essay about pleating on David Geiger's web site] it says:
The necessity of adequate local curvature in tensile
membranes is axiomatic. In the tent-form structures this
generally means finding an anticlastic prestressed form with
appropriately small radii of curvature.
Horst Berger expresses a similar sentiment even more bluntly
in "Light Structures - Structures of Light" - on page 50:
All tensile structures must have anticlastic shapes.
It certainly seems as though the tensile structure
industry's products are dominated by structures which put
their membranes into configurations which exhibit
Some pleated designs which use parallel ridge and valley
cables make use of classical anticlastic surfaces with small
radii - e.g.:
However, looking at many of the existing deployed pleated
designs, the extent of the anticlastic curves is often very
slight - sometimes practically to the point of being
Consider, for example the surface of the Komatsu dome.
There may be a case to be made that the membrane surface has
a slight curvature in one direction - but the
tension in the cables seems to do a pretty good job of
eliminating any doubly-curved surfaces.
Use of an anticlastic surface is an effective way of
stabilising a membrane in space.
Pleating takes another approach to stabilisation - it ensures
that the membrane is always close to a steel cable.
By regularly supporting the fabric, the importance of ensuring
that the fabric itself forms anticlastic surfaces declines.
In fact the combination of regular membrane stabilisation
and the fact that no membrane is parallel to the ground
means that prestressing the membrane is not so much of an
issue as it would be if the membrane were playing more of
a structural role.
In pleated designs, the membrane acts a bit like a guitar
string - pulled between two adjacent cables. Like a guitar
string, it offers little resistance to small perturbations
perpendicular to its surface - and can be expected to
oscillate up and down. It lacks what engineers call
linear stability: to a first order approximation,
there is no restoring force opposing such small
However, unlike a guitar string, the membrane faces
considerable damping from air resistance. In fact, such
motion is nothing to be concerned about. The membrane is
never very far from a cable - and so non-linear restoring
forces kick in quickly.
Increasing anticlastic curvature
Some pleated structures attempt to increase the level of
anticlastic curvature in their membranes.
The following diagram shows one approach - involving the ridge
cables not lying parallel to the valley cables.
Dallas Fort Worth Airport Terminal D
Anticlastic curvature and pleating
It seems possible to me that the issue of anticlastic
curvature may have something to do with the neglect of
If the use of anticlasitic curved surfaces is considered to
be axiomatic, it isn't hard to understand why pleated
designs - that often hardly use that type of curvature at
all - have been relatively overlooked.