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Most of the existing complex beam elements are shown to be special cases of the new formulation.
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The superconvergent property of the beam element is shown by comparing the convergence rate of this beam element to the reduced integrated FSDT beam element formed using the linear shape functions.
The major elements are shown here.
The results of the eigen-analysis show that the curvature-based beam elements are free of locking and are efficient.
First, beam longitudinal and transverse rebars are welded to beam end plates and the remaining rebars in beam elements are installed (Fig. 1a, b).
The mass and stiffness matrices of the beam elements are determined using Timoshenko beam elements including shear deformation and rotatory inertial effects.
The scheme of the beam element formulation is shown in Fig. 11, only one integration point is used for one element to save computational time in explicit analysis.
Furthermore two node beam elements were used to model beams.
The use of beam elements is also not exceptional.
Following sensitivity analysis, the average length of the beam elements was 0.9 mm with a final mesh resulting in 2371 elements, while the average size of shell elements was 0.8 mm for a total of 13004 elements.
The developed finite element method described and validated in above is used to design a deep beam, whose dimensions are shown in Fig. 5.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com