Expression of strain tensor in orthogonal curvilinear coordinates

• Main Authors: Xuyan Liu, Yingfeng Ji, Quanqiang Liang
• Format: Article
• Language: English
• Published: KeAi Communications Co., Ltd. 2010-01-01
• Series: Geodesy and Geodynamics
• Subjects: Orthogonal Curvilinear Coordinates (OCC); Cartesian coordinates; strain tensor; transformation matrix; universal expression
• Online Access: http://www.sciencedirect.com/science/article/pii/S1674984715302160

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.