# 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.

## Model Files

Before you begin, copy the file(s) used in this problem to your working directory.

## Benchmark Model

Here, you solve several problems to calculate the critical load on different conditions. The model is a simply supported beam of height 1 mm, breadth 2 mm and length 100 mm 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