Derivation of an efficient non-prismatic thin curved beam element using basic displacement functions

Article type: Research Article

Authors: Shahba, Ahmad^; | Attarnejad, Reza^; | Eslaminia, Mehran

Affiliations: School of Civil Engineering, University College of Engineering, University of Tehran, Tehran, Iran | Centre of Numerical Methods in Engineering, University of Tehran, Iran | Department of Civil, Construction and Environmental Engineering, North Carolina State University, Raleigh, NC, USA

Note: [] Corresponding author. Tel.: +98 2161112225; Fax: +98 2166403808; E-mail: shahba@ut.ac.ir; ah.shahba@gmail.com

Abstract: The efficiency and accuracy of the elements proposed by the Finite Element Method (FEM) considerably depend on the interpolating functions, namely shape functions, used to formulate the displacement field within an element. In this paper, a new insight is proposed for derivation of elements from a mechanical point of view. Special functions namely Basic Displacement Functions (BDFs) are introduced which hold pure structural foundations. Following basic principles of structural mechanics, it is shown that exact shape functions for non-prismatic thin curved beams could be derived in terms of BDFs. Performing a limiting study, it is observed that the new curved beam element successfully becomes the straight Euler-Bernoulli beam element. Carrying out numerical examples, it is shown that the element provides exact static deformations. Finally efficiency of the method in free vibration analysis is verified through several examples. The results are in good agreement with those in the literature.

Keywords: Basic displacement functions, structural mechanics, shape functions, non-prismatic curved beam, static analysis, free vibration

DOI: 10.3233/SAV-2011-0623

Journal: Shock and Vibration, vol. 19, no. 2, pp. 183-200, 2012