|
Civil-Comp Proceedings ISSN 1759-3433
CCP: 83 PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY
Edited by: B.H.V. Topping, G. Montero and R. Montenegro
Paper 29 Dynamic Analysis of Three-Dimensional Composite Beam Elements Including Warping and Shear Deformation Effects
E.J. Sapountzakis and V.G. Mokos Institute of Structural Analysis and Aseismic Research, School of Civil Engineering, National Technical University of Athens, Greece
Full Bibliographic Reference for this paper
E.J. Sapountzakis, V.G. Mokos, "Dynamic Analysis of Three-Dimensional Composite Beam Elements Including Warping and Shear Deformation Effects", in B.H.V. Topping, G. Montero, R. Montenegro, (Editors), "Proceedings of the Eighth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 29, 2006. doi:10.4203/ccp.83.29
Keywords: nonuniform torsion, warping, shear deformation, bar, beam, dynamic analysis, boundary element method, stiffness matrix, mass, damping, composite.
Summary
In this paper the dynamic analysis of 3D composite beam elements restrained at
their edges by the most general linear torsional, transverse or longitudinal boundary
conditions and subject to arbitrarily distributed dynamic twisting, bending,
transverse or longitudinal loading is presented.
In order to include the warping behavior in the study of the aforementioned
element in each node at the element ends a seventh degree of freedom is added to
the well known six DOFs of the classical three-dimensional frame element. The
additional DOF is the first derivative of the angle of twist
d d denoting the
rate of change of the angle of twist
, which can be regarded as the
torsional curvature of the cross section.
For the solution of the problem at hand, a boundary element method is developed
for the construction of the
stiffness matrix and the nodal load vector, of a
member of an arbitrarily composite cross section, taking into account both warping
and shear deformation effects, which together with the corresponding mass and
damping matrices lead to the formulation of the equation of motion. The composite
member consists of materials in contact each of which can surround a finite number
of inclusions. To account for shear deformations, the concept of shear deformation
coefficients is used. In this investigation the definition of these factors is
accomplished using a strain energy approach [1], instead of Timoshenko's and
Cowper's definitions, for which several authors have pointed out that one obtains
unsatisfactory results or definitions given by other researchers, for which these
factors take negative values. Eight boundary value problems with respect to the
variable along the bar angle of twist, to the primary warping function, to a fictitious
function, to the beam transverse and longitudinal displacements and to two stress
functions are formulated and solved employing a pure BEM approach [2], that is
only boundary discretization is used. Both free and forced transverse, longitudinal or
torsional vibrations are considered, taking also into account effects of transverse,
longitudinal, rotatory, torsional and warping inertia and damping resistance.
Numerical examples are presented to illustrate the method and demonstrate its
efficiency and accuracy. The influence of the warping effect, especially in composite
members of open form cross section is analyzed through examples demonstrating
the importance of the inclusion of the warping degrees of freedom in the dynamic
analysis of a space frame. Moreover, the discrepancy in the dynamic analysis of a
member of a spatial structure arising from the ignorance of the shear deformation
effect necessitates the inclusion of this additional effect, especially in thick walled
cross section members.
Figure 1:
Prismatic beam of an arbitrarily shaped composite cross section.
|
References
- 1
- V.G. Mokos, E.J. Sapountzakis, "A BEM Solution to Transverse Shear Loading of Composite Beams", Int. J. Solids Structures, 42, 3261-3287, 2005. doi:10.1016/j.ijsolstr.2004.11.005
- 2
- E.J. Sapountzakis, "Torsional Vibrations of Composite Bars by BEM", Composite Structures, 70, 229-239, 2005. doi:10.1016/j.compstruct.2004.08.031
purchase the full-text of this paper (price £20)
go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £140 +P&P)
|