Continuum Models for Beam- and Platelike Lattice Structures

Noor, Ahmed K.; Anderson, M. S.; Greene, William H.

doi:10.2514/3.61036

Cited by 164 publications

(36 citation statements)

References 3 publications

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“…For many years, researchers have developed methods of modeling large-area truss structures with equivalent-continuum models [26][27][28][29][30][31]. These studies indicate that various methods and assumptions have been employed in which equivalent-continuum models have been developed that adequately represent truss structures.…”

Section: Equivalent-continuum Modelmentioning

confidence: 99%

Equivalent-continuum modeling of nano-structured materials

Odegard

2002

Composites Science and Technology

581

302

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A method has been proposed for developing structure-property relationships of nano-structured materials. This method serves as a link between computational chemistry and solid mechanics by substituting discrete molecular structures with equivalent-continuum models. It has been shown that this substitution may be accomplished by equating the molecular potential energy of a nano-structured material with the strain energy of representative truss and continuum models. As important examples with direct application to the development and characterization of singlewalled carbon nanotubes and the design of nanotube-based structural devices, the modeling technique has been applied to two independent examples: the determination of the effectivecontinuum geometry and bending rigidity of a graphene sheet. A representative volume element of the chemical structure of graphene has been substituted with equivalent-truss and equivalentcontinuum models. As a result, an effective thickness of the continuum model has been determined. The determined effective thickness is significantly larger than the inter-planar spacing of graphite. The effective bending rigidity of the equivalent-continuum model of a graphene sheet was determined by equating the molecular potential energy of the molecular model of a graphene sheet subjected to cylindrical bending (to form a nanotube) with the strain energy of an equivalent-continuum plate subjected to cylindrical bending.

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Section: Equivalent-continuum Modelmentioning

confidence: 99%

Equivalent-continuum modeling of nano-structured materials

Odegard

2002

Composites Science and Technology

581

302

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“…In the literature, much attention has been paid to lattices of beams interconnected by clamping constraints and to trusses [Németh and Kocsis 2014;Liew et al 2000;Noor et al 1978]. However, the existence of so called "floppy modes" at the microlevel in the pantographic structures requires the most attentive consideration.…”

Section: Micromodeling Of Pantographic Latticesmentioning

confidence: 99%

Linear pantographic sheets: Asymptotic micro-macro models identification

Boutin

Dell’Isola

Giorgio

et al. 2017

Math. Mech. Compl. Sys.

166

120

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In this paper we consider linear pantographic sheets, which in their natural configuration are constituted by two orthogonal arrays of straight fibers interconnected by internal pivots. We introduce a continuous model by means of a micro-macro identification procedure based on the asymptotic homogenization method of discrete media. The rescaling of the mechanical properties and of the deformation measures is calibrated in order to comply with the specific kinematics imposed by the quasi-inextensibility of the fibers together with the large pantographic deformability. The obtained high-order continuum model shows interesting and exotic features related to its extreme anisotropy and also to the subcoercivity of its deformation energy. Some initial numerical simulations are presented, showing that the model can account for experimental uncommon phenomena occurring in pantographic sheets. The paper focuses on the precise analysis and the understanding of the effective behavior based on a well-calibration of the extension and bending phenomena arising at the local scale. In an upcoming work, the analysis will be extended to oblique arrays, some analytical solutions to proposed equations and some further applications.

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“…Concerning the previous researches relative to the construction of a ROM for complex beam-like structures having a high-modal density in the LF range, most of them are based on the introduction of an equivalent beam model [8,9] or on the use of homogenization methods [10]. The development of such simplified models requires an expertise concerning the dynamical behavior for this type of complex beam-like structure and provide a quite good approximation of the dynamical responses in the LF range in terms of the global displacements.…”

Section: Introductionmentioning

confidence: 99%