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

Товстик, П. Е.; Товстик, Т. П.

doi:10.1002/zamm.201600052

Cited by 32 publications

(32 citation statements)

References 20 publications

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“…Equation (18) may be obtained in the frames of the Kirchhoff-Love Hypotheses with the corresponding value of the equivalent longitudinal stiffness c 0 (see (6)). The zero and the second approximations coincide with those obtained in [7] - [9] for a transversely isotropic plate, because at c h = c 1 = 0 the both problems are described by the same Eqs. (11).…”

Section: The Asymptotic Solution Of the Problem (11)supporting

confidence: 79%

“…For anisotropic materials with a general anisotropy (with 21 elastic modules) the additional difficulties arise [1,2,3,4,5]. The more exact equations of second-order accuracy for beams and plates made of a transversely isotropic heterogeneous (or multi-layered) material were constructed in [6,7,8,9]. In the case of the general anisotropy the construction of models of second-order accuracy is more difficult.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Harmonic and Random Vibrations of an Anisotropic Beam

Товстик¹,

Товстик²,

Naumova³

2017

Proceedings of the 6th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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Keywords: anisotropic beam, equations of second order accuracy, forced harmonic and random vibrations.Abstract. Vibrations of a thin elastic beam-strip are studied. A beam is made of an anisotropic material heterogeneous in the thickness direction. The 1D model of second-order accuracy is delivered by using asymptotic expansions in powers of the relative beam thickness. A special attention is paid to the slanted anisotropy with 6 elastic modules. A spectrum of bending vibrations in the case of simply supported ends of a beam is constructed. Forced vibrations under action of a harmonic and a random excitations are studied. In the last case, the root-meansquare of deflections are found in dependence of a type of excitation.

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Section: The Asymptotic Solution Of the Problem (11)supporting

confidence: 79%

Section: Introductionmentioning

confidence: 99%

Harmonic and Random Vibrations of an Anisotropic Beam

Товстик¹,

Товстик²,

Naumova³

2017

Proceedings of the 6th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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“…As might be expected, the cut-off frequencies are not observed over the low-frequency range in the non-contrast case, see Figure 2. In the next section, we further simplify asymptotic dispersion relation (20) by specifying coefficients γ j for two chosen scenarios, (13) and (14).…”

Section: Statement Of the Problemmentioning

confidence: 99%

Asymptotic analysis of an anti-plane dynamic problem for a three-layered strongly inhomogeneous laminate

Prikazchikova

Aydın

Erbaş

et al. 2018

Mathematics and Mechanics of Solids

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Anti-plane dynamic shear of a strongly inhomogeneous dynamic laminate with traction-free faces is analysed. Two types of contrast are considered, including those for composite structures with thick or thin stiff outer layers. In both cases, the value of the cut-off frequency corresponding to the lowest antisymmetric vibration mode tends to zero. For this mode, the shortened dispersion relations and the associated formulae for displacement and stresses are obtained. The latter motivate the choice of appropriate settings, supporting the limiting forms of the original anti-plane problem. The asymptotic equation derived for a three-layered plate with thick faces is valid over the whole low-frequency range, whereas the range of validity of its counterpart for another type of contrast is restricted to a narrow vicinity of the cut-off frequency.

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“…In the papers [7,8] the GTR model for plates that are heterogeneous in the thickness direction was introduced. According to this model, a shell that is heterogeneous can be replaced by a homogeneous shell with the equivalent bending and transversal shear stiffness.…”

Section: Approximate Models For Computing Static Deflectionmentioning

confidence: 99%

“…Thus, the equivalent shear stiffness is determined. In the papers [7,8] the error of this approach is estimated by comparison with test examples showing the exact solution.…”

Section: Introductionmentioning

confidence: 99%

Bending of Multilayered Plates and Cylindrical Shells

Zelinskaia¹

2019

Proceedings of the 7th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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In this paper, the bending of thin multilayered plates and cylindrical shells are considered. The generalized Timoshenko-Reissner (GTR) model, the bending equation of secondorder accuracy (the SA model) and the equivalent single layer (ESL) model will be used here.According to the GTR model, a shell that is heterogeneous can be replaced by a homogeneous shell with the equivalent bending and transversal shear stiffness. In this paper, these models are used for the equations that take into account the transversal shear. The ESL model is developed by Grigoliuk and Kulikov and completely based on the generalized kinematic hypothesis of Timoshenko for the whole laminated packet.As an example, thin multilayered plates and cylindrical shells consisting of isotropic layers with hinged edges are considered. It is assumed that each layer has a constant thickness. The exact numerical solution is compared with the results of the GTR model and the SA model and the ESL model.

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

Cited by 32 publications

References 20 publications

Harmonic and Random Vibrations of an Anisotropic Beam

Harmonic and Random Vibrations of an Anisotropic Beam

Asymptotic analysis of an anti-plane dynamic problem for a three-layered strongly inhomogeneous laminate

Bending of Multilayered Plates and Cylindrical Shells

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