A fast multiple-scale polynomial solution for the inverse Cauchy problem of elasticity in an arbitrary plane domain. (August 2016)

• Record Type: Journal Article
• Authors: Liu, Chein-Shan
• Is Part Of: Computers & mathematics with applications. Volume 72:issue 4(2016)
• Page Start: 1205
• Page End: 1224
• Publication Date: 2016-08
• Subjects: Linear elasticity -- Pascal polynomial triangle -- Inverse Cauchy problems -- Underspecified Cauchy problem -- Multiple-scale Pascal polynomial method; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2016.06.044
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: The polynomial expansion method together with the collocation technique is a cheap yet simple method to solve the Navier equations of elasticity, which is easily arranged to satisfy the governing equations and boundary conditions pointwise. In this paper we propose a novel numerical algorithm for the solution of an overspecified/underspecified Cauchy problem of linear elasticity in an arbitrary plane domain, by using the multiple-scale Pascal polynomial expansion method (MSPEM), of which the scales are determined a priori by the collocation points, according to the idea of equilibrated matrix. In the numerical tests of a direct problem as well as the overspecified/underspecified Cauchy problems, the MSPEM is very accurate and stable against large relative noise up to 20 % for the unknown displacements recovery problem, and up to 100 % absolute noise for the recovery of unknown loading force. The present method is convergent very fast for most cases within 100 iteration steps.