• Structural Engineering and Mechanics
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• v.72 no.1
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• pp.71-81
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• 2019

The objective of this paper is to develop a size-dependent nonlinear model of beams for fluid-conveying nanotubes with an initial deflection. The nonlinear frequency response of the nanotube is analysed via an Euler-Bernoulli model. Size influences on the behaviour of the nanosystem are described utilising the nonlocal strain gradient theory (NSGT). Relative motions at the inner wall of the nanotube is taken into consideration via Beskok-Karniadakis model. Formulating kinetic and elastic energies and then employing Hamilton's approach, the nonlinear motion equations are derived. Furthermore, Galerkin's approach is employed for discretisation, and then a continuation scheme is developed for obtaining numerical results. It is observed that an initial deflection significantly alters the frequency response of NSGT nanotubes conveying fluid. For small initial deflections, a hardening nonlinearity is found whereas a softening-hardening nonlinearity is observed for large initial deflections.

• Structural Engineering and Mechanics
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• v.19 no.4
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• pp.413-423
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• 2005

This paper presents the solution of large static deflection due to uniformly distributed self weight and the critical or maximum applied uniform loading that a simply supported beam with variable-arc-length can resist. Two analytical approaches are presented and validated experimentally. The first approach is a finite-element discretization of the span length based on the variational formulation, which gives the solution of large static sag deflections for the stable equilibrium case. The second approach is the shooting method based on an elastica theory formulation. This method gives the results of the stable and unstable equilibrium configurations, and the critical uniform loading. Experimental studies were conducted to complement the analytical results for the stable equilibrium case. The measured large static configurations are found to be in good agreement with the two analytical approaches, and the critical uniform self weight obtained experimentally also shows good correlation with the shooting method.

• Steel and Composite Structures
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• v.33 no.2
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• pp.225-243
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• 2019

Cold-formed steel (CFS) sections when used as primary load carrying members often require additional strengthening for retrofitting purposes. In some cases, it is also necessary to reduce deflections in order to satisfy serviceability requirements. The introduction of angle sections, screwed to the webs so as to act as external stiffeners, has the potential to both increase flexural strength as well as reduce deflections. This paper presents the results of ten four-point bending tests, on built-up CFS sections, both open and closed, with different stiffening arrangements. In the laboratory tests, the stiffening arrangements increased the moment capacity and stiffness of the CFS beams by up to 85% and 100% respectively. The increase in moment capacity was more evident for the open sections, while that reduction in deflection was largest for the closed sections.

• Steel and Composite Structures
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• v.37 no.6
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• pp.733-740
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• 2020

The subject of the paper pertains to simply supported beams with bisymmetrical cross sections under three-point bending with consideration of the shear effect. The deformation of a planar cross section of the beam is described taking into account the assumed nonlinear hypothesis-theory. Two differential equations of equilibrium are obtained based on the principle of stationary potential energy. This system is analytically solved and the shear coefficients and deflections of the beams are derived. Moreover, the Young's modules of the materials and deflections of the beams are experimentally determined on a test stand. The results of the studies are specified in tables and compared.

• Structural Engineering and Mechanics
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• v.83 no.3
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• pp.283-292
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• 2022

A nonlinear vibrational analysis of sandwich curved panels having multi-scale face sheets has been performed in this article based on differential quadrature method (DQM). All mechanical properties of multi-scale skins have been established in the context of three-dimensional Mori-Tanaka scheme for which the influences of glass fibers and random carbon nanotubes (CNTs) have been taken into account. The governing equations for sandwich the panel have been developed based upon thin shell formulation in which geometry nonlinearities have been taken into account. Next, DQ approach has been applied to solve the governing equations for determining the relationships of frequencies with deflections for curved panels. It will be demonstrated that the relationships of frequencies with deflections are dependent on the changing of CNT weight fractions, fibers alignment, fibers volume, panel radius and skin thickness.

• Journal of the Korean Society for Precision Engineering
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• v.10 no.4
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• pp.54-63
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• 1993

This paper presents the dynamic modeling and control methodology to arrest structural deflections of industrial robotic manipulators featuring elastic members retrofitted with surface bonded pizoelectric actuators and sensors. The cynamic modeling is accomplished by employing a variational theorem, prior to developing a finite element formulation. This finite element formulation accounts for both original robot member elements and also bonded piezoelectric material elements. The governing equation of motion is then modified by condensing the electric potential vectors and subsequently two different negative velocity feedback controllers are established; a constant-gain feedback controller and a constant- amplitude feedback controller. By adopting a Model P50 articulating industrial robot manufactured by Gerneral Electric Company, conputer simulations are underlaken in order to demonstrate superior performance characteristics to be accrued from this proposed methodology such as smaller deflections at the end-effector.

• Steel and Composite Structures
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• v.51 no.1
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• pp.1-8
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• 2024

Transient dynamic behavior of a sandwich beam under thermal and impulsive loads has been researched in the context of higher-order beam theory. The impulse load of blast type has been enforced on the top exponent of the sandwich beam while it is in a thermal environment. The core of the sandwich beam is cellular with auxetic rectangular pattern, whereas the layers have been built with the incorporation of graphene oxide powder (GOP) and are micromechanically introduced through Halpin-Tsai formulization. Governing equations for the sandwich beam have been solved through inverse Laplace transform style for obtaining the dynamical deflections. The connection of beam deflections on temperature variability, GOP quantity, pulse load situation and core relative density has been surveyed in detail.

• 한국도로학회:학술대회논문집
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• 2005.11a
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• pp.145-154
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• 2005

• 한국도로학회:학술대회논문집
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• 1999.11a
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• pp.35-40
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• 1999

• Journal of The Korean Astronomical Society
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• v.37 no.5
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• pp.427-431
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• 2004

We use simulations of large-scale structure formation to study the build-up of magnetic fields (MFs) in the intergalactic medium. Our basic assumption is that cosmological MFs grow in a magnetohy-drodynamical (MHD) amplification process driven by structure formation out of a magnetic seed field present at high redshift. This approach is motivated by previous simulations of the MFs in galaxy clusters which, under the same hypothesis that we adopt here, succeeded in reproducing Faraday rotation measurements (RMs) in clusters of galaxies. Our ACDM initial conditions for the dark matter density fluctuations have been statistically constrained by the observed large-scale density field within a sphere of 110 Mpc around the Milky Way, based on the IRAS 1.2-Jy all-sky redshift survey. As a result, the positions and masses of prominent galaxy clusters in our simulation coincide closely with their real counterparts in the Local Universe. We find excellent agreement between RMs of our simulated galaxy clusters and observational data. The improved numerical resolution of our simulations compared to previous work also allows us to study the MF in large-scale filaments, sheets and voids. By tracing the propagation of ultra high energy (UHE) protons in the simulated MF we construct full-sky maps of expected deflection angles of protons with arrival energies $E = 10^{20}\;eV$ and $4 {\times} 10^{19}\;eV$, respectively. Accounting only for the structures within 110 Mpc, we find that strong deflections are only produced if UHE protons cross galaxy clusters. The total area on the sky covered by these structures is however very small. Over still larger distances, multiple crossings of sheets and filaments may give rise to noticeable deflections over a significant fraction of the sky; the exact amount and angular distribution depends on the model adopted for the magnetic seed field. Based on our results we argue that over a large fraction of the sky the deflections are likely to remain smaller than the present experimental angular sensitivity. Therefore, we conclude that forthcoming air shower experiments should be able to locate sources of UHE protons and shed more light on the nature of cosmological MFs.