Title

Structural Relaxation And Crystallization Processes In Cu 55Hf 25Ti 15Pd 5 Metallic Glassy Alloy

Keywords

Deflections of thin flat plates; Discrete residual error analysis; Föppl-von Kármán equations; Homotopy analysis; Non-linear PDEs; Perturbation methods

Abstract

We discuss the method of linearization and construction of perturbation solutions for the Föppl-von Kármán equations, a set of non-linear partial differential equations describing the large deflections of thin flat plates. In particular, we present a linearization method for the Föppl-von Kármán equations which preserves much of the structure of the original equations, which in turn enables us to construct qualitatively meaningful perturbation solutions in relatively few terms. Interestingly, the perturbation solutions do not rely on any small parameters, as an auxiliary parameter is introduced and later taken to unity. The obtained solutions are given recursively, and a method of error analysis is provided to ensure convergence of the solutions. Hence, with appropriate general boundary data, we show that one may construct solutions to a desired accuracy over the finite bounded domain. We show that our solutions agree with the exact solutions in the limit as the thickness of the plate is made arbitrarily small. © 2012 Elsevier Ltd. All rights reserved.

Publication Date

4-1-2012

Publication Title

Intermetallics

Volume

23

Issue

3

Number of Pages

177-181

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.intermet.2011.11.019

Socpus ID

84856961985 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84856961985

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