Analysis1

### MESH:

Entity | Size
--- | ---
Nodes | 522
Elements | 1540

### ELEMENT TYPE:

Connectivity | Statistics
--- | ---
TE4 | 1540 ( 100.00% )

### ELEMENT QUALITY:

Criterion | Good | Poor | Bad | Worst | Average
--- | --- | --- | --- | --- | ---
Stretch | 1540 ( 100.00% ) | 0 ( 0.00% ) | 0 ( 0.00% ) | 0.324 | 0.579
Aspect Ratio | 1286 ( 83.51% ) | 253 ( 16.43% ) | 1 ( 0.06% ) | 5.029 | 2.108

### Materials.1

Material | Iron
Young's modulus | 2.11e+011N_m2
Poisson's ratio | 0.291
Density | 7870kg_m3
Coefficient of thermal expansion | 1.21e-005_Kdeg
Yield strength | 3.1e+008N_m2

# Buckling Case

### Boundary Conditions

Figure 1

See also solutions:

Static Case Solution.1

### STRUCTURE Computation

Number of nodes | : | 522 |
Number of elements | : | 1540 |
Number of D.O.F. | : | 1566 |
Number of Contact relations | : | 0 |
Number of Kinematic relations | : | 0 |

Linear tetrahedron | : | 1540 |

### RESTRAINT Computation

Name: Restraints.1

Number of S.P.C : 81

### LOAD Computation

Name: Loads.1

Applied load resultant :

Fx | = | 0 | . | 000e+000 | N
Fy | = | 0 | . | 000e+000 | N
Fz | = | 0 | . | 000e+000 | N
Mx | = | 0 | . | 000e+000 | Nxm
My | = | 0 | . | 000e+000 | Nxm
Mz | = | 0 | . | 000e+000 | Nxm

### STIFFNESS Computation

Number of lines | : | 1566 |  |
Number of coefficients | : | 25578 |  |
Number of blocks | : | 1 |  |
Maximum number of coefficients per bloc | : | 25578 |  |
Total matrix size | : | 0 | . | 30 | Mb

### SINGULARITY Computation

Restraint: Restraints.1

Number of local singularities | : | 0 |
Number of singularities in translation | : | 0 |
Number of singularities in rotation | : | 0 |
Generated constraint type | : | MPC |

### CONSTRAINT Computation

Restraint: Restraints.1

Number of constraints | : | 81 |
Number of coefficients | : | 0 |
Number of factorized constraints | : | 81 |
Number of coefficients | : | 0 |
Number of deferred constraints | : | 0 |

### FACTORIZED Computation

Method | : | SPARSE |
Number of factorized degrees | : | 1485 |  |
Number of supernodes | : | 290 |  |
Number of overhead indices | : | 8178 |  |
Number of coefficients | : | 56007 |  |
Maximum front width | : | 93 |  |
Maximum front size | : | 4371 |  |
Size of the factorized matrix (Mb) | : | 0 | . | 427299 |
Number of blocks | : | 1 |  |
Number of Mflops for factorization | : | 2 | . | 913e+000 |
Number of Mflops for solve | : | 2 | . | 315e-001 |
Minimum relative pivot | : | 1 | . | 059e-004 |

Minimum and maximum pivot

Value | Dof | Node | x (mm) | y (mm) | z (mm)
--- | --- | --- | --- | --- | ---
6.3710e+005 | Tz | 522 | 1.0031e+001 | 7.6721e+001 | 3.6248e+000
1.0033e+010 | Ty | 433 | -1.8033e-002 | 2.2352e+002 | -6.6586e-003

Minimum pivot

Value | Dof | Node | x (mm) | y (mm) | z (mm)
--- | --- | --- | --- | --- | ---
7.0817e+005 | Tx | 522 | 1.0031e+001 | 7.6721e+001 | 3.6248e+000
1.3537e+007 | Tx | 379 | -4.4170e+000 | 4.9146e+001 | 2.8828e+000
1.4496e+007 | Tz | 379 | -4.4170e+000 | 4.9146e+001 | 2.8828e+000
3.7463e+007 | Tz | 239 | 7.6711e+000 | 2.5459e+002 | 3.7413e+000
3.9112e+007 | Tx | 239 | 7.6711e+000 | 2.5459e+002 | 3.7413e+000
7.1969e+007 | Tz | 520 | 2.2228e+000 | 1.8364e+002 | -2.2606e+000
1.1446e+008 | Tz | 521 | 9.2267e+000 | 6.5701e+001 | -3.1445e+000
1.2943e+008 | Ty | 522 | 1.0031e+001 | 7.6721e+001 | 3.6248e+000
1.7060e+008 | Tz | 372 | -5.2622e+000 | 3.9000e+001 | -3.6108e-001

Translational pivot distribution

Value | Percentage
--- | ---
10.E5 --> 10.E6 | 1.3468e-001
10.E6 --> 10.E7 | 0.0000e+000
10.E7 --> 10.E8 | 3.3670e-001
10.E8 --> 10.E9 | 1.4141e+001
10.E9 --> 10.E10 | 8.5253e+001
10.E10 --> 10.E11 | 1.3468e-001

### DIRECT METHOD Computation

Name: Static Case Solution.1

Restraint: Restraints.1

Load: Loads.1

Strain Energy : 1.628e+002 J

Equilibrium

Components | Applied Forces | Reactions | Residual | Relative Magnitude Error
--- | --- | --- | --- | ---
Fx (N) | 0.0000e+000 | 2.4793e-009 | 2.4793e-009 | 3.0460e-014
Fy (N) | 0.0000e+000 | 1.6153e-008 | 1.6153e-008 | 1.9845e-013
Fz (N) | 0.0000e+000 | -1.9363e-009 | -1.9363e-009 | 2.3789e-014
Mx (Nxm) | 0.0000e+000 | -7.3582e-010 | -7.3582e-010 | 3.0134e-014
My (Nxm) | 0.0000e+000 | -8.0504e-012 | -8.0504e-012 | 3.2968e-016
Mz (Nxm) | 0.0000e+000 | -1.2609e-010 | -1.2609e-010 | 5.1638e-015

### GEOSTIFFNESS Computation

Name: GeoStiffnessStaticSet.1

Number of lines | : | 1566 |  |
Number of coefficients | : | 9048 |  |
Number of blocks | : | 1 |  |
Maximum number of coefficients per bloc | : | 9048 |  |
Total matrix size | : | 0 | . | 11 | Mb

### BUCKLING Computation

Buckling: Buckling Case Solution.2

Static: Static Case Solution.1

Restraint: Restraints.1

Load: Loads.1

Number of computed modes | : | 10 |  |
Number of iterations already performed | : | 0 |  |
Total Number of iterations performed | : | 5 |  |
Relative eigenvalues tolerance required | : | 1 | . | 000e-003 |
Relative eigenvalues tolerance obtained | : | 7 | . | 487e-004 |

Mode number | Buckling factor | Stability
--- | --- | ---
1 | 2.5385e-001 | 3.5074e-012
2 | 2.6282e-001 | 4.0172e-012
3 | 1.2271e+000 | 4.3755e-008
4 | 1.2829e+000 | 3.1803e-008
5 | 2.5338e+000 | 1.4141e-006
6 | 2.6543e+000 | 1.0859e-006
7 | 5.5696e+000 | 2.7619e-004
8 | 5.6732e+000 | 5.1181e-004
9 | 6.6642e+000 | 5.0747e-004
10 | 7.0790e+000 | 7.4867e-004

### Buckling Case Solution.2 - Deformed mesh.2

#### Occurrence 1

Figure 2

On deformed mesh ---- On boundary ---- Over all the model

#### Occurrence 2

Figure 3

On deformed mesh ---- On boundary ---- Over all the model

#### Occurrence 3

Figure 4

On deformed mesh ---- On boundary ---- Over all the model

#### Occurrence 4

Figure 5

On deformed mesh ---- On boundary ---- Over all the model

#### Occurrence 5

Figure 6

On deformed mesh ---- On boundary ---- Over all the model

#### Occurrence 6

Figure 7

On deformed mesh ---- On boundary ---- Over all the model

#### Occurrence 7

Figure 8

On deformed mesh ---- On boundary ---- Over all the model

#### Occurrence 8

Figure 9

On deformed mesh ---- On boundary ---- Over all the model

#### Occurrence 9

Figure 10

On deformed mesh ---- On boundary ---- Over all the model

#### Occurrence 10

Figure 11

On deformed mesh ---- On boundary ---- Over all the model

### Global Sensors

Sensor Name | Sensor Value
--- | ---
Buckling Factors | 0.2538535 0.262824833 1.227078557 1.282869101 2.533826351 2.654270887 5.569595337 5.673193455 6.6642313 7.079024315