Nonlinear Analysis of Cantilever

[ Problem Description ] [ Finite Element Analyses ] [ Input File ]

PROBLEM DESCRIPTION

A cantilever beam with rectangular cross section is subjected to a concentrated load at the tip of the cantilever.

Figure 1 : Cantilever Beam and Point End Load

The length of the cantilever L is 10 in, width is 1 in and thickness is 1 in.

The initial load in z direction is P = -300 lbf.

FINITE ELEMENT ANALYSES

Again two cases are studied. Four through-thickness integration points are used in both cases.

Case 1 : In the first case, the material is a Bi-Linear stress-strain curve with isotropic hardening. The Young`s modulus is E = 2.9E+7 psi, Possion ratio is 0.2, Et = 0.1 E and the yield stress is 36 ksi. The load steps are illustrated in Figure 1, and the results for the hysteresis loop is given in Figure 2.

Figure 1 : Load Steps for Cantilever Subjected to a Tip Load

Figure 2: Hysteresis Loop of a Cantilever beam under Tip Load

Case 2 : In the second case, the material model is a Ramberg-Osgood stress-strain curve with isotropic hardening. The young's modulus is E = 2.9E+7 psi, Possion ratio is 0.2, the Ramberg-Osgood coefficient is alpha = 3/7, the strain hardening exponent is n = 6. The yield stress is 36 ksi.

The load steps are illustrated in Figure 3, and the results for the hysteresis loop are given in Figure 4.

Figure 3 : Load Steps for Cantilever Subjected to Tip Load

Figure 4 : Hysteresis Loop of a Cantilever beam under Tip Load

INPUT FILE

Developed in April 1996 by Xiaoguang Chen and Mark Austin
Last Modified April 17, 1996
Copyright © 1996, Xiaoguang Chen and Mark Austin, Department of Civil Engineering, University of Maryland