NL5: Straight cantilever with end moment

This problem provides evidence that Abaqus can reproduce the result from the benchmark defined by NAFEMS and cited as the reference solution.

The following topics are discussed:

Elements tested
Problem description
Reference solution
Results and discussion
Input files

ProductsAbaqus/Standard

Elements tested

B22

Problem description

Material:

Linear elastic, Young's modulus = 210 GPa, Poisson's ratio = 0.0.

Boundary conditions:

$u_{x} = u_{y} = ϕ_{z}$ = 0 at point B.

Loading:

A concentrated moment at point A applied in increments up to a maximum value of

\frac{M L}{2 π E I} = 1.0, where I = \frac{1}{12} t d {}^{3}.

Reference solution

This is a test recommended by the National Agency for Finite Element Methods and Standards (U.K.): Test NL5 from NAFEMS Publication NNB, Rev. 1, “NAFEMS Non-Linear Benchmarks,” October 1989.

$\frac{M L}{2 π E I}$	Deformation at A
$\frac{M L}{2 π E I}$	$\frac{u_{x}}{L}$	$\frac{u_{y}}{L}$	$\frac{ϕ_{z}}{2 π}$
0.5	1.000	0.637	0.500
1.0	1.000	0.000	1.000

Results and discussion

The results are shown in the following table. The values enclosed in parentheses are percentage differences with respect to the reference solution.

$\frac{M L}{2 π E I}$	Deformation at A
$\frac{M L}{2 π E I}$	$\frac{u_{x}}{L}$	$\frac{u_{y}}{L}$	$\frac{ϕ_{z}}{2 π}$
0.5	1.000 (0.0%)	0.637 (0.0%)	0.500 (0.0%)
1.0	1.000 (0.0%)	2.0 × 10⁻⁷	1.000 (0.0%)

Input files

nnl5x22x.inp: B22 elements.