# OS-V: 0080 Buckling of Shells and Composites with Offset

A test of influence of offset on buckling solution for shells, including composite with offset Z0 and element offset ZOFFS.

## Benchmark Model

Here, you solve several problems to calculate the critical load on different conditions. The model is a simply supported beam of height 1mm, breadth 2mm and length 100mm with one end constrained in all DOFs and an axial load applied on the other end.

The material properties for the beam are:
MAT1
Young's Modulus
1 x 106 N/mm2
Poisson's Ratio
0.0
Density
2 kg/mm3
Thermal Expansion Coefficient
1 x 10-4 ºC-1
300ºC
The different case description of the problem are:
1. Buckling without offset.
2. Buckling with moment equivalent to offset.
3. Buckling with offset created by a frame.
4. Buckling with offset applied through ZOFFS.
5. Buckling of composite with non-symmetrical layup.
6. Buckling of composite with offset.
The theoretical critical buckling load is calculated using the Euler Buckling equation:(1)
${f}_{crit}=\pi \frac{EI}{{\left(KL\right)}^{2}}$
Where,
${f}_{crit}$
Maximum or critical force
$E$
Modulus of elasticity
$I$
Area moment of inertia (second moment of area)
$L$
Unsupported length of the beam
$K$
Column effective length factor (for one end fixed and the other end free, $K$ =2)

## Results

Quantity Theoretical No-offset Normalized
$\lambda$ cr(1) 4.1123 4.1208 0.997937
$\lambda$ cr(2) 16.449 16.513 0.996124
$\lambda$ cr(3) 37.011 37.701 0.981698
$\lambda$ cr(4) 102.81 108.19 0.950273
Quantity Theoretical No-offset + Moment Normalized
$\lambda$ cr(1) 4.1123 4.1208 0.997937
$\lambda$ cr(2) 16.449 16.513 0.996124
$\lambda$ cr(3) 37.011 37.701 0.981698
$\lambda$ cr(4) 102.81 108.19 0.950273
Quantity Theoretical C-Frame Normalized
$\lambda$ cr(1) 4.1123 4.1208 0.997937
$\lambda$ cr(2) 16.449 16.513 0.996124
$\lambda$ cr (3) 37.011 37.700 0.981724
$\lambda$ cr(4) 102.81 108.19 0.950273
Quantity Theoretical ZOFFS Normalized
$\lambda$ cr(1) 4.1123 4.1208 0.997937
$\lambda$ cr(2) 16.449 16.513 0.996124
$\lambda$ cr(3) 37.011 37.700 0.981724
$\lambda$ cr(4) 102.81 108.19 0.950273
Quantity Theoretical Non-symmetric Layup Normalized
$\lambda$ cr(1) 4.1123 4.1203 0.998058
$\lambda$ cr(2) 16.449 16.510 0.996305
$\lambda$ cr(3) 37.011 37.663 0.982689
$\lambda$ cr(4) 102.81 107.89 0.952915
Quantity Theoretical Offset Composite Normalized
$\lambda$ cr(1) 4.1123 4.1203 0.998058
$\lambda$ cr(2) 16.449 16.510 0.996305
$\lambda$ cr(3) 37.011 37.663 0.982689
$\lambda$ cr(4) 102.81 107.89 0.952915

## Model Files

Refer to Access the Model Files to download the required model file(s).

The model files used in this problem include:

s100_buckl.zip
• s100comp_buckl.fem
• s100compmom_buckl.fem
• s100comp_frame_buckl.fem
• s100comp_buckl_zoffs.fem
• s100comp2ply_buckl.fem
• s100compoffs_buckl.fem