Year: 2020
Author: Andi Makarim Katili, Irwan Katili
Advances in Applied Mathematics and Mechanics, Vol. 12 (2020), Iss. 6 : pp. 1565–1586
Abstract
This paper presents a new concept called Unified and Integrated Method for a shear deformable beam element. In this method, Timoshenko beam theory is unified and integrated in such a way that takes into account the effect of transverse shear and maintains the shear locking free condition at the same time to generate proper behavior in the analysis of thin to thick beams. The unified and integrated method is applied to finite element analysis (FEA) and isogeometric analysis (IGA) on two-node beam element. This method will be used to analyze uniformly loaded beams with various boundary conditions. A shear influence factor of $\phi$, which is a function of beam thickness ratio $(L/h)$, is expressed explicitly as control of the transverse shear strain effect. The analysis gives interesting results showing that applying the unified and integrated method in FEA and IGA will yield exact values of DOF's and displacement function even when using only a single element. Numerical examples demonstrate the validity and efficiency of the unified and integrated methods.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2018-0255
Advances in Applied Mathematics and Mechanics, Vol. 12 (2020), Iss. 6 : pp. 1565–1586
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Finite element analysis isogeometric analysis unified and integrated method timoshenko beam theory.