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

Abstract

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.

Keywords

deformacijske količine;konstantne deformacije;nelinearna teorija nosilcev;prostorski nosilci;prostorske rotacije;strain measure;constant strain;non-linear beam theory;three-dimensional beam;three-dimensional rotation;

Data

Language: English
Year of publishing:
Typology: 1.01 - Original Scientific Article
Organization: UL FGG - Faculty of Civil and Geodetic Engineering
Publisher: Elsevier
UDC: 531:624.072.2
COBISS: 5825121 Link will open in a new window
ISSN: 0020-7683
Views: 2304
Downloads: 856
Average score: 0 (0 votes)
Metadata: JSON JSON-RDF JSON-LD TURTLE N-TRIPLES XML RDFA MICRODATA DC-XML DC-RDF RDF

Other data

Secondary language: English
Secondary keywords: deformacijske količine;konstantne deformacije;nelinearna teorija nosilcev;prostorski nosilci;prostorske rotacije;
File type: application/pdf
Type (COBISS): Not categorized
Pages: str. 1802-1817
Volume: ǂLetn. ǂ49
Issue: ǂšt. ǂ13
Chronology: 2012
DOI: 10.1016/j.ijsolstr.2012.03.033
ID: 8312465