TY - JOUR
T1 - Two-dimensional displacement discontinuity method for transversely isotropic materials
AU - Shen, Baotang
AU - Shi, Jingyu
AU - Rinne, Mikael
AU - Siren, Topias
AU - Suikkanen, Johannes
AU - Kwon, Saeha
AU - Min, Ki Bok
PY - 2016/3/1
Y1 - 2016/3/1
N2 - This paper presents the fundamental solution for a two-dimensional displacement discontinuity method (DDM) for transversely isotropic elastic materials. We follow the procedures shown in the literature, in which there are some typographic errors and a lack of proper explanations for some expressions. Based on the fundamental solution of deformation due to a single point force in transversely isotropic materials, the formulation for deformation from force dipoles has been revisited. Generalised Hooke's Law is used to establish the relationship between dipole strengths and displacement discontinuities, which leads to the fundamental formulation of DDM for transversely isotropic materials. We present the full details of derivation and corrections to some expressions which have previously been presented with errors. In addition, we present the fundamental solution expressions for DDM for one situation which was not included in the literature. The fundamental solutions are implemented in an existing DDM code, FRACOD, and the method is verified by some examples with an analytic solution and finite element method. Furthermore an engineering application is simulated with the scheme.
AB - This paper presents the fundamental solution for a two-dimensional displacement discontinuity method (DDM) for transversely isotropic elastic materials. We follow the procedures shown in the literature, in which there are some typographic errors and a lack of proper explanations for some expressions. Based on the fundamental solution of deformation due to a single point force in transversely isotropic materials, the formulation for deformation from force dipoles has been revisited. Generalised Hooke's Law is used to establish the relationship between dipole strengths and displacement discontinuities, which leads to the fundamental formulation of DDM for transversely isotropic materials. We present the full details of derivation and corrections to some expressions which have previously been presented with errors. In addition, we present the fundamental solution expressions for DDM for one situation which was not included in the literature. The fundamental solutions are implemented in an existing DDM code, FRACOD, and the method is verified by some examples with an analytic solution and finite element method. Furthermore an engineering application is simulated with the scheme.
KW - DDM
KW - Force dipole
KW - Rock engineering
KW - Transversely isotropic
UR - http://www.scopus.com/inward/record.url?scp=84955265708&partnerID=8YFLogxK
U2 - 10.1016/j.ijrmms.2016.01.012
DO - 10.1016/j.ijrmms.2016.01.012
M3 - Article
AN - SCOPUS:84955265708
SN - 1365-1609
VL - 83
SP - 218
EP - 230
JO - International Journal of Rock Mechanics and Mining Sciences
JF - International Journal of Rock Mechanics and Mining Sciences
ER -