TY - JOUR
T1 - Dynamic analysis of finitely stretched and rotated three-dimensional space-curved beams
AU - Iura, M.
AU - Atluri, S. N.
N1 - Funding Information:
Acknowledgements-The work describedh erein has been pendent pressure loads in nonlinear* finite element 5. K. Schweizerhofa nd E. Ramm. Disolacementd e- supportedb y AFOSR under contract F49620-87-C-0064. analysis.C omput. Struct. 18, 1099-l1 14( 1984). The encouragemenotf Dr. A. K. Amos is sincerelya ppre-J. H. Argyris,P . C. Dunnea ndD. W. Scharpf,O n large 6, ciated.M s. Cindi Andersoni s thankedf or her assistancien displacement-smasllt rain analysis of stucturesw ith the preparationo f this paper. rotational degreeso f freedom.C omput. Meth. Appl. Mech. Engng 14, 401-451 (1978).
PY - 1988
Y1 - 1988
N2 - The problem of transient dynamics of highly flexible three-dimensional space-curved beams, undergoing large rotations and stretches, is treated. The case of conservative force loading, which may also lead to configuration-dependent moments on the beam, is considered. Using the three parameters associated with a conformal rotation vector representation of finite rotations, a well-defined Hamilton functional is established for the flexible beam undergoing finite rotations and stretches. This is shown to lead to a symmetric tangent stiffness matrix at all times. In the present total Langrangian description of motion, the mass-matrix of a finite element depends linearly on the linear accelerations, but nonlinearly on the rotation parameters and attendant accelerations; the stiffness matrix depends nonlinearly on the deformation; and an 'apparent' damping matrix depends nonlinearly on the rotations and attendant velocities. A Newmark time-integration scheme is used to integrate the semi-discrete finite element equations in time. Several examples of transient dynamic response of highly flexible beam-like structures, including those in free flight, are presented to illustrate the validity of the theoretical methodology developed in this paper.
AB - The problem of transient dynamics of highly flexible three-dimensional space-curved beams, undergoing large rotations and stretches, is treated. The case of conservative force loading, which may also lead to configuration-dependent moments on the beam, is considered. Using the three parameters associated with a conformal rotation vector representation of finite rotations, a well-defined Hamilton functional is established for the flexible beam undergoing finite rotations and stretches. This is shown to lead to a symmetric tangent stiffness matrix at all times. In the present total Langrangian description of motion, the mass-matrix of a finite element depends linearly on the linear accelerations, but nonlinearly on the rotation parameters and attendant accelerations; the stiffness matrix depends nonlinearly on the deformation; and an 'apparent' damping matrix depends nonlinearly on the rotations and attendant velocities. A Newmark time-integration scheme is used to integrate the semi-discrete finite element equations in time. Several examples of transient dynamic response of highly flexible beam-like structures, including those in free flight, are presented to illustrate the validity of the theoretical methodology developed in this paper.
UR - http://www.scopus.com/inward/record.url?scp=0023851144&partnerID=8YFLogxK
U2 - 10.1016/0045-7949(88)90355-0
DO - 10.1016/0045-7949(88)90355-0
M3 - Article
AN - SCOPUS:0023851144
VL - 29
SP - 875
EP - 889
JO - Computers and Structures
JF - Computers and Structures
SN - 0045-7949
IS - 5
ER -