granicznym do ciała o nieskończonej sztywności. W końcu, zademonstrowano problemy interakcji między płynem a strukturą na przykładzie zdyskretyzowanego ciała zanurzonego w cieczy.