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Kinematically exact curved and twisted strain-based beam
ID
Češarek, Peter
(
Author
),
ID
Saje, Miran
(
Author
),
ID
Zupan, Dejan
(
Author
)
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MD5: 3FBF7E91905C13F66082586F8C84BDC3
PID:
20.500.12556/rul/37fab994-733d-4478-bb14-14522b4b670c
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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.
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
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3403
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Record is a part of a journal
Title:
International journal of solids and structures
Shortened title:
Int. j. solids struct.
Publisher:
Pergamon Press
ISSN:
0020-7683
COBISS.SI-ID:
997903
Secondary language
Language:
English
Keywords:
deformacijske količine
,
konstantne deformacije
,
nelinearna teorija nosilcev
,
prostorski nosilci
,
prostorske rotacije
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