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Civil-Comp Proceedings
ISSN 1759-3433 CCP: 81
PROCEEDINGS OF THE TENTH INTERNATIONAL CONFERENCE ON CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING COMPUTING Edited by: B.H.V. Topping
Paper 98
Transport Matrix Based Dynamic Stiffness Matrix of a Circular Helicoidal Bar S.A. Alghamdi
Department of Civil Engineering, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia Full Bibliographic Reference for this paper
S.A. Alghamdi, "Transport Matrix Based Dynamic Stiffness Matrix of a Circular Helicoidal Bar", in B.H.V. Topping, (Editor), "Proceedings of the Tenth International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 98, 2005. doi:10.4203/ccp.81.98
Keywords: dynamic stiffness matrix, helicoidal beams, transport matrix formulation, structural analysis.
Summary
Starting from the solution of differential equations governing stress and
deformation states using the transport (transfer) matrix method, this paper outlines
matrix formulations used to numerically construct the dynamic structural stiffness
matrix for a circular helicoidal beam within the framework of linear elasticity [1].
Specifically the paper emphasizes the main features of a Fortran computer code
developed for this purpose and compares it to the general finite element method [2].
With reference to a helicoidal bar [1] with helix angle
in which a state sub-vector ![]() ![]() ![]()
The governing scaled differential matrix equation for a helicoid differential
segment of mass
and the Cayley-Hamilton Theorem [3,5] is used to write the solution of the equation in terms of powers of a (12x12) matrix ![]() from which the (12x1) scaled transport load vector ![]() The above condensed matrix form is identified as the stiffness matrix equation for a helicoid beam segment. The two sub-vectors of the column vector on the right hand-side of equation (10) represent stiffness load vectors ![]() ![]() ![]()
The computer code in its present form has been designed to construct and solve
the scaled matrix equations (10) for a stand-alone helicoidal beam instead of using
less specialized isoparametric finite elements [2]. It requires only few parameters to
define the geometry and material characteristics of the beam. The structural
geometry is defined by radius R, helix angle
References
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