VM26

VM26
Large Deflection of a Cantilever

Overview

Reference:

K. J. Bathe, E. N. Dvorkin, "A Formulation of General Shell Elements - The Use of Mixed Interpolation of Tensorial Components", Int. Journal for Numerical Methods in Engineering, Vol. 22 No. 3, 1986, pg. 720.

Analysis Type(s):

Static, Large Deflection Analysis (ANTYPE = 0)

Element Type(s):

4-Node Finite Strain Shell (SHELL181)

8-Node Finite Strain Shell (SHELL281)

Input Listing:

vm26.dat

Test Case

A cantilevered plate of length , width b, and thickness t is fixed at one end and subjected to a pure bending moment M at the free end. Determine the true (large deflection) free-end displacements and rotation, and the top surface stress at the fixed end, using shell elements.

Figure 34: Cantilever Problem Sketch

Material Properties

Geometric Properties

E = 1800 N/mm²

υ = 0.0

= 12 mm

b = 1 mm

t = 1 mm

M = 15.708 N-mm

Analysis Assumptions and Modeling Notes

The large deflection option is chosen (NLGEOM,ON) and shell elements are used to match the reference's assumptions and test case definition. Since the geometry is closer to that of a beam, a shell element is not the usual element type to solve problems of this geometry.

The free-end nodes are coupled in y-rotations so that the bending moment M can be applied to only one end node. The load is applied in two equal increments, using the analysis restart option (solely for validation and demonstration of ANTYPE,,REST).

Results Comparison

		Target [1]	Mechanical APDL	Ratio
SHELL181	UX, node 4 (mm)	-2.90	-2.77	0.95
	UZ, node 4 (mm)	-6.50	-6.71	1.03
	ROTY, node 4 (rad)	1.26	1.26	1.00
	Stress_x , node 1 (N/mm²)	94.25	94.25	1.00
SHELL281	UX, node 4 (mm)	-2.90	-2.91	1.01
	UZ, node 4 (mm)	-6.50	-6.60	1.02
	ROTY, node 4 (rad)	1.26	1.26	1.00
	Stress_x , node 1 (N/mm²)	94.25	94.28	1.00

to accuracy of graphical readout