Title: Non-prismatic Beams: a Simple and Effective Timoshenko-like Model
Language: English
Authors: Balduzzi, Giuseppe
Aminbaghai, Mehdi
Sacco, Elio
Füssl, Josef
Eberhardsteiner, Josef 
Auricchio, Ferdinando
Category: Research Article
Keywords: Non-prismatic Timoshenko beam; beam modeling; analytical solution; tapered beam; arches
Issue Date: 2016
Journal: International Journal of Solids and Structures
The present paper discusses simple compatibility, equilibrium, and constitutive equations for a non-prismatic planar beam. Specifically, the proposed model is based on standard Timoshenko kinematics (i.e., planar cross-section remain planar in consequence of a deformation, but can rotate with respect to the beam centerline). An initial discussion of a 2D elastic problem highlights that the boundary equilibrium deeply influences the cross-section stress distribution and all unknown fields are represented with respect to global Cartesian coordinates. A simple beam model (i.e. a set of Ordinary Differential Equations (ODEs)) is derived, describing accurately the effects of non-prismatic geometry on the beam behavior and motivating equation’s terms with both physical and mathematical arguments. Finally, several analytical and numerical solutions are compared with results existing in literature. The main conclusions can be summarized as follows. (i) The stress distribution within the cross-section is not trivial as in prismatic beams, in particular the shear stress distribution depends on all generalized stresses and on the beam geometry. (ii) The derivation of simplified constitutive relations highlights a strong dependence of each generalized deformation on all the generalized stresses. (iii) Axial and shear-bending problems are strictly coupled. (iv) The beam model is naturally expressed as an explicit system of six first order ODEs. (v) The ODEs solution can be obtained through the iterative integration of the right hand side term of each equation. (vi) The proposed simple model predicts the real behavior of non-prismatic beams with a good accuracy, reasonable for the most of practical applications.
DOI: 10.1016/j.ijsolstr.2016.02.017
Library ID: AC15065601
URN: urn:nbn:at:at-ubtuw:3-3584
ISSN: 0020-7683
Organisation: E202 - Institut für Mechanik der Werkstoffe und Strukturen 
Publication Type: Article
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