TY - JOUR

T1 - A Trefftz collocation method (TCM) for three-dimensional linear elasticity by using the Papkovich-Neuber solutions with cylindrical harmonics

AU - Wang, Guannan

AU - Dong, Leiting

AU - Atluri, Satya N.

PY - 2018/3

Y1 - 2018/3

N2 - A Trefftz collocation method (TCM) is proposed for solving three-dimensional (3D) linear-elastic boundary value problems. By using the Papkovich-Neuber (P-N) general solutions, Trefftz trial functions are expressed in terms of cylindrical harmonics. Both non-singular and singular harmonic functions are included, facilitating the study of interior and exterior problems. To mitigate the problem of ill-conditioned functions, two steps are adopted: the first step is to introduce a characteristic length of the domains of interests into the Laplace equation, and the second step is to scale each column of the coefficient matrix in the established system of linear equations using another multi-scale characteristic length, letting each column have the equal norms. Several examples are presented to validate the proposed 3D Trefftz collocation method. The completeness of the trial functions, the effect of the scaling techniques, and the accuracy of solutions are also discussed.

AB - A Trefftz collocation method (TCM) is proposed for solving three-dimensional (3D) linear-elastic boundary value problems. By using the Papkovich-Neuber (P-N) general solutions, Trefftz trial functions are expressed in terms of cylindrical harmonics. Both non-singular and singular harmonic functions are included, facilitating the study of interior and exterior problems. To mitigate the problem of ill-conditioned functions, two steps are adopted: the first step is to introduce a characteristic length of the domains of interests into the Laplace equation, and the second step is to scale each column of the coefficient matrix in the established system of linear equations using another multi-scale characteristic length, letting each column have the equal norms. Several examples are presented to validate the proposed 3D Trefftz collocation method. The completeness of the trial functions, the effect of the scaling techniques, and the accuracy of solutions are also discussed.

KW - 3D elasticity

KW - Cylindrical harmonics

KW - Ill-conditioning

KW - Papkovich-Neuber solution

KW - Scaling technique

KW - Trefftz method

UR - http://www.scopus.com/inward/record.url?scp=85040091597&partnerID=8YFLogxK

U2 - 10.1016/j.enganabound.2017.12.009

DO - 10.1016/j.enganabound.2017.12.009

M3 - Article

AN - SCOPUS:85040091597

VL - 88

SP - 93

EP - 103

JO - Engineering Analysis with Boundary Elements

JF - Engineering Analysis with Boundary Elements

SN - 0955-7997

ER -