TY - JOUR
T1 - Locking-free thick-thin rod/beam element based on a von Karman type nonlinear theory in rotated reference frames for large deformation analyses of space-frame structures
AU - Zhu, H. H.
AU - Cai, Y. C.
AU - Paik, J. K.
AU - Atluri, S. N.
PY - 2010
Y1 - 2010
N2 - This paper presents a new shear flexible beam/rod element for large deformation analyses of space-frame structures, comprising of thin or thick beams. The formulations remain uniformly valid for thick or thin beams, without using any numerical expediencies such as selective reduced integrations, etc. A von Karman type nonlinear theory of deformation is employed in the co-rotational reference frame of the present beam element, to account for bending, stretching, torsion and shearing of each element. Transverse shear strains in two independant directions are introduced as additional variables, in order to eliminate the shear locking phenomenon. An assumed displacement approach is used to derive an explicit expression for the (16x16) symmetric tangent stiffness matrix of the beam element in the co-rotational reference frame. Numerical examples demonstrate that the present element is free from shear locking and is suitable for the large deformation analysis of spaced frames with thick/thin members. Significantly, this paper provides a text-book example of an explicit expression for the (16x16) symmetric tangent stiffness matrix of a finitely deforming beam element, which can be employed in very simple analyses of large deformations of space-frames. The present methodologies can be extended to study the very large deformations of plates and shells as well, and can be shown to be theoretically valid for thick or thin plates and shells, without using selective reduced integrations and without the need for stabilizing the attendant zero-energy modes.
AB - This paper presents a new shear flexible beam/rod element for large deformation analyses of space-frame structures, comprising of thin or thick beams. The formulations remain uniformly valid for thick or thin beams, without using any numerical expediencies such as selective reduced integrations, etc. A von Karman type nonlinear theory of deformation is employed in the co-rotational reference frame of the present beam element, to account for bending, stretching, torsion and shearing of each element. Transverse shear strains in two independant directions are introduced as additional variables, in order to eliminate the shear locking phenomenon. An assumed displacement approach is used to derive an explicit expression for the (16x16) symmetric tangent stiffness matrix of the beam element in the co-rotational reference frame. Numerical examples demonstrate that the present element is free from shear locking and is suitable for the large deformation analysis of spaced frames with thick/thin members. Significantly, this paper provides a text-book example of an explicit expression for the (16x16) symmetric tangent stiffness matrix of a finitely deforming beam element, which can be employed in very simple analyses of large deformations of space-frames. The present methodologies can be extended to study the very large deformations of plates and shells as well, and can be shown to be theoretically valid for thick or thin plates and shells, without using selective reduced integrations and without the need for stabilizing the attendant zero-energy modes.
KW - Explicit tangent stiffness
KW - Large deformation
KW - Locking
KW - Space frames
KW - Thick Beam
KW - Thick Rod
KW - Updated Lagrangian formulation
UR - http://www.scopus.com/inward/record.url?scp=77951969671&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:77951969671
VL - 57
SP - 175
EP - 204
JO - CMES - Computer Modeling in Engineering and Sciences
JF - CMES - Computer Modeling in Engineering and Sciences
SN - 1526-1492
IS - 2
ER -