Abstract and Applied Analysis

A Generalized Version of a Low Velocity Impact between a Rigid Sphere and a Transversely Isotropic Strain-Hardening Plate Supported by a Rigid Substrate Using the Concept of Noninteger Derivatives

Abdon Atangana, O. Aden Ahmed, and Necdet Bıldık

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Abstract

A low velocity impact between a rigid sphere and transversely isotropic strain-hardening plate supported by a rigid substrate is generalized to the concept of noninteger derivatives order. A brief history of fractional derivatives order is presented. The fractional derivatives order adopted is in Caputo sense. The new equation is solved via the analytical technique, the Homotopy decomposition method (HDM). The technique is described and the numerical simulations are presented. Since it is very important to accurately predict the contact force and its time history, the three stages of the indentation process, including (1) the elastic indentation, (2) the plastic indentation, and (3) the elastic unloading stages, are investigated.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 671321, 9 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393448858

Digital Object Identifier
doi:10.1155/2013/671321

Mathematical Reviews number (MathSciNet)
MR3039156

Zentralblatt MATH identifier
1364.74039

Citation

Atangana, Abdon; Ahmed, O. Aden; Bıldık, Necdet. A Generalized Version of a Low Velocity Impact between a Rigid Sphere and a Transversely Isotropic Strain-Hardening Plate Supported by a Rigid Substrate Using the Concept of Noninteger Derivatives. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 671321, 9 pages. doi:10.1155/2013/671321. https://projecteuclid.org/euclid.aaa/1393448858


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