A hierarchic high-order Timoshenko beam finite element. (March 2016)

• Record Type: Journal Article
• Authors: Tai, C.-Y.; Chan, Y.J.
• Is Part Of: Computers & structures. Volume 165(2016)
• Page Start: 48
• Page End: 58
• Publication Date: 2016-03
• Subjects: Timoshenko beam -- p-Version finite element method; Structural engineering -- Data processing -- Periodicals; Electronic data processing -- Structures, Theory of -- Periodicals; 624.171
• DOI: 10.1016/j.compstruc.2015.12.002
• Languages: English
• ISSNs: 0045-7949

Abstract

Highlights: The super-convergent Timoshenko beam element is improved with hierarchic high-order shape functions. Fractional error of the 2nd cantilever beam natural frequency with the p -version model is 1% of the h -version counterpart. Error in estimating natural frequency split in rotors is also reduced. The proposed element is successfully applied to estimate natural frequencies in experiments. Abstract: Timoshenko beam theory (TBT) is suitable for vibration studies as it describes beams with small models. The super-convergent Timoshenko beam element is improved by adding hierarchic high-order shape functions using Legendre polynomials, and correction terms were added where necessary. The proposed element is validated in static, dynamic and rotordynamic analyses. With the same model size, the fractional error of the 2nd cantilever beam natural frequency with the p -version beam element is 1/100th of the h -version counterpart, and error in estimating natural frequency split in rotors is reduced. The proposed element is also applied to estimate natural frequencies in experiments.