Large deflections of point loaded cantilevers with nonlinear behaviour
Document Type
Article
Publication Date
1-1983
Department
Department of Civil, Environmental, and Geospatial Engineering; Department of Mathematical Sciences; Department of Computer Science
Abstract
Thin beams, being flexible, form a curve with large deflections when subjected to sufficiently large transverse loads. Therefore, geometrical nonlinearity occurs, and the problem must be formulated in terms of the nonlinear theory of bending. In this paper, the beam is constructed from nonlinear elastic material, and subjected to several transverse concentrated loads. Due to the large deflection of the beam, the exact expression of the curvature of the deflected shape is used in the Bernoulli-Euler relationship. Therefore, this leads to a second order nonlinear differential equation for the transverse deflection. The solution of this equation is obtained by using the fourth-order Runge-Kutta method, and the arc length is evaluated using Simpson's Rule. The results obtained from this procedure are compared with previously published results for thin beams of linear elastic materials in order to verify the theory and the method of analysis.
Publication Title
ZAMP Zeitschrift für angewandte Mathematik und Physik
Recommended Citation
Monasa, F.,
&
Lewis, G.
(1983).
Large deflections of point loaded cantilevers with nonlinear behaviour.
ZAMP Zeitschrift für angewandte Mathematik und Physik,
34(1), 124-130.
http://doi.org/10.1007/BF00962621
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/4278