Buckling Mode Classification

The SG-X buckling analysis computes a spectrum of linear (Euler) buckling load factors and their mode shapes. Some modes are the whole structure swaying or toppling (structure buckling); others are a single slender member bowing while the rest of the structure barely moves (single member buckling). A raw eigenvalue solve mixes the two and reports whichever factor is lowest, even when that lowest factor is one local member rather than the structure as a whole.

The Paradise and Wavefront solvers report only the structure buckling factor; they cannot report the single member buckling of a hinged member modelled as a single element. SG-X does capture those single member modes, so for the same model it often reports a lower buckling load factor.

$image\ebx_-1773499217.gif$ A lower SG-X factor is not a cause for alarm.
At that lower factor one or more members may have buckled while the structure as a whole is still stable. A lower SG-X number is not a reason to panic: it flags a single member buckle the existing solvers cannot see, not a weaker structure. To make that distinction visible, SG-X runs a buckling mode classifier that labels each mode as structure buckling or single member buckling. The classifier powers the “Structure buckling only” option (the default).

The options sit in the Buckling Analysis dialog and its SG-X Advanced Settings popup

How SG-X Meshes Members for Buckling

A few deliberate meshing choices make the classification both possible and simple.

For a buckling analysis, SG-X meshes every SPACE GASS member with two node elements: standard members become two node beam elements, while cable, truss, tension only, and compression only members keep the axial element formulations described earlier. The four node beam element is never used for buckling, and the analysis always uses small displacement theory, regardless of the Theory selection in the analysis dialog (see the note in the Standard Beam and Frame Elements section).

$image\ebx_-1773499217.gif$ Members versus plates

This applies to member (line) elements. Plates, if present, are still meshed with the three node triangle and four node quadrilateral shell elements described earlier.

The “Buckling Analysis” option chooses between two paths that differ only in member subdivision. Under Include single member buckling the engineer sets “Split members into”, so a member becomes one or more elements. Under Structure buckling only (the default) the split is forced to 1, so every member is a single element.

SG-X buckling analysis
“Buckling Analysis” option, SG-X Advanced Settings

↙

↘

Include single
member buckling

Structure buckling only
(default)

↓

Member subdivision is
the engineer’s choice:
“Split members into” ≥ 1

Member subdivision is forced to 1

↓

A member is one
or more elements

Every member is
exactly one element

The Energy Classifier

“Structure buckling only” uses the classifier to tell structure modes from single member modes. It labels each mode by where its destabilising energy concentrates.

What It Measures

The buckling solver assembles the geometric stiffness matrix K_g and returns mode shapes normalised against it, so that ϕ^TK_gϕ = 1 for each mode ϕ. For one mode it forms the destabilising (geometric) energy of each degree of freedom and sums it onto the owning node.

Per degree of freedom r, the destabilising energy is

e_r = φ_r (K_g φ)_r

and each node’s energy is the sum over its degrees of freedom:

E_node =

∑

r ∈ node

e_r ,

∑

all nodes

E_node ≈ +1 (by K_g normalisation).

The peak node is the one carrying the greatest aggregated energy.

How It Decides

Under “Structure buckling only” each member is a single element, so the destabilising energy of a mode can only peak in one of two places: at one of the structure’s joints, or at a released (hinged) member end. The location of the peak gives the verdict directly:

peak at a joint of the structure ⇒ structure buckling;
peak at a released member end ⇒ single member buckling.

When a mode is classified as single member buckling, the solver identifies the member concerned so that the end of analysis message can report it.

$image\ebx_-1773499217.gif$ Why energy, and not just motion

Energy is weighted by the axial load in the member. A lightly loaded member that merely rides along with a global sway moves a lot but stores little destabilising energy, so it is not mislabelled as a single member buckle; a genuinely overloaded member that bows stores a large share of the energy and is correctly labelled as single member buckling. Motion alone would flag any member that moves, even one only riding a global mode.

What “Structure Buckling Only” Does

“Structure buckling only” is the default option, available for the SG-X solver when the model contains members. The setting is held in memory only (not saved with the job), so a reopened job opens at “Structure buckling only” again.

The two options differ as summarised in the table below. Under “Structure buckling only” the wider search spectrum (default 20 modes) gives the classifier enough of the spectrum to find the first structure mode above any local buckles, and the engineer’s own mode count becomes the number of structure modes saved; if no structure mode is found at all, all computed modes are saved instead. Either way the solve and the saved results format are unchanged: only the reporting and the mode count differ.

Aspect	Include single member buckling	Structure buckling only (default)
Modes solved	Engineer’s requested count	“Modes to search” value (default 20)
Member subdivision	From “Split members into”	Forced to 1 (single element)
Modes saved	All computed, natural order	First N structure modes only (N = requested count)
Finish message	Single lowest factor	Structure factor, plus a local warning if relevant

The End of Analysis Message

With “Structure buckling only” on, the message leads with the structure factor and adds a local warning only when the overall lowest mode is itself a single member buckle. The templates (the {} placeholders are filled at run time) are:

The lowest structure buckling load factor is {} (load case {})

If no structure mode is found within the searched spectrum, that line is replaced by:

No structure buckling mode was found within the first {} modes. You may want to increase 'Modes to search for structure buckling' under SG-X Advanced Settings and re run the buckling analysis.

When the overall lowest mode is a single member buckle (a lower factor than the structure mode), the warning, the local factor line (with the member when it can be resolved), and the reassurance line are added:

Warning: a local member buckling occurs at a lower load factor. The lowest local member buckling load factor is {} (load case {}), occurring in member {}. This is a local buckling only. The structure will remain stable after this member has buckled.

$image\ebx_-1773499217.gif$ When the lowest mode is already a structure mode

If the overall lowest mode is itself a structure (global) mode, only the structure factor line is shown; there is no lower local buckle to warn about.

Edge cases.

Lowest mode local but the member cannot be resolved: the local line is shown without a member number rather than inventing one.
Fewer modes available than requested: the solver caps the count; the logic is unaffected.
Multiple load cases: the governing lowest factor and the governing lowest structure factor are independent minima and may come from different load cases; each is shown with its own.

Examples: Paradise versus SG-X

The two solvers were run on the same structure for the two models below. In each case Paradise reports a single buckling factor, while SG-X reports a comparable structure factor plus a lower single member buckle that Paradise does not detect, with the note that the structure stays stable.

2D Frame

Member 4 is the slender diagonal.

Paradise: lowest buckling load factor > 1000 (structure buckling only).
SG-X: structure factor > 1000, plus a local member buckle of member 4 at 0.840.

Paradise Solver:

SG-X Solver:

Warehouse

A full 3D warehouse model

Paradise: lowest buckling load factor 1.129 (load case 112).
SG-X: lowest structure factor 1.191 (load case 112), close to Paradise, plus a local member buckle of member 386 at 0.4407 (load case 62) that Paradise does not report.

Here the governing structure factor and the local buckle even come from different load cases (112 and 62), the independent minima noted earlier.

Paradise Solver:

SG-X Solver:

Summary of Buckling Mode Classification

SG-X also captures single member buckles, so it can report a lower factor than the existing solvers; the classifier identifies which kind each factor is.
Per mode the verdict comes from where the destabilising energy peaks: a joint of the structure means structure buckling, a released member end means single member buckling.
Structure buckling only (the default) reports the structure factor, adding a single member warning only when a lower local buckle exists. Include single member buckling reports the lowest factor with no classification.

$image\ebx_-1773499217.gif$ Practical reading of the result

A structure buckling factor tells the engineer how much the load can grow before the structure as a whole becomes unstable. A separate, lower local factor with a named member flags a member that would buckle first in isolation; the message states that the structure stays stable after that, so it points the engineer at the member to stiffen or restrain rather than at the structure.