On a stress analysis in the infinite elastic body with two neighbouring curved fibres

Akbarov, S. D.; Köşker, Reşat

doi:10.1016/s1359-8368(02)00077-x

Cited by 18 publications

(10 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Now we consider the contact conditions for each approximation, which are derived from (5). For this purpose, we substitute the expressions (8) and (9) into (5) and expand the quantities σ…”

Section: Solution Methodsmentioning

confidence: 99%

The Self-Balanced Shear Stresses in the Elastic Body with a Locally Curved Covered Fiber

Alan

Akbarov²

2010

Advances in Mechanical Engineering

Self Cite

View full text Add to dashboard Cite

Within the framework of the piecewise homogenous body model, with the use of the three-dimensional geometrically nonlinear exact equations of the theory of elasticity, the method developed for the determination of the stress distribution in the composites with unidirectional locally curved covered fibers is used for investigation of the shear stresses acting along the fibers. All the investigations are carried out for an infinite elastic body containing a single locally curved covered fiber, for the case where there exists the bond covering cylinder with constant thickness between fiber and matrix material are considered. It is assumed that the considered material is loaded at infinity by uniformly distributed normal forces in the fiber lying direction. Under formulation and mathematical solution of the boundary value problem, the boundary form perturbation method is used. The numerical results related to stress distribution in considered body and the influence of geometrical nonlinearity to this distribution are presented and interpreted.

show abstract

Section: Solution Methodsmentioning

confidence: 99%

The Self-Balanced Shear Stresses in the Elastic Body with a Locally Curved Covered Fiber

Alan

Akbarov²

2010

Advances in Mechanical Engineering

Self Cite

View full text Add to dashboard Cite

show abstract

“…At the same time, the initial-imperfection method allows us to analyze not only the instability of fibers or layers in an elastic or viscoelastic matrix, but also the stress-strain state in such composite materials in a geometrical nonlinear statement prior to loss of stability under external compressive force. Consequently, this statement was followed in [7,8,10,11,65,66] to study the stress distribution in an infinite elastic body containing two neighboring fibers [7,8,65,66] and a periodical row of fibers [10,11].…”

Section: Fibrous Compositesmentioning

confidence: 99%

“…4. Development of the approach proposed in [1,9,[1][2][3][4][5][6][7][8]22] for time-dependent materials with more complicated constitutive relations. …”

Section: Conclusion: Areas Of Furthermentioning

confidence: 99%

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

Akbarov

2007

Int Appl Mech

View full text Add to dashboard Cite

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...

show abstract

“…To investigate associated problems, a method was developed in [1] based on a piecewise-homogeneous body model and the three-dimensional linear theory of elasticity, and corresponding numerical results were analyzed in [2]. In [6,7,14], this method was extended to the case of two neighboring fibers in an infinite elastic matrix, and numerical results were analyzed. The latter model allows one to obtain some information on the interaction of curved fibers in determining the self-balanced stresses.…”

mentioning

confidence: 99%

“…However, in fact, the inquiry into the interaction of such fibers requires a more complicated model. Therefore, in [8], the approach of [6,7,14] was extended to a periodically located row of fibers in an infinite matrix, and corresponding numerical results were presented. Note that it was assumed in [8] that the fibers curve in phase relative to one another.…”

mentioning

confidence: 99%

Stress distribution in a composite materialwith a row of antiphase periodically curved fibers

2006

View full text Add to dashboard Cite

The stress distribution in an infinite matrix containing a row of antiphase periodically curved fibers is studied using the piecewise-homogeneous body model and the exact three-dimensional equations of elasticity theory for anisotropic bodies. It is assumed that the midlines of the fibers are located in the same plane and the materials of the fibers are the same. Numerical results are presented for the case where the materials of the fibers and matrix are isotropic and homogeneous Keywords: unidirectional fibrous composite, row of fibers, self-balanced stresses, curved fibers 1. Introduction. Fibers in unidirectional fibrous composites may be curved for design purposes or by various factors during technological process [3,10,15]. According to a large number of theoretical and experimental investigations described in [3-5, 10, 15], the curving may lead to separation of fibers from the matrix under uniaxial tension or compression along the fibers. This separation gives rise to macrocracks, which when accumulate may change significantly the stiffness and strength properties of composites [12]. Therefore, theoretical investigations of self-balanced stresses due to fiber curving are of great theoretical and practical significance. To investigate associated problems, a method was developed in [1] based on a piecewise-homogeneous body model and the three-dimensional linear theory of elasticity, and corresponding numerical results were analyzed in [2]. In [6,7,14], this method was extended to the case of two neighboring fibers in an infinite elastic matrix, and numerical results were analyzed. The latter model allows one to obtain some information on the interaction of curved fibers in determining the self-balanced stresses. However, in fact, the inquiry into the interaction of such fibers requires a more complicated model. Therefore, in [8], the approach of [6,7,14] was extended to a periodically located row of fibers in an infinite matrix, and corresponding numerical results were presented. Note that it was assumed in [8] that the fibers curve in phase relative to one another. An analysis of sections of various composites shows that neighboring fibers may also curve in antiphase relative to each other. In this connection, here the results of [8] are extended to an antiphase-curved row of fibers in an infinite matrix. The corresponding instability problems were studied in [9, 10].2. Problem Formulation. Let us formulate a mathematical problem. We associate Cartesian O x x x

show abstract

On a stress analysis in the infinite elastic body with two neighbouring curved fibres

Cited by 18 publications

References 5 publications

The Self-Balanced Shear Stresses in the Elastic Body with a Locally Curved Covered Fiber

The Self-Balanced Shear Stresses in the Elastic Body with a Locally Curved Covered Fiber

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

Stress distribution in a composite materialwith a row of antiphase periodically curved fibers

Contact Info

Product

Resources

About