TY - JOUR
T1 - Finite element theory for curved and twisted beams based on exact solutions for three-dimensional solids. Part 1
T2 - Beam concept and geometrically exact nonlinear formulation
AU - Petrov, E.
AU - Géradin, M.
N1 - Funding Information:
The first author acknowledges the financial support of the Belgian Office for Scientific, Technical and Cultural Affairs (SSTC) to accomplish this work. The second author acknowledgesa lso the support of SSTC under contract PAI P4/24.
PY - 1998/11/2
Y1 - 1998/11/2
N2 - A geometrically exact and completely consistent finite element theory for curved and twisted beams is proposed. It is based on the kinematical hypothesis generally formulated for large deformation and accounts for all kinds of deformation of a three-dimensional solid: translational and rotational displacements of the cross-sections, warping of their plane and distortion of their contours. The principle of virtual work is applied in a straightforward manner to all non-zero six components of the strain and stress tensors. Expressions are given for tangent matrices of elastic, inertia and external forces and specific techniques for discretization and updating are developed for the analysis of beams in inertial and non-inertial frames. Finally, the numerical properties of the finite element models are demonstrated through examples.
AB - A geometrically exact and completely consistent finite element theory for curved and twisted beams is proposed. It is based on the kinematical hypothesis generally formulated for large deformation and accounts for all kinds of deformation of a three-dimensional solid: translational and rotational displacements of the cross-sections, warping of their plane and distortion of their contours. The principle of virtual work is applied in a straightforward manner to all non-zero six components of the strain and stress tensors. Expressions are given for tangent matrices of elastic, inertia and external forces and specific techniques for discretization and updating are developed for the analysis of beams in inertial and non-inertial frames. Finally, the numerical properties of the finite element models are demonstrated through examples.
UR - http://www.scopus.com/inward/record.url?scp=0038959155&partnerID=8YFLogxK
U2 - 10.1016/S0045-7825(98)00061-9
DO - 10.1016/S0045-7825(98)00061-9
M3 - Article
AN - SCOPUS:0038959155
SN - 0045-7825
VL - 165
SP - 43
EP - 92
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
IS - 1-4
ER -