Mode Definitions

Based on an analysis of the GBT methodology, we put forth the following criteria as the critical mechanical assumptions necessary for defining the buckling modes. (Coord. system as in Figure 1.)

Criterion #1, membrane deformations:

• у = 0, membrane (in-plane) shear strains are zero,

• ex = 0, membrane transverse strains are zero, and

• v = f(x), long. displacements are linear in x within an element/strip.

Criterion #2, longitudinal warping,

• ey Ф 0, long. strains/displacements are non-zero along the length.

Criterion #3, transverse flexure,

• к = 0, no flexure in the transverse direction.

The buckling modes can then be defined as follows (see also Table 1).

• Global modes are those deformation patterns that satisfy all three criteria.

• Distortional modes are those deformation patterns that satisfy criteria #1 and #2, but do not satisfy criterion #3 (i. e., transverse flexure occurs).

• Local modes are those deformation patterns that satisfy criterion #1, but do not satisfy criterion #2 (i. e., no longitudinal warping occurs) while criterion #3 is irrelevant.

• Other modes are those deformations that do not satisfy criterion #1. Note, other modes do not exist in conventional GBT, but must exist in FSM due to the inclusion of membrane DOF.

G

D

L

O

modes

modes

modes

modes

yxy = 0, ex = 0, v is linear

Yes

Yes

Yes

No

ey Ф 0

Yes

Yes

No

II

о

Yes

No

Table 1. Mode classification table