Timoshenko beam formulation for in-plane behaviour of tapered monosymmetric I-beams: Analytical solution and exact stiffness matrix

2021 ◽  
Vol 162 ◽  
pp. 107604
Author(s):  
S. Naresh Chockalingam ◽  
V. Pandurangan ◽  
M. Nithyadharan
Keyword(s):  
Analytical Solution ◽  
Timoshenko Beam ◽  
Stiffness Matrix ◽  
Exact Stiffness Matrix

An Exact Three-Dimensional Beam Element With Nonuniform Cross Section

2010 ◽  
Vol 77 (6) ◽  
Author(s):  
M. Jafari ◽  
M. J. Mahjoob
Keyword(s):  
Cross Section ◽  
Stiffness Matrix ◽  
Degrees Of Freedom ◽  
Direct Method ◽  
Three Dimensional ◽  
Curved Beams ◽  
Element Analysis ◽  
Shear Loads ◽  
Line Passing ◽  
Exact Stiffness Matrix

In this paper, the exact stiffness matrix of curved beams with nonuniform cross section is derived using direct method. The considered element has two nodes and 12 degrees of freedom, with three forces and three moments applied at each node. The noncoincidence effect of shear center and center of area is also considered in this element. The deformations of the beam are due to bending, torsion, tensile, and shear loads. The line passing through center of area is a general three-dimensional curve and the cross section properties may change arbitrarily along it. The method is extended to deal with distributed loads on the curved beams. The stiffness matrix of some selected types of beams is determined by this method. The results are compared (where possible) with previously published results, simple beam finite element analysis and analytic solution. It is shown that the determined stiffness matrix is exact and that any type of beam can be analyzed by this method.

scholarly journals Comparison of 1D and 2D solutions for a beam under transverse impact

2018 ◽  
Vol 148 ◽  
pp. 05005 ◽  
Author(s):  
Vítězslav Adámek
Keyword(s):  
Analytical Solution ◽  
Timoshenko Beam ◽  
Elastic Beam ◽  
Beam Theory ◽  
Two Dimensional ◽  
Transverse Impact ◽  
Dimensional Theory ◽  
Beam Geometry ◽  
Stationary Vibration ◽  
Main Factors

The problem of non-stationary vibration of an elastic beam caused by a transverse impact loading is studied in this work. In particular, two different approaches to the derivation of analytical solution of the problem are compared. The first one is based on the Timoshenko beam theory, the latter one follows the exact two-dimensional theory. Both mentioned methods are used for finding the response of an infinite homogeneous isotropic beam. The obtained analytical results are then compared and their agreement is discussed in relation to main factors, i.e. the beam geometry, the character of loading and times and points at which the beams responses are studied.

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