Geometrically-exact, intrinsic theory for dynamics of moving composite plates

Hodges, Dewey H.; Yu, Wenbin; Patil, Mayuresh

doi:10.1016/j.ijsolstr.2008.05.005

Cited by 35 publications

(5 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Helpful comments on the physical meaning of the Cosserat model can be found in ref . Eringen , contributed to the further development of this theoretical approach, which was comprehensively presented in several review articles. − In the linear case, the medium is characterized by three lateral and three flexural elasticities, which have been experimentally determined for different media. , Original algorithms have been developed for numerical solution of the respective mathematical problems. − The Cosserat model has been applied for theoretical description of thin shells, − cell membranes, , and large deformations of linear continua . A systematic description of the elasticity theory of 3D, 2D, and 1D media of linear rheology was given in ref in terms of tensor analysis.…”

Section: Introductionmentioning

confidence: 99%

“…25,26 Original algorithms have been developed for numerical solution of the respective mathematical problems. [27][28][29][30] The Cosserat model has been applied for theoretical description of thin shells, [31][32][33][34] cell membranes, 35,36 and large deformations of linear continua. 37 A systematic description of the elasticity theory of 3D, 2D, and 1D media of linear rheology was given in ref 38 in terms of tensor analysis.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Elastic Langmuir Layers and Membranes Subjected to Unidirectional Compression: Wrinkling and Collapse

2009

View full text Add to dashboard Cite

We apply the two-dimensional elastic continuum model to describe the wrinkling of elastic Langmuir layers (membranes) subjected to unidirectional compression. The effects of the dilatational, shear, and bending elasticities are taken into account. Among the numerous solutions of the generalized Laplace equation, corresponding to different membrane tensions, we determine the membrane shape as the profile that minimizes the energy of the system. In the case of small deformations, the problem can be linearized. Its solution predicts a wavelike shape of the compressed membrane. At negligibly small bending elasticity, the energy of the system is minimal for a sinusoidal profile, whose amplitude and wavelength tend to zero. In the opposite limiting case, where the effect of bending elasticity prevails over the effect of gravity, the membrane has a half-wave profile. When the two effects are comparable, the membrane shape exhibits multiple periodic wrinkles (ripples). An expression is derived for calculating the bending elasticity (rigidity) from the wavelength, and reasonable values are obtained from available experimental data. To determine the membrane shape at larger out-of-plane deformations, we solved numerically the respective nonlinear problem. Depending on the values of the physical parameters, the theory predicts various shapes: nonharmonic oscillations, toothed profiles, and profiles with two characteristic wavelengths. The results can be used for determining the bending elastic modulus of Langmuir films (membranes) as well as for the interpretation of buckling and collapse of monolayers.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Elastic Langmuir Layers and Membranes Subjected to Unidirectional Compression: Wrinkling and Collapse

2009

View full text Add to dashboard Cite

show abstract

“…A fully intrinsic formulation, i.e. devoid of displacement and rotation variables, for the dynamics of a moving composite plate has been presented by Hodges et al (2009). A variable-order finite element technique is presented and applied to beams by Patil and Hodges (2011).…”

Section: Introductionmentioning

confidence: 99%

Efficient High-Fidelity, Geometrically Exact, Multiphysics Structural Models

Yu¹

2011

Self Cite

View full text Add to dashboard Cite

“…describe shell displacements in the low-frequency branches, which have been studied in brief in Section 2.3. According to Ref [51],. the 2-D generalized strain and velocity fields are expressed in terms ofū 2d α can be calculated from Eq.…”

mentioning

confidence: 99%

Dynamic Variational-Asymptotic Procedure for Laminated Composite Shells—Part II: High-Frequency Vibration Analysis

Lee

Hodges

2008

Journal of Applied Mechanics

Self Cite

View full text Add to dashboard Cite

Shell theories intended for low-frequency vibration analysis are frequently constructed from a generalization of the classical shell theory in which the normal displacement (to a first approximation) is constant through the thickness. Such theories are not suitable for the analysis of complicated high-frequency effects in which displacements may change rapidly along the thickness coordinate. Clearly, to derive by asymptotic methods, a shell theory suitable for high-frequency behavior requires a different set of assumptions regarding the small parameters associated with the characteristic wavelength and timescale. In Part I such assumptions were used to perform a rigorous dimensional reduction in the long-wavelength low-frequency vibration regime so as to construct an asymptotically correct energy functional to a first approximation. In Part II the derivation is extended to the long-wavelength high-frequency regime. However, for short-wavelength behavior, it becomes very difficult to represent the three-dimensional stress state exactly by any two-dimensional theory; and, at best, only a qualitative agreement can be expected. To rectify this difficult situation, a hyperbolic short-wave extrapolation is used. Unlike published shell theories for this regime, which are limited to homogeneous and isotropic shells, all the formulas derived herein are applicable to shells in which each layer is made of a monoclinic material.

show abstract

Geometrically-exact, intrinsic theory for dynamics of moving composite plates

Cited by 35 publications

References 18 publications

Elastic Langmuir Layers and Membranes Subjected to Unidirectional Compression: Wrinkling and Collapse

Elastic Langmuir Layers and Membranes Subjected to Unidirectional Compression: Wrinkling and Collapse

Efficient High-Fidelity, Geometrically Exact, Multiphysics Structural Models

Dynamic Variational-Asymptotic Procedure for Laminated Composite Shells—Part II: High-Frequency Vibration Analysis

Contact Info

Product

Resources

About