Anticlastic

The major Poisson s ratio is vl2 and E = E2/El is the ratio of the transverse to longitudinal modulus. Equation 8.24 gives the induced curvature for anticlastic deformation of an unsymmetric cross-ply laminate. The curvature is dependent on the thermal and chemical strain mismatch (e, — e2), lamina mechanical properties (v12, E) and the half-thickness, h. 

Fig. 4. (a) Anticlastic deformation of a bimorph in a magnetic field (saddle form), (b) Fixation of a bimorph on its sample holder and measurement principle of the deformation of any magnetostrictive bimorph using the... 

In the vicinity of elliptic points, the surface can be fitted to an ellipsoid, whose radii of curvature are equal to those at that point (Fig. 1.5a). The surface lies entirely to one side of its tangent plane, it is "synclastic" and both curvatures have the same sign. About a parabolic point, the surface resembles a cylinder, of radius equal to the inverse of the single nonzero principal curvature (Fig. 1.5b). H3rperbolic ("anticlastic") points can be fitted to a saddle, whic is concave in some directions, flat in others, and convex in others (Fig. 1.5c). At hyperbolic points, the surface lies both above and below its tangent plane. 

In principle the different bending methods result in planar strain deformations. This planar strain deformation is only a correct assumption at sufficient distance from the ends of the bend lines (a multiple of the sheet thickness) where strains in the bend line direction are restricted by symmetrically behaving neighbouring material. The stress and strain components in this case are shown in Fig. 3. Near the ends of a bend line this assumption is not valid and the so called anticlastic effect can be observed (Fig. 4). 

In accordance with Rgs 6.1 and 6.2, two principal construction methods can be distinguished for ETFE-foU constructions, differentiated by the type of pre-stressing (mechanical or pneumatic pre-stressing), as well as the type of predominant surface curvature (synclastic or anticlastic Gaussian curvature). 

The stabilisation of one-layer ETFE-foil constructions takes place by mechanical pre-stressing.The shortened foil has to be mechanically stretched in order to be mounted on the boundary. In the pre-stressing state, these foil geometries display anticlastic curved surfaces, i.e. surfaces curved in the opposite direction in both principal stress directions. The Gaussian curvature as the product of both main curvatures ki and of the foil geometry is less than zero. 

Mechanically pre-stressed single-layer ETFE-foil structure with anticlastic curvature. 

Synclastic and anticlastic areas of a square ETFE-foil cushion. 

The above descriptions of the various projects show that there are no limitations in principle to the great variety of shapes in ETFE-foil constructions. As pneumatically pre-stressed foil cushions or as single-layer mechanically pre-stressed foil membranes, anticlastically or synclastically curved surfaces can be formed across nearly any ground plan. The feasible spans of the foil constructions vary according to the ground plan geometry, boundary conditions, construction system, and load effect. 

Anticlastic surfaces (a) conic (b) saddle/ hypar (c) arch supported (d) wave form (photos John Chilton). 

Anticlastic surfaces are generally stressed between a series of high and low points, at which the surface forces become concentrated. To prevent the point support from punching through the membrane it is necessary to distribute the concentrated reaction into the surface as smoothly as possible. This may be accomplished by means of details such as mast rings, umbrellas and tear drop cable loops. 

The membrane construction has an anticlastic curvature and is mechanically pre-stressed. The overall construction comprises three layers. The... 

Anticlastic or hyperbolic surfaces with l/f ii 2<0 are of the saddle type curvatures at a point are of different sign. They are sensitive to the way they are supported and to various secondary effects, such as temperature, shrinkage. 

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