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Deriving matrix of guiding cosines of calculated section of the rod, taking into account its geometry in space during deformation


Article Information

Title: Deriving matrix of guiding cosines of calculated section of the rod, taking into account its geometry in space during deformation

Authors: Alexander Shein, Olga Zemtsova

Journal: ARPN Journal of Engineering and Applied Sciences

HEC Recognition History
Category From To
Y 2023-07-01 2024-09-30
Y 2022-07-01 2023-06-30
Y 2021-07-01 2022-06-30
X 2020-07-01 2021-06-30

Publisher: Khyber Medical College, Peshawar

Country: Pakistan

Year: 2019

Volume: 14

Issue: 22

Language: English

Categories

Abstract

The movement of the flat section of the rod during the deformation is represented as a set of section's progressive movement with original, local to this section, coordinate system, the spherical movement of section and fixed to this section additional coordinate system related to the total beginning of coordinate systems. The rotational movement is characterized by three rotation corners around the axes of progressively moving coordinate system. The angles of rotation around transverse axes are recorded in the functions of transverse motions. For the equations of equilibrium of internal and external forces of the rod related to the local coordinate system of the rod we should have a matrix of direction cosines with certain angles between the local and the spherically moving coordinate system. The article defines the components of this matrix. Usage of this matrix significantly clarifies the stress-strain state of the rod system [1, 2].


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