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

Allam M. N. M., Tantawy R., Yousof A., Zenkour A. M.

Archive of Mechanical Engineering

2017

Vol. LXIV, nr 4

423--440

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.

Finding of incomes of HM-network with limited waiting times in queues by means of the successive approximations method

Kosarava K., Matalytski M., Rozau K.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2012

Vol. 11, nr 1

41-52

The article is devoted to the successive approximations method combined with the series method and its application for finding of expected incomes in HM-network systems with limited waiting times in queues and one-type messages. The properties of successive approximations were researched. The example of implementation of the described method is calculated.