Effect of the non-homogenity on the composite infinite cylinder of orthotropic material

Abd-Alla, A. M.; Nofal, Taher A.; Farhan, A. M.

doi:10.1016/j.physleta.2007.08.029

Cited by 12 publications

(3 citation statements)

References 12 publications

(4 reference statements)

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“…Abd-Alla et al [21] investigated the effect of the nonhomogeneity on the composite infinite cylinder of isotropic material. Abd-Alla and Farhan [22] investigated the effect of the nonhomogeneity on the composite infinite cylinder of orthotropic materials. Abd-Alla et al [23] investigated the effect of magnetic field and nonhomogeneity on the radial vibrations in hollow rotating elastic cylinder.…”

Section: Introductionmentioning

confidence: 99%

Solution of a Problem Linear Plane Elasticity with Mixed Boundary Conditions by the Method of Boundary Integrals

Hussein

2014

Mathematical Problems in Engineering

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A numerical boundary integral scheme is proposed for the solution to the system ofeld equations of plane. The stresses are prescribed on one-half of the circle, while the displacements are given. The considered problem with mixed boundary conditions in the circle is replaced by two problems with homogeneous boundary conditions, one of each type, having a common solution. The equations are reduced to a system of boundary integral equations, which is then discretized in the usual way, and the problem at this stage is reduced to the solution to a rectangular linear system of algebraic equations. The unknowns in this system of equations are the boundary values of four harmonic functions which define the full elastic solution and the unknown boundary values of stresses or displacements on proper parts of the boundary. On the basis of the obtained results, it is inferred that a stress component has a singularity at each of the two separation points, thought to be of logarithmic type. The results are discussed and boundary plots are given. We have also calculated the unknown functions in the bulk directly from the given boundary conditions using the boundary collocation method. The obtained results in the bulk are discussed and three-dimensional plots are given. A tentative form for the singular solution is proposed and the corresponding singular stresses and displacements are plotted in the bulk. The form of the singular tangential stress is seen to be compatible with the boundary values obtained earlier. The efficiency of the used numerical schemes is discussed.

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Section: Introductionmentioning

confidence: 99%

Solution of a Problem Linear Plane Elasticity with Mixed Boundary Conditions by the Method of Boundary Integrals

Hussein

2014

Mathematical Problems in Engineering

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“…flywheels, turbines, etc.). Abd-Alla et al [1,2] investigated effect of the non-homogeneity on the composite infinite cylinder of isotropic and orthotropic material. El-Naggar et al [3,4] studied the rotation of a non-homogeneous composite infinite cylinder of orthotropic material and the stresses in a rotation of a non-homogeneous composite cylinder of isotropic material.…”

Section: Introductionmentioning

confidence: 99%

Effect of the rotation on a non-homogeneous infinite cylinder of orthotropic material

Abd-Alla

Mahmoud

Shehri

2011

Applied Mathematics and Computation

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“…Based on the energy principle of buckling and the mixed hardening constitutive relation of orthotropic materials, Zeng and Fu [3] deduced the formula of elasto-plastic critical stresses and calculated critical stresses of simply-supported orthotropic circular cylindrical shells under axial compression. Abd-Alla and Farhan [4] developed the solution of the non-homogeneous orthotropic elastic cylinder for plane strain problems. Analytical expressions for displacement and stresses were obtained.…”

Section: Introductionmentioning

confidence: 99%

Stress field of orthotropic cylinder subjected to axial compression

Zhong

Song

Chen

et al. 2010

Appl. Math. Mech.-Engl. Ed.

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Based on the constancy hypothesis of material volume, the circumferential and radial stresses of a cylinder specimen are analyzed when the cylinder is subject to a loading along the axial direction. The circumferential and radial stress distribution is a power function of radius parameter when the constitutive relation of specimen material is orthotropic. The stress distribution is a quadratic function of radius parameter for transversely isotropic material. Along the cylinder axial line, the circumferential and radial stresses are maximum and equal to each other. In the circumference boundary surface, the radial stress is zero and the circumferential stress value is minimal. The failure theory of maximum tensile circumferential strain is applied to calculate the critical axial loading. The circumference-boundary-layer failure criterion of orthotropic cylinders is described with the Hill-Tsai strength theory. The obtained strength theory is related to axial stress and mechanical properties of specimen material and to the specimen axialdeformation strain rate and the change rate of strain rate.

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Effect of the non-homogenity on the composite infinite cylinder of orthotropic material

Cited by 12 publications

References 12 publications

Solution of a Problem Linear Plane Elasticity with Mixed Boundary Conditions by the Method of Boundary Integrals

Solution of a Problem Linear Plane Elasticity with Mixed Boundary Conditions by the Method of Boundary Integrals

Effect of the rotation on a non-homogeneous infinite cylinder of orthotropic material

Stress field of orthotropic cylinder subjected to axial compression

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