Kinematically exact curved and twisted strain-based beam

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

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.

• Jezik: Angleški jezik
• Ključne besede: strain measure, constant strain, non-linear beam theory, three-dimensional beam, three-dimensional rotation
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FGG - Fakulteta za gradbeništvo in geodezijo
• Založnik: Elsevier
• Leto izida: 2012
• Št. strani: Str. 1802-1817
• Številčenje: Letn. 49, št. 13
• PID: 20.500.12556/RUL-32172
• UDK: 531:624.072.2
• ISSN pri članku: 0020-7683
• DOI: 10.1016/j.ijsolstr.2012.03.033
• COBISS.SI-ID: 5825121
• Datum objave v RUL: 10.07.2015

Gradivo je del revije

• Naslov: International journal of solids and structures
• Skrajšan naslov: Int. j. solids struct.
• Založnik: Pergamon Press
• ISSN: 0020-7683
• COBISS.SI-ID: 997903

Sekundarni jezik

• Jezik: Angleški jezik
• Ključne besede: deformacijske količine, konstantne deformacije, nelinearna teorija nosilcev, prostorski nosilci, prostorske rotacije