On the asymptotic nature of approximate models of beams, plates, and shells

Товстик, П. Е.

doi:10.3103/s1063454107030041

Cited by 15 publications

(20 citation statements)

References 1 publication

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“…All these constants may be found in the frames of the KL hypothesis about a straight normal; in the dimensionless form they are contained in Eqs. (20), (25), which describe the deflection of the second-order accuracy. The problem is to chose the shear stiffness .…”

Section: Generalized Timoshenko-reissner Model For a Beammentioning

confidence: 99%

“…(54) is quadratic www.zamm-journal.org in , it has the small root (1) and the large root (2) . The root (2) describes the second (high-frequency) branch of the dispersion curve [20], and it is not studied here. The root (1) is close to the value (25).…”

Section: Generalized Timoshenko-reissner Model For a Beammentioning

confidence: 99%

“…The KL model is asymptotically correct for an isotropic homogeneous plate . It gives the results of first‐order accuracy with respect to the small thickness parameter μ.…”

Section: Introductionmentioning

confidence: 97%

“…Numerous investigations were devoted to the derivation of 2D equations by using asymptotic expansions in power series in the small parameter

μ = h / L

, which is equal to the dimensionless plate thickness ( h and L are, respectively, the thickness and the typical wave length in the tangential directions). The other possibility is the direct derivation of 2D equations of plates and shells without referring to the 3D media.…”

Section: Introductionmentioning

confidence: 99%

“…(20)), and (iii) with the value w T R , which corresponds to the generalized TR model. This model follows from Eq (20). with N 0 = 0 and A = A g .…”

mentioning

confidence: 99%

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Generalized Timoshenko‐Reissner models for beams and plates, strongly heterogeneous in the thickness direction

Товстик

2016

Z Angew Math Mech

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The paper is concerned with a thin beam and a thin plate made of a transversally isotropic linearly elastic material heterogeneous in the thickness direction. The ordinary Kirchhoff–Love and Timoshenko–Reissner models are known to be unacceptable for a strongly heterogeneous material or for a multilayered material with large ratio between the Young moduli of layers. A generalized Timoshenko–Reissner model is proposed for bending and free vibrations of such beams/plates. A multilayered beam/plate is reduced to one‐layer one with the equivalent elastic parameters. The range of application of such a model is very wide.

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Section: Generalized Timoshenko-reissner Model For a Beammentioning

confidence: 99%

Section: Generalized Timoshenko-reissner Model For a Beammentioning

confidence: 99%

“…The KL model is asymptotically correct for an isotropic homogeneous plate . It gives the results of first‐order accuracy with respect to the small thickness parameter μ.…”

Section: Introductionmentioning

confidence: 97%

“…Numerous investigations were devoted to the derivation of 2D equations by using asymptotic expansions in power series in the small parameter

μ = h / L

Section: Introductionmentioning

confidence: 99%

“…(20)), and (iii) with the value w T R , which corresponds to the generalized TR model. This model follows from Eq (20). with N 0 = 0 and A = A g .…”

mentioning

confidence: 99%

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Generalized Timoshenko‐Reissner models for beams and plates, strongly heterogeneous in the thickness direction

Товстик

2016

Z Angew Math Mech

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A Vekua‐type linear theory of thick elastic shells

Zhavoronok

2013

Z Angew Math Mech

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This paper presents an effective variational formalism of construction of the thick anisotropic linear shell theory of Vekua‐type of an arbitrary order. The dynamic equations are formulated as the Lagrange equations of the second kind, independent from expansion functions. The asymmetric stress tensor is used to obtain the compact form of the dynamic equations similar to the classical shell theories. The proposed approach allows one for computer‐aided derivation of all equations using computer algebra software supporting main tensor operations. Some solutions of test problems are presented.

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