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Ritz analysis of discontinuous beams using local trigonometric functions

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Abstract

The objective of the current paper is to present a Ritz-type analytical model for predicting the behavior of discontinuous beams such as thin-walled beams with cracks and multiply-stepped beams. The beam is discretized in the cracked as well as the un-cracked domains for a cracked thin-walled beam and in uniform beams for a multiple-stepped beam. A set of local trigonometric trial functions is used to define the twist angle for the cracked domain and the un-cracked domains, as well as to define the displacement field for uniform domains. A global equation system of unknown Ritz coefficients is derived by minimizing the Lagrangian functional or the total potential energy. In the present Ritz model, the interface continuity conditions between sub-domains are investigated and enforced into the global equation system using the condensation procedure or the Lagrange multipliers. Examples are presented to illustrate the effectiveness of the current model for free vibration and torsional analysis. Results obtained from the current model are found to agree well with those obtained using a detailed finite element method or with existing results in literature. The proposed model offers an efficient approach to reduce the modeling efforts and computational time required to analyze complex beams with cracks or multiple steps.

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Author notes

  1. Thi D. Dang

    Present address: School of Mechanical Engineering, Hanoi University of Science and Technology, Hanoi, Vietnam

Authors and Affiliations

  1. Department of Aerospace and Ocean Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA, 24061-0203, USA

    Thi D. Dang, Rakesh K. Kapania & Mayuresh J. Patil

Authors
  1. Thi D. Dang
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  2. Rakesh K. Kapania
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  3. Mayuresh J. Patil
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Correspondence to Thi D. Dang.

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Dang, T.D., Kapania, R.K. & Patil, M.J. Ritz analysis of discontinuous beams using local trigonometric functions. Comput Mech 47, 235–250 (2011). https://doi.org/10.1007/s00466-010-0540-y

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  • DOI: https://doi.org/10.1007/s00466-010-0540-y

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