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research-article

CURVATURE DEFINITION IN THE LARGE DISPLACEMENT ANALYSIS OF PLANAR BEAMS

[+] Author and Article Information
Yinhuan Zheng

School of Mechanical and Electronic Engineering, Wuhan University of Technology, Wuhan, Hubei, P.R.China, 430070
zhengyinhuan@whut.edu.cn

Ahmed A. Shabana

Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, Chicago, Illinois 60607
shabana@uic.edu

Dayu Zhang

National Key Laboratory of Aerospace Flight Dynamics, School of Astronautics, Northwestern Polytechnical University, Xi'an 710072, Shaanxi, P.R. China
dyzhang@mail.nwpu.edu.cn

1Corresponding author.

ASME doi:10.1115/1.4037226 History: Received April 03, 2017; Revised June 19, 2017

Abstract

While several curvature expressions have been used in the literature, some of these expressions are not consistent with basic geometry definitions and are not consistent with the fact that the bending and shear deformations are independent. These inconsistencies are attributed to the fact that when low order of interpolation is used for the finite element (FE) position field, non-zero curvature cannot be defined, thereby leaving only the option of using expressions that are inconsistent with differential geometry and basic mechanics principles. This paper uses three different elastic force formulations in order to examine the effect of the curvature definition in the large displacement analysis of beams. In the first elastic force formulation, a general continuum mechanics approach (Method 1) based on nonlinear strain-displacement relationship is used. The second approach (Method 2) is based on a classical nonlinear beam theory, in which a curvature expression consistent with differential geometry and independent of the shear deformation is used. The third elastic force formulation (Method 3) employs a curvature expression obtained from the shear angle. In the literature, one resorted to using this latter inconsistent curvature definition because of the use of low order finite elements in which non-zero curvature cannot be defined within the element.

Copyright (c) 2017 by ASME
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