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
Reference Temperature for Thermal Loading: 300ºC

The different case description of the problem are:

Buckling without offset.
Buckling with moment equivalent to offset.
Buckling with offset created by a frame.
Buckling with offset applied through ZOFFS.
Buckling of composite with non-symmetrical layup.
Buckling of composite with offset.

The theoretical critical buckling load is calculated using the Euler Buckling equation:(1)

f_{c r i t} = π \frac{E I}{{(K L)}^{2}}

Where,

$f_{c r i t}$: 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
$λ$ _cr⁽¹⁾	4.1123	4.1208	0.997937
$λ$ _cr⁽²⁾	16.449	16.513	0.996124
$λ$ _cr⁽³⁾	37.011	37.701	0.981698
$λ$ _cr⁽⁴⁾	102.81	108.19	0.950273

Quantity	Theoretical	No-offset + Moment	Normalized
$λ$ _cr⁽¹⁾	4.1123	4.1208	0.997937
$λ$ _cr⁽²⁾	16.449	16.513	0.996124
$λ$ _cr⁽³⁾	37.011	37.701	0.981698
$λ$ _cr⁽⁴⁾	102.81	108.19	0.950273

Quantity	Theoretical	C-Frame	Normalized
$λ$ _cr⁽¹⁾	4.1123	4.1208	0.997937
$λ$ _cr⁽²⁾	16.449	16.513	0.996124
$λ$ _cr⁽³⁾	37.011	37.700	0.981724
$λ$ _cr⁽⁴⁾	102.81	108.19	0.950273

Quantity	Theoretical	ZOFFS	Normalized
$λ$ _cr⁽¹⁾	4.1123	4.1208	0.997937
$λ$ _cr⁽²⁾	16.449	16.513	0.996124
$λ$ _cr⁽³⁾	37.011	37.700	0.981724
$λ$ _cr⁽⁴⁾	102.81	108.19	0.950273

Quantity	Theoretical	Non-symmetric Layup	Normalized
$λ$ _cr⁽¹⁾	4.1123	4.1203	0.998058
$λ$ _cr⁽²⁾	16.449	16.510	0.996305
$λ$ _cr⁽³⁾	37.011	37.663	0.982689
$λ$ _cr⁽⁴⁾	102.81	107.89	0.952915

Quantity	Theoretical	Offset Composite	Normalized
$λ$ _cr⁽¹⁾	4.1123	4.1203	0.998058
$λ$ _cr⁽²⁾	16.449	16.510	0.996305
$λ$ _cr⁽³⁾	37.011	37.663	0.982689
$λ$ _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