Expression of strain tensor in orthogonal curvilinear coordinates

被引：1

作者：

Liu, Xuyan ^{[1
]}

Ji, Yingfeng ^{[1
]}

Liang, Quanqiang ^{[2
]}

机构：

[1] Earthquake Adm Fujian, Fuzhou 350003, Fujian, Peoples R China

[2] Xiamen Res Ctr Earthquake Survey, Xiamen 361021, Peoples R China

来源：

GEODESY AND GEODYNAMICS | 2010年 / 1卷 / 01期

关键词：

Orthogonal Curvilinear Coordinates (OCC); Cartesian coordinates; strain tensor; transformation matrix; universal expression;

D O I：

10.3724/SP.J.1246.2010.00048

中图分类号：

P3 [地球物理学]; P59 [地球化学];

学科分类号：

0708 ; 070902 ;

摘要：

Based on an analysis of connotation and extension of the concept of the orthogonal curvilinear coordinates, we have deduced a platform of strain tensor expression of Cartesian coordinates, which turns out to be a function of Lame coefficient and unit vector. By using transform matrix between Cartesian coordinates and orthogonal curvilinear coordinates, we have deduced a mathematical expression for correcting displacement vector differential in orthogonal curvilinear coordinates, and given a general expression of strain tensor in orthogonal curvilinear coordinates.

引用

页码：48 / 56

页数：9

共 50 条

[31] Use of Curvilinear Orthogonal Coordinates for Potential Fields Computation.
Grach, I.M.
Izvestiya Vysshikh Uchebnykh Zavedenij i Energeticheskikh Ob''edinenij Sng. Energetika, 1980, (01): : 21 - 27
[32] A New and Fast Coupled Method in Hybrid Orthogonal Curvilinear Coordinates
Gao, Shanguo
Liu, Jiyuan
Lyu, Yaohui
Song, Jun
Lu, Minghua
OCEANS 2017 - ABERDEEN, 2017,
[33] A SIMPLE NOTATION FOR DIFFERENTIAL VECTOR EXPRESSIONS IN ORTHOGONAL CURVILINEAR COORDINATES
BOLTON, EW
GEOPHYSICAL JOURNAL INTERNATIONAL, 1993, 115 (03) : 654 - 666
[34] ANOTHER LOOK AT ORTHOGONAL CURVILINEAR COORDINATES IN KINEMATIC AND DYNAMIC ANALYSES
LIU, CQ
HUSTON, RL
JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME, 1992, 59 (04): : 1033 - 1035
[35] From Ramond fermions to Lame equations for orthogonal curvilinear coordinates
Manas, M
Alonso, LM
PHYSICS LETTERS B, 1998, 436 (3-4) : 316 - 322
[36] Second strain gradient theory in orthogonal curvilinear coordinates: Prediction of the relaxation of a solid nanosphere and embedded spherical nanocavity
Ojaghnezhad, Farzaneh
Shodja, Hossein M.
APPLIED MATHEMATICAL MODELLING, 2019, 76 : 669 - 698
[37] Hamiltonian for a particle in a magnetic field on a curved surface in orthogonal curvilinear coordinates
Shikakhwa, M. S.
Chair, N.
PHYSICS LETTERS A, 2016, 380 (36) : 2876 - 2880
[38] NUMERICAL-CALCULATION OF VARIABLE PROPERTY FLOWS IN CURVILINEAR ORTHOGONAL COORDINATES
HUMPHREY, JAC
CANADIAN JOURNAL OF CHEMICAL ENGINEERING, 1978, 56 (05): : 624 - 626
[39] Calculation of flow pattern in rivers by the orthogonal curvilinear coordinates and 'condensation' technique
Cheng, Wenhui
Wang, Chuanhai
Shuili xuebao, 1988, (06): : 18 - 25
[40] SOLUTION OF THE PROBLEMS ON BENDING OF COMPLEX SHAPE PLATES IN ORTHOGONAL CURVILINEAR COORDINATES
GRIGORENKO, YM
TIMONIN, AM
DOPOVIDI AKADEMII NAUK UKRAINSKOI RSR SERIYA A-FIZIKO-MATEMATICHNI TA TECHNICHNI NAUKI, 1987, (02): : 50 - 52

← 1 2 3 4 5 →