Structural anisotropy in viscoelasticity

Pobedrya, B. E.

doi:10.1007/bf00857005

Cited by 15 publications

(13 citation statements)

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“…To solve the quasi-static problem of the linear theory for a viscoelastic composite material, we can use the method of reducing the inhomogeneous isotropic viscoelastic problem to a sequence of successive homogeneous anisotropic ones, as is done in the elastic case (see [26]). For a given set of values ofω, the corresponding elastic problem is solved numerically with P(t) = 1.…”

Section: Illyushin's Approximation Methodsmentioning

confidence: 99%

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Bending of a fiber-reinforced viscoelastic composite plate resting on elastic foundations

2009

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Composite structures on an elastic foundation are being widely used in engineering applications. Bending response of inhomogeneous viscoelastic plate as a composite structure on a two-parameter (Pasternak's type) elastic foundation is investigated. The formulations are based on sinusoidal shear deformation plate theory. Trigonometric terms are used in the present theory for the displacements in addition to the initial terms of a power series through the thickness. The transverse shear correction factors are not needed because a correct representation of the transverse shear strain is given. The interaction between the plate and the foundation is included in the formulation with a two-parameter Pasternak's model. The effective moduli and Illyushin's approximation methods are used to derive the viscoelastic solution. The effects played by foundation stiffness, plate aspect ratio, and other parameters are presented.

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Section: Illyushin's Approximation Methodsmentioning

confidence: 99%

“…The effects of foundation stiffness on bending of composite plates are presented. In deriving the governing equations the effective moduli method [26] is used. The viscoelastic problem can be solved by applying Illyushin's approximation method [19].…”

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confidence: 99%

Bending of a fiber-reinforced viscoelastic composite plate resting on elastic foundations

2009

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“…The method of effective moduli is used to reduce this problem to that of a FG anisotropic material with elastic coefficients E 0 r , E 0 θ , ν θr and ν r θ . Then, one obtains (see Pobedrya [30]):…”

Section: Fiber-reinforced Viscoelastic Disksmentioning

confidence: 99%

Elastic and Viscoelastic Stresses of Nonlinear Rotating Functionally Graded Solid and Annular Disks with Gradually Varying Thickness

Allam

Tantawy

Yousof

et al. 2017

Archive of Mechanical Engineering

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Analytical and numerical nonlinear solutions for rotating variable-thickness functionally graded solid and annular disks with viscoelastic orthotropic material properties are presented by using the method of successive approximations. Variable material properties such as Young's moduli, density and thickness of the disk, are first introduced to obtain the governing equation. As a second step, the method of successive approximations is proposed to get the nonlinear solution of the problem. In the third step, the method of effective moduli is deduced to reduce the problem to the corresponding one of a homogeneous but anisotropic material. The results of viscoelastic stresses and radial displacement are obtained for annular and solid disks of different profiles and graphically illustrated. The calculated results are compared and the effects due to many parameters are discussed.

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“…Using the method of effective moduli [24] , this problem reduces to that of a homogeneous isotropic material with elastic coefficients:…”

Section: Elastic and Viscoelastic Solutions To Rotating Functionally mentioning

confidence: 99%

“…According to Illyushin's approximation method [24] , the functions σ i can be represented in the form:…”

Section: Elastic and Viscoelastic Solutions To Rotating Functionally mentioning

confidence: 99%

Elastic and viscoelastic solutions to rotating functionally graded hollow and solid cylinders

Zenkour

Elsibai

Mashat

2008

Appl. Math. Mech.-Engl. Ed.

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Analytical solutions to rotating functionally graded hollow and solid long cylinders are developed. Young's modulus and material density of the cylinder are assumed to vary exponentially in the radial direction, and Poisson's ratio is assumed to be constant. A unified governing equation is derived from the equilibrium equations, compatibility equation, deformation theory of elasticity and the stress-strain relationship. The governing second-order differential equation is solved in terms of a hypergeometric function for the elastic deformation of rotating functionally graded cylinders. Dependence of stresses in the cylinder on the inhomogeneous parameters, geometry and boundary conditions is examined and discussed. The proposed solution is validated by comparing the results for rotating functionally graded hollow and solid cylinders with the results for rotating homogeneous isotropic cylinders. In addition, a viscoelastic solution to the rotating viscoelastic cylinder is presented, and dependence of stresses in hollow and solid cylinders on the time parameter is examined.

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Structural anisotropy in viscoelasticity

Cited by 15 publications

References 0 publications

Bending of a fiber-reinforced viscoelastic composite plate resting on elastic foundations

Bending of a fiber-reinforced viscoelastic composite plate resting on elastic foundations

Elastic and Viscoelastic Stresses of Nonlinear Rotating Functionally Graded Solid and Annular Disks with Gradually Varying Thickness

Elastic and viscoelastic solutions to rotating functionally graded hollow and solid cylinders

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