TY - JOUR

T1 - Application of the trefftz method, on the basis of Stroh formalism, to solve the inverse Cauchy problems of anisotropic elasticity in multiply connected domains

AU - Zhang, Tao

AU - Dong, Leiting

AU - Alotaibi, Abdullah

AU - Atluri, Satya N.

N1 - Funding Information:
The first author acknowledges the financial support of the China Scholarship Council (Grant no. 201206020059 ); the National High-tech R&D Program of China (Grant no. 2012AA112201 ); the National Natural Science Foundation of China (Grant no. 10772013 ); the Aeronautical Science Foundation of China (Grant no. 20100251007 ). This work was partially funded by the Deanship of Scientific Research (DSR) , King Abdulaziz University , under grant no. ( 3-130-25-HiCi ). The authors, therefore, acknowledge technical and financial support of KAU.

PY - 2014/6

Y1 - 2014/6

N2 - In this paper, the Trefftz collocation method is applied to solve the inverse Cauchy problem of anisotropic elasticity, wherein both tractions as well as displacements are prescribed at a small part of the boundary of an arbitrary simply/multiply connected anisotropic elastic domain. The Stroh formalism is used to construct the Trefftz basis functions. Negative and positive power series are used together with conformal mapping to approximate the complex potentials of the Stroh formalism. For inverse problems where noise is present in the measured data, Tikhonov regularization is used together with the L-curve parameter selection method, in order to mitigate the inherent ill-posed nature of inverse problems. By several numerical examples, we show that this simple and elegant method can successfully solve inverse problems of anisotropic elasticity, with noisy measurements, in both simply and multiply connected domains.

AB - In this paper, the Trefftz collocation method is applied to solve the inverse Cauchy problem of anisotropic elasticity, wherein both tractions as well as displacements are prescribed at a small part of the boundary of an arbitrary simply/multiply connected anisotropic elastic domain. The Stroh formalism is used to construct the Trefftz basis functions. Negative and positive power series are used together with conformal mapping to approximate the complex potentials of the Stroh formalism. For inverse problems where noise is present in the measured data, Tikhonov regularization is used together with the L-curve parameter selection method, in order to mitigate the inherent ill-posed nature of inverse problems. By several numerical examples, we show that this simple and elegant method can successfully solve inverse problems of anisotropic elasticity, with noisy measurements, in both simply and multiply connected domains.

KW - Anisotropic elasticity

KW - Characteristic length

KW - Ill-posed

KW - Inverse problem

KW - Stroh formalism

UR - http://www.scopus.com/inward/record.url?scp=84899583841&partnerID=8YFLogxK

U2 - 10.1016/j.enganabound.2014.03.012

DO - 10.1016/j.enganabound.2014.03.012

M3 - Article

AN - SCOPUS:84899583841

SN - 0955-7997

VL - 43

SP - 95

EP - 104

JO - Engineering Analysis with Boundary Elements

JF - Engineering Analysis with Boundary Elements

ER -