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On the dynamic behaviour of the Timoshenko beam finite elements

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Abstract

First, various finite element models of the Timoshenko beam theory for static analysis are reviewed, and a novel derivation of the 4 × 4 stiffness matrix (for the pure bending case) of the superconvergent finite element model for static problems is presented using two alternative approaches: (1) assumed-strain finite element model of the conventional Timoshenko beam theory, and (2) assumed-displacement finite element model of a modified Timoshenko beam theory. Next, dynamic versions of various finite element models are discussed. Numerical results for natural frequencies of simply supported beams are presented to evaluate various Timoshenko beam finite elements. It is found that the reduced integration element predicts the natural frequencies accurately, provided a sufficient number of elements is used.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Texas A & M University, 77843-3123, College Station, TX, USA

    J N Reddy

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  1. J N Reddy
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Correspondence to J N Reddy.

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The research reported herein is supported by theOscar S. Wyatt Endowed Chair.

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Reddy, J.N. On the dynamic behaviour of the Timoshenko beam finite elements. Sadhana 24, 175–198 (1999). https://doi.org/10.1007/BF02745800

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  • DOI: https://doi.org/10.1007/BF02745800

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