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. (30th March 2013)

• Record Type: Journal Article
• Authors: Atangana, Abdon; Ahmed, O. Aden; Bıldık, Necdet
• Other Names: Eltayeb Hassan Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2013(2013)
• Publication Date: 2013-03-30
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2013/671321
• Languages: English
• ISSNs: 1085-3375

Abstract

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.