The loss of stability analyses of an elastic and viscoelastic composite circular plate in the framework of three-dimensional linearized theory

Kutug, Zafer; Yahnioğlu, Nazmiye; Akbarov, S. D.

doi:10.1016/s0997-7538(03)00034-2

Cited by 13 publications

(17 citation statements)

References 9 publications

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“…We will also compare these results with those obtained in [69] for clamped (20) and simply supported (21) (19) and (20) are in close agreement too. These results guarantee the validity of the approach and FEM modeling used in [69]. Also, according to [69], we will compare the results produced by the TDLTSDB and approximate plate theories for a purely elastic plate.…”

Section: Fibrous Compositessupporting

confidence: 65%

“…According to [69], we will now consider the values of p E cr / ( ) 0 1 obtained in [27,81] from an analytic solution and compare them with those obtained in [69]. We will also compare these results with those obtained in [69] for clamped (20) and simply supported (21) (19) and (20) are in close agreement too. These results guarantee the validity of the approach and FEM modeling used in [69].…”

Section: Fibrous Compositesmentioning

confidence: 80%

“…The paper [69] investigated rotationally symmetric instability problem for a circular plate made of a viscoelastic composite material, and the method from [1,22,23] was developed to solve the problem. The investigations are conducted for various lateral boundary conditions, some of which were not satisfied even for an elastic circular plate.…”

Section: Fibrous Compositesmentioning

confidence: 99%

“…It is assumed that the material of the reinforcing layers is elastic and has mechanical characteristics E ( ) 2 and n ( ) 2 , while the material of the matrix layers is viscoelastic with operators (11) and (12) and instantaneous Young's modulus E 0 1 ( ) and Poisson's ratio n 0 1 ( ) . To compare the results produced by approximate theories and the TDLTSDB, we will consider in detail some results from [69] for the following three types of boundary conditions on the lateral surface of the plate. The first type of conditions is the same as in [27,81]:…”

Section: Fibrous Compositesmentioning

confidence: 99%

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Three-dimensional instability problems for viscoelastic composite materials and structural members

Akbarov

2007

Int Appl Mech

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Investigations of viscoelastic composite materials and structural members carried out using the TDLTSDB and initial-imperfection method are reviewed. The investigations address the internal and surface loss of stability of layered and fibrous composites, the loss of stability of plates, and the delamination (buckling) of plates with cracks. Each of these problems is reviewed separately. New areas of further research are proposed. The review focuses on the investigations carried out by the author and his students Keywords: buckling, crack, delamination, plate, instability, viscoelastic composite material 1. Introduction. As in [33,[41][42][43][44][45] and many other publications, by three-dimensional instability problems will be understood here instability problems investigated employing the three-dimensional linearized theory of stability of deformable bodies (TDLTSDB). The investigations regarding the construction of the TDLTSDB are detailed in the paper [46] and in the monographs [33,[41][42][43]45]. It was noted there that the tendencies to construct the theory, which allows us (i) to describe the buckling phenomenon for a well-defined three-dimensional stress-strain state and (ii) to obtain reliable data on the critical parameters for thin-walled and massive structural elements, contributed to the creation of the TDLTSDB. Historically, the TDLTSDB began to be developed in the first half of the 20th century, and the basic TDLTSDB relations were obtained in [30, 31-33, 35, 38, 45, 63, 71-73, 80, 84, 85] using either a strict and exact approach based on the linearization of the exact and strict relations of the nonlinear three-dimensional theory or an approximate approach based on a physical and, in part, linearization of certain relations. Development and detailed analyses of the results from these investigations were presented in the monographs [41,42,45].In the second half of the 20th century, the main attention of researchers was focused on the solution to separate classes of TDLTSDB problems. At the same time, general aspects of the TDLTSDB were also developed. It should be noted that the results of these studies were the subject of many monographs such as [41][42][43][44][45] and were reviewed in many papers such as [28,46,47,49,52,55,56,58].It follows from the search of the foregoing and other numerous inquiries that the TDLTSDB was mainly applied to analyze the stability of structural members made of time-independent materials. Moreover, these investigations used the bifurcation (Euler) approach. The Euler approach is known to be generally unsuitable for investigating instability problems for structural elements made of time-dependent materials and subjected to external static loading. This is why a dynamic investigation method was suggested in [40,45] to examine these problems. Note that this method represents the sought quantities with a multiplier exp(iWt) and determines the critical parameters of the problems from the requirement ImW = 0. However, if the dynamic investigation method is applied with...

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Section: Fibrous Compositessupporting

confidence: 65%

Section: Fibrous Compositesmentioning

confidence: 80%

Section: Fibrous Compositesmentioning

confidence: 99%

Section: Fibrous Compositesmentioning

confidence: 99%

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Three-dimensional instability problems for viscoelastic composite materials and structural members

Akbarov

2007

Int Appl Mech

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“…In conclusion it should be emphasized that nowadays the ideas of Russian Academician Rabotnov are widely used worldwide for solving intricate static and dynamic problems dealing with behaviour of hereditarily elastic bodies (see as examples the papers [1]- [5], [7,8], [15]- [21], etc. ), since Rabotnov's fractional order operator models allow one to decode rather easily different combinations of viscoelastic operators appearing in problems of mechanics of hereditary elastic bodies.…”

Section: −γ Imentioning

confidence: 99%

Centennial jubilee of Academician Rabotnov and contemporary handling of his fractional operator

Rossikhin

Shitikova

2014

Fract Calc Appl Anal

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This note is dedicated to the centennial jubilee of the Russian Academician Yury Rabotnov, who was a pioneer in the application of fractional operators in Mechanics of Solids. In the present Note, the authors wish to present a contemporary handling of Rabotnov operators introduced in 1948 and to show their connectedness with fractional derivatives, what provides the ageless interest to his ideas and results.MSC 2010 : 01A60, 26A33, 33E12, 34A08, 74D05, 74G50 Key Words and Phrases: fractional calculus, Rabotnov fractional exponential function, generalized Rabotnov fractional operator model * On February 24, 2014, Russian science and fractional calculus community all over the world celebrated the centennial anniversary of the birthday of the Russian Academician Yury Nikolaevich Rabotnov who was an outstanding scientist in the field of Solid Mechanics and made a basic contribution to the development of the theory of elasticity and plasticity, the theory of shells and stability of elastic and viscoplastic systems, the creep theory of metals and the hereditary theory of elasticity. He actively worked in the new directions of damage and fracture mechanics and mechanics of composite materials.

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Buckling and Post-buckling of Circular/Annular Plates

Eslami

2017

Buckling and Postbuckling of Beams, Plates, and Shells

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The loss of stability analyses of an elastic and viscoelastic composite circular plate in the framework of three-dimensional linearized theory

Cited by 13 publications

References 9 publications

Three-dimensional instability problems for viscoelastic composite materials and structural members

Three-dimensional instability problems for viscoelastic composite materials and structural members

Centennial jubilee of Academician Rabotnov and contemporary handling of his fractional operator

Buckling and Post-buckling of Circular/Annular Plates

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