Kinematically exact curved and twisted strain-based beam

Češarek, Peter (author), Saje, Miran (author), Zupan, Dejan (author)

The paper presents a formulation of the geometrically exact three-dimensional beam theory where the shape functions of three-dimensional rotations are obtained from strains by the analytical solution of kinematic equations. In general it is very demanding to obtain rotations from known rotational strains. In the paper we limit our studies to the constant strain field along the element. The relation between the total three-dimensional rotations and the rotational strains is complicated even when a constant strain field is assumed. The analytical solution for the rotation matrix is for constant rotational strains expressed by the matrix exponential. Despite the analyticalrelationship between rotations and rotational strains, the governingequations of the beam are in general too demanding to be solved analytically. A finite-element strain-based formulation is presented in which numerical integration in governing equations and their variations is completely omitted and replaced by analytical integrals. Some interesting connections between quantities and non-linear expressions of the beam are revealed. These relations can also serve as useful guidelines in the development of new finite elements, especially in the choice of suitable shapefunctions.

• Language: English
• Keywords: strain measure, constant strain, non-linear beam theory, three-dimensional beam, three-dimensional rotation
• Typology: 1.01 - Original Scientific Article
• Organization: FGG - Faculty of Civil and Geodetic Engineering
• Publisher: Elsevier
• Year: 2012
• Number of pages: Str. 1802-1817
• Numbering: Letn. 49, št. 13
• PID: 20.500.12556/RUL-32172
• UDC: 531:624.072.2
• ISSN on article: 0020-7683
• DOI: 10.1016/j.ijsolstr.2012.03.033
• COBISS.SI-ID: 5825121
• Publication date in RUL: 10.07.2015

Record is a part of a journal

• Title: International journal of solids and structures
• Shortened title: Int. j. solids struct.
• Publisher: Elsevier
• ISSN: 0020-7683
• COBISS.SI-ID: 997903

Secondary language

• Language: English
• Keywords: deformacijske količine, konstantne deformacije, nelinearna teorija nosilcev, prostorski nosilci, prostorske rotacije